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Topics in U.S. healthcare

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Content TOPICS IN U.S. HEALTHCARE

Topics in U.S. Healthcare

by

Sushant Joshi

A Dissertation Presented to the
FACULTY OF THE USC SOL PRICE SCHOOL OF PUBLIC POLICY
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PUBLIC POLICY AND MANAGEMENT

December 2022

Copyright 2022 Sushant Joshi
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Acknowledgments
This long journey could not have been possible without numerous people’s help,
guidance, and understanding. My Ph.D. advisor Neeraj Sood was instrumental in the completion
of my dissertation. He is the best advisor I could have. His guidance was unparalleled, and he
provided unwavering support throughout. In addition to my dissertation, he helped me participate
in different research projects throughout my Ph.D.
I am also deeply indebted to my other committee members, Alice Chen and Teryl
Nuckols. I constantly received useful, practical, and helpful comments on my work. Their
constructive criticism, insightful suggestions, and advice improved my work. I also enjoyed
working with Teryl Nuckols on other projects and greatly benefited from them.
I want to thank Erin Trish and John Romley, who were part of my qualifying committee.
I want to thank Julie Kim and Christine Wilson at USC Sol Price, who helped me
navigate and resolve administrative matters.
I will forever be thankful to previous mentors and teachers: Arnab Mukherji, Kali Rath,
and Terence Johnson. Arnab Mukherji provided excellent guidance on applying to graduate
school.
I would also like to acknowledge friends and family who supported me. Special thanks to
my friends Bishnu Thapa and Richa Joshi for their constant support and encouragement. Saakar
Byahut for his help and support during challenging times. My cousin Sadhana Joshi and her
husband, Sandeep Pandey, for their emotional support. My brother’s family, Prashant Joshi,
Grishma Joshi, nephew Pratyush Joshi, and niece Ishika Joshi, for being there when I needed
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them. Pratyush and Ishika were a constant presence and provided abundant joy to me when I was
in Nepal for a significant period.
Finally, I would like to mention my parents, Huta Raj Joshi and Makhana Joshi. This
journey would not have been possible without their hard work and sacrifice. The accomplishment
is as much mine as it is theirs.

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Table of Contents
Acknowledgments........................................................................................................................... ii
List of Tables .................................................................................................................................. v
List of Figures ............................................................................................................................... vii
Abstract ........................................................................................................................................ viii
Introduction ..................................................................................................................................... 1
Chapter 2: Incentives of the Skilled Nursing Facility Value-Based Purchasing (SNF VBP)
Program ............................................................................................................................... 5
Abstract .......................................................................................................................... 5
Introduction .................................................................................................................... 7
Methods ........................................................................................................................ 12
Results .......................................................................................................................... 19
Discussion .................................................................................................................... 26
Limitations ................................................................................................................... 28
Conclusion ................................................................................................................... 29
Chapter 3: Regression to the Mean in the Medicare Hospital Readmissions Reduction
Program ............................................................................................................................. 31
Abstract ........................................................................................................................ 31
Introduction .................................................................................................................. 33
Methods ........................................................................................................................ 35
Results .......................................................................................................................... 39
Discussion .................................................................................................................... 46
Limitations ................................................................................................................... 48
Conclusion ................................................................................................................... 49
Chapter 4: Staffing Shortages, Staffing Hours, and Resident Deaths in U.S. Nursing Homes
During the COVID-19 Pandemic...................................................................................... 50
Abstract ........................................................................................................................ 50
Introduction .................................................................................................................. 52
Methods ........................................................................................................................ 54
Results .......................................................................................................................... 58
Discussion .................................................................................................................... 68
Limitations ................................................................................................................... 70
Conclusion ................................................................................................................... 71
References ..................................................................................................................................... 72
Appendix ....................................................................................................................................... 78
Appendix A: Steps in Calculation of Incentive Payment Multiplier and MERRIPM . 78
Appendix B: Regression to the Mean Additional Analysis ......................................... 86
Appendix C: Calculation of Regression to the Mean................................................... 90
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List of Tables
Table 1: Characteristics of the Skilled Nursing Facilities in the Study Sample ........................... 20
Table 2: Intermediate Values in Estimation of the Marginal Effect of Readmissions
Reduction on Incentive Payment Multiplier (MERRIPM) ............................................... 22
Table 3: The Association of Change in Risk-Standardized Readmission Rate Across Years
with the Baseline Risk-Standardized Readmission Rate (RSRR) .................................... 23
Table 4: Association of Changes in the Readmission Rate Between FY2018 and FY2016
and the SNF VBP Program Incentives.............................................................................. 25
Table 5: Association of Changes in the Readmission Rate Between FY2018 and FY2016
and the SNF VBP Program Incentives, Dropping Poor Performing and Best
Performing Deciles ........................................................................................................... 26
Table 6: Hospital Characteristics, by Target’s Summary Statistics by Conditions ...................... 39
Table 7: Change in Excess Readmissions Rates (ERRs) Explained by Regression to the
Mean (RTM) for Hospitals in Right Tail of ERR Distribution ........................................ 42
Table 8: Change in Excess Readmissions Rates (ERRs) Explained by Regression to the
Mean (RTM) for COPD .................................................................................................... 42
Table 9: Changes in Excess Readmissions Rates (ERRs) Explained by Regression to the
Mean (RTM) ..................................................................................................................... 46
Table 10: Nursing Home Characteristics, Week and Facility Level ............................................ 61
Table 11: Association Between Nursing Staff Shortages and Nurse Staffing Hours per
Resident............................................................................................................................. 63
Table 12: Association Between Staffing Shortage and Deaths Due to COVID-19 and Other
Causes ............................................................................................................................... 64
Table 13: Association Between Long-Term Staffing Shortages and Resident Deaths in
Nursing Homes ................................................................................................................. 65
Table 14: Association of Resident Deaths with Staffing Shortages During Different Periods
of the COVID-19 Pandemic.............................................................................................. 66
Table 15: Association Between Nursing Staff Shortages and Nurse Staffing Hours per
Resident (Complete Panel Only) ...................................................................................... 67
Table 16: Association Between Nursing Staff Shortages and Nurse Staffing Hours per
Resident (Complete Panel Only) ...................................................................................... 68
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Table 17: Association Between Nursing Staff Shortages and Resident Deaths in Nursing
Homes (Complete Panel Only) ......................................................................................... 68

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List of Figures
Figure 1: The Distribution of the Marginal Effect of Readmissions Reduction on Incentive
Payment Multiplier (MERRIPM) on Baseline RSRR ...................................................... 21
Figure 2: Periods Relevant to Analyses 1 to 3 .............................................................................. 37
Figure 3: Changes in Excess Readmissions Rate (ERRs) from FY2013 Measurement Period
to 3-years Post-measurement. ........................................................................................... 41
Figure 4: Changes in Excess Readmissions Rate (ERRs) for COPD prior to inclusion of
COPD in the HRRP .......................................................................................................... 43
Figure 5: Changes in Excess Readmissions Rates (ERRs) from an Alternate Measurement
Period to 3-years Post-measurement (i.e. FY2013 Measurement Period). ....................... 44
Figure 6: Changes in Excess Readmissions Rates (ERRs) from FY2013 Measurement Period
to Pre-measurement Period. .............................................................................................. 45
Figure 7: Staffing Shortages and Resident Deaths in Nursing Homes, Week Ending on May
31, 2020 to Week Ending on May 15, 2022 ..................................................................... 59
Figure 8: Improvement in Performance on Baseline Performance ............................................... 83
Figure 9: Distribution of Achievement Score ............................................................................... 83
Figure 10: Distribution of Improvement Score ............................................................................. 84
Figure 11: Distribution of Performance Score .............................................................................. 84
Figure 12: Distribution of Logit Transformed Performance Score .............................................. 85
Figure 13: Distribution of Incentive Payment Multiplier ............................................................. 85
Figure 14: Movement Across Quartiles Between CY2015 and CY2017 ..................................... 87
Figure 15: Change in RSRR and Baseline RSRR Between CY2015 and CY2017 ...................... 88
Figure 16: Adjusted Change in RSRR and Baseline RSRR Between CY2015 and CY2017 ...... 89

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Abstract

This dissertation studies topics in U.S. healthcare. In Chapters 2 and 3, I study Center for
Medicare & Medicaid Services (CMS) value-based programs. CMS implements value-based
programs to improve the quality of care provided to patients as well as lower the cost of
healthcare by rewarding healthcare providers for delivering better quality of care. Chapter 2
shows that a nationally implemented skilled nursing value-based purchasing program (SNF
VBP) did not reduce hospital readmissions of nursing home residents. In chapter 3, in joint work
with Teryl Nuckols, Jose Escarce, Peter Huckfeldt, Ioana Popescu, and Neeraj Sood, we study
the mean reversion of hospital readmissions in one of the largest value-based programs for
hospitals, hospital readmissions reduction program (HRRP). We found that not accounting for
mean reversion over-states the decline in hospital readmissions due to the program. In chapter 4,
I study the impact of staffing shortages on nursing homes during the COVID-19 pandemic. As
staffing is crucial in providing quality care to residents in nursing homes, I find that staffing
shortages were associated with declining staffing hours and increasing resident deaths.
Keywords: healthcare, value-based purchasing, hospitals, nursing homes, staffing
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Topics in U.S. Healthcare
Introduction
My dissertation explores two topics in U.S. healthcare, with quality of care as its
underlying theme. The first topic is value-based programs implemented by the Center for
Medicare and Medicaid Services (CMS). The rationale for value-based programs is to improve
the value of care provided by rewarding healthcare providers for providing higher-quality care to
patients. Value-based programs are meant to pay providers based on the quality of care they
provide to patients rather than on the quantity of care. In addition to providing better care for
individuals, value-based programs also aim to better the health of populations and to lower the
cost of healthcare. CMS’s value-based programs are becoming increasingly important, as a larger
share of payments to healthcare providers are tied to these programs. My dissertation studies
value-based programs that target nursing homes and hospitals. I studied the recently
implemented skilled nursing facility value-based purchasing (SNF VBP) program and its impact
on hospital readmissions of nursing home residents. My dissertation also estimates the role of
regression to mean in assessing the impact of the hospital readmissions reduction program
(HRRP). The second topic of my dissertation is staffing in nursing homes. Adequate staffing is
crucial for providing high quality care to residents in nursing homes. My dissertation investigates
staffing shortages and their impact on staffing hours and resident outcomes in nursing homes
during the COVID-19 pandemic.
In chapter 2, entitled “Incentives of the Skilled Nursing Facility Value-Based Purchasing
(SNF VBP) Program,” I study the impact of the SNF VBP program on hospital readmissions of
patients discharged to skilled nursing facilities. Prior literature argues that SNFs contribute to
hospital readmissions, the latter being a valid measure of the quality of SNFs. The rationale for
SNF VBP is to financially reward SNFs for reducing readmissions for patients who are
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discharged to SNFs from hospitals. To understand the program's impact, I first estimated the
marginal effect of readmissions reduction on incentive payment multiplier (MERRIPM).
MERRIPM fundamentally captures the additional payments for each SNF due to a decline in
readmissions. I interrelated MERRIPM with the share of Medicare patients in order to capture
the overall program incentives. We expect SNFs with a higher MERRIPM to be more likely to
reduce readmissions than SNFs with a lower MERRIPM, even when the Medicare share is the
same, because the former have more to gain. Similarly, SNFs with higher Medicare shares would
likely try harder to reduce readmissions than SNFs with lower Medicare shares, even when the
MERRIPM is the same. Using the interaction of MERRIP and Medicare shares as overall
program incentives, I showed that SNF VBP is not associated with a decline in the readmission
rate of patients discharged to SNFs from hospitals. These results suggest that the SNF VBP
program may not have performed as expected.
In chapter 3, entitled “Regression to the Mean in the Medicare Hospital Readmissions
Reduction Program,” we study the role of regression to the mean in explaining the decline in
readmission rate after the program's implementation. When programs target or incentivize
healthcare providers to improve their performance, performance may improve or worsen due to
chance. This phenomenon is particularly pronounced if the measures used as incentives are
noisy. Additionally, chance may have a non-trivial role if healthcare providers are penalized or
rewarded when they are at the tail of the performance distribution. We analyzed excess
readmissions in the context of the hospital readmission reduction program (HRRP) so as to
understand the role of chance. The HRRP was implemented after the passage of the Affordable
Care Act in 2010 in order to rein in higher readmission rates at U.S. hospitals. Hospital
readmissions are costly and burdensome to patients, suggesting a lack of quality care during the
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initial admission and a lack of integration with other healthcare services. We studied the role of
regression to the mean, a phenomenon where measures further away from the mean converge to
the mean in subsequent measurements, in explaining the decline in risk-adjusted readmissions
under the program. Our findings provide evidence that regression to the mean explains a large
portion of the decline in excess readmissions. This suggests that chance played an important role
in hospital performance and associated penalties under the program. This chapter was possible
through joint work with Teryl Nuckols, Jose Escarce, Peter Huckfeldt, Ioana Popescu, and
Neeraj Sood.
In chapter 4, entitled “Staffing Shortages, Staffing Hours, and Resident Deaths in U.S.
Nursing Homes During the COVID-19 Pandemic,” I studied the association of staffing shortages
in nursing homes with staffing hours and resident outcomes during the COVID-19 pandemic.
Staffing plays a crucial role in providing quality care in nursing homes. Prior work has shown
that nursing homes with higher staffing levels are associated with better quality of care. During
the pandemic, staffing was a major concern for nursing homes. First, I studied the association of
self-reported nursing home staffing shortages and staffing hours. I found that staffing shortages
were associated with a decline in staffing hours. Second, I studied the association of staffing
shortages with resident deaths and found that staffing shortages were associated with an increase
in resident deaths. These results suggest that nursing homes with staffing issues saw a reduction
in staffing hours and an increase in resident deaths due to both COVID-19 and other causes
during the pandemic. Given this evidence, staffing in nursing homes should be prioritized when
there is increased stress on these institutions.
In conclusion, my work shows that care should be taken when implementing value-based
programs. First, I found that the SNF VBP program may not have worked as anticipated,
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meaning it did not reduce hospital readmissions of nursing home patients. Secondly, CMS-
implemented value-based programs may also be subject to chance, as in HRRP, suggesting that
the program may be penalizing and rewarding hospitals not on actual changes in quality of care
but on other reasons that are not related to the program. This may undermine the program in the
long run. Finally, I showed that staffing is crucial in providing quality care to beneficiaries in
nursing homes. I hope these findings can help other researchers and policymakers design future
value-based policies and evaluate programs that have already been implemented.

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Chapter 2: Incentives of the Skilled Nursing Facility Value-Based Purchasing (SNF VBP)
Program
1

Abstract
Background: The Centers for Medicare & Medicaid Services (CMS) skilled nursing facility
value-based purchasing (SNF VBP) program awards incentive payments to skilled nursing
facilities (SNFs) based on their performance on a single measure of hospital readmission rate.
Objective: To evaluate whether the SNF VBP program was associated with improved SNF
performance as measured by hospital readmission rate.
Data Sources: We downloaded VBP program data at the level of individual SNFs for Fiscal Year
(FY)2019 and FY2020 from the CMS website. We obtained data on SNF characteristics from
LTCfocus.org and data on payments from the Nursing Home Compare website.
Exposure: SNF VBP program incentives.
Measure: Changes in readmission rate for each SNF.
Study Design: We used linear regression to examine the association between the SNF VBP
program incentives and changes in the readmission rate for SNFs. To derive the overall program
incentives, we calculated the marginal effect of readmission reduction on incentive payment
multiplier (MERRIPM). This is an additional reward SNFs would receive due to a decline in
readmission rate from baseline, conditional on other SNFs’ readmission rates remaining the
same. Because SNFs with larger shares of Medicare beneficiaries are more heavily impacted by
this Medicare policy, we interacted the MERRIPM with each SNF’s Medicare share. The effect
of MERRIPM on the reduction in readmission rate might be confounded by the mean reversion,

1
I would like to thank my committee members, Alice Chen, Teryl Nuckols, and Neeraj Sood, for their detailed comments and
suggestions on this chapter. I would also like to thank the participants at ASHEcon 2022, who provided valuable comments.
TOPICS IN U.S. HEALTHCARE

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as MERRIPM is a function of the baseline readmission rate. Thus, we calculated changes in the
readmission rate adjusted for the mean reversion.
Principal Findings: The SNF VBP program incentives were associated with a 0.14 percentage
points increase in the readmission rate (P < 0.05). However, in our sensitivity analyses, we found
that this association was between 0.12 and 0.03 percentage points and not statistically significant.
Conclusion: Incentives in the SNF VBP were not associated with a decline in SNF readmission
rates.

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Introduction
Skilled nursing facilities (SNFs) are the most common form of post-acute care for
Medicare beneficiaries discharged from an acute care hospital and account for the largest share
of Medicare payments for institutional post-acute care (Neuman, Wirtalla, & Werner, 2014;
Werner & Konetzka, 2018). Poor quality of care in SNFs has been a long-standing problem
(Institute of Medicine (US) Committee on Nursing Home Regulation, 1986; National Academies
of Sciences Engineering & Medicine, 2022; Office of Inspector General, 2014; US Government
Accountability Office, 2020). For example, 33% of Medicare beneficiaries have experienced
adverse events or temporary harm events, and 59% of these were clearly or likely preventable
(Office of Inspector General, 2014). Given the concerns about the quality of care, the Centers for
Medicare and Medicaid Services (CMS) launched the Skilled Nursing Facilities Value-Based
Purchasing (SNF VBP) program. The rationale for a value-based purchasing program was to link
payments to performance on quality measures, thereby motivating SNFs to improve quality. Our
study assesses whether the incentives introduced by the SNF VBP have been effective in
reducing the hospital readmission rates of SNFs.
The SNF VBP is a national program that ties an SNF’s Medicare payments to its hospital
readmission rate. The Protecting Access to Medicare Act (PAMA) of 2014 authorized the SNF
VBP program, which CMS implemented on October 1, 2018. CMS funds the program through
an incentive pool created by withholding two percent of fee-for-service (FFS) payments. CMS
redistributes part of this withheld value to SNFs via an incentive pool and keeps the rest as
savings. Depending on performance, the incentive paid to an individual SNF may be greater, less
than, or equal to their withheld amount. While Medicare employs various quality measures in its
SNF Care Compare public reporting program, the SNF VBP program assesses performance
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using a single measure: hospital readmission rate. This measure assesses SNF patients’ hospital
readmission rates within 30 days of discharge from a prior hospital stay.
The SNF VBP program has several distinctive elements that play critical roles in creating
incentives. First, the program uses hospital readmissions as the single measure to assess
performance, whereas several other value-based payment programs, such as the Hospital Value-
Based Purchasing (VBP) Program and the Hospital-Acquired Condition Reduction Program, use
multiple measures. Second, the program tracks absolute and relative changes in hospital
readmissions across different periods. Third, the SNFs earn incentive payments based on their
changes in readmissions. The program names incentive payments as incentive payment
multipliers. An incentive payment multiplier larger or smaller than one means that SNFs receive
more or less, respectively, than without the program. To derive the incentive payment multiplier,
changes in the readmission rate are transformed to total performance scores based on relative and
absolute changes. As given in the SNF prospective payment system final rule, these total
performance scores are later transformed using a logistic exchange function. This implies that the
program has stronger incentives for reducing the readmission rate for SNFs in the middle of the
baseline distribution rather than in the left or the right tail.
In summary, in the SNF VBP program, a decline in the hospital readmission rate of an
SNF impacts future rewards or penalties through an incentive payment multiplier. Therefore, the
SNFs’ incentive to reduce their readmissions under SNF VBP program depends on their
expected change in the incentive payment multiplier given a decline in readmissions. The
structure of the program implies that the expected change in penalties due to a decline in the
readmission rate might vary for different SNFs. We use the structure of the SNF VBP to measure
the marginal effect of readmissions reduction on incentive payment multiplier (MERRIPM) to
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capture these incentives. The MERRIPM is an additional increase in the incentive payment
multiplier due to a decline in the readmission rate. In the paper, the MERRIPM is calculated as a
change in the incentive payment multiplier when SNFs reduce the readmission rate by one
standard deviation of the baseline readmission rate conditional on all other SNFs’ readmission
rate remaining the same. Along with MERRIPM, the share of Medicare revenue provides an
additional source of incentive. SNFs with a larger share of Medicare revenue should strongly
respond to the program since it has a greater impact on their payments. A larger share of
Medicare patients would imply that the share of Medicare revenue is higher. Therefore, the
interaction of the MERRIPM and the share of Medicare patients is the key independent variable
to estimate aggregate program incentives. We expected a larger reduction in the readmission rate
for SNFs with larger program incentives. However, hospital readmission rates are subject to
mean reversion when tracked over time (Joshi et al., 2019; Press et al., 2013). Mean reversion
implies that hospital readmission rates farther from the mean in one period are likely to fall
closer to the mean in the next period due to random chance. Therefore, any assessment of the
program should account for mean reversion in hospital readmission rate.
Prior work on SNF VBP program has primarily studied the association between SNFs’
characteristics and program penalties. In the program's first year, SNFs serving minority
populations were more likely to be penalized and perform worse than SNFs serving non-minority
populations (Hefele, Wang, & Lim, 2019). Penalties were also associated with negative profit
margins (Sharma, Hefele, Xu, Conkling, & Wang, 2020). In addition, SNFs with higher shares of
frail patients (as measured by patient complexity), SNFs located in low-income zip codes, and
SNFs with lower 5-star quality ratings were more likely to be penalized, while hospital-based
providers were less likely to be penalized (Qi, Luke, Crecelius, & Maddox, 2020). In the first
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year of the program a small fraction of SNFs were able to improve their readmission rate enough
to avoid a financial penalty (Burke, Xu, & Rose, 2022). A study of the program's first two years
found that larger SNFs, SNFs in rural locations, and SNFs with higher registered nurse (RN)
staffing levels were more likely to receive rewards than other SNFs (Daras et al., 2021). Higher
payment adjustments were associated with SNFs with lower average clinical risk scores, lower
shares of fully dual-eligible beneficiaries treated, or larger facilities in the program's first three
years (MEDPAC, 2021). However, whether SNFs reduced readmissions as a result of program
incentives in the SNF VBP program has not been studied. We contribute to the literature by
estimating the program incentives that are embedded in MERRIPM and Medicare share and use
this to estimate the impact of the SNF VBP program on hospital readmission of SNFs.
To better understand the SNF VBP program, this paper studies how program incentives
embedded in the program were associated with changes the SNFs readmission rate. It is possible
that SNFs reduced their readmissions as targeted by the program. Likewise, it is also possible
that the program had minimal impact on the readmission rate due to the complexity of the
program or due to mean reversion. The next section provides an overview of the SNF VBP
program. Thereafter, we describe the conceptual model, empirical strategy, and results. We
conclude with the implications of our research.
SNF VBP Program Overview
The SNF VBP program began adjusting FFS payments to SNFs beginning Fiscal Year
(FY) 2019; however, in October 2016, it had started to provide SNFs with confidential feedback
reports on their performance. The program is focused on FFS beneficiaries and excludes MA
beneficiaries in assessing and rewarding performance, using a single measure to gauge
performance. Performance is measured by the risk-adjusted 30-day all-cause, all-condition,
hospital readmission rate. The baseline and performance periods are defined and the
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performances of the SNFs are estimated in each period. The baseline and performance periods
are each one year long, with the baseline period preceding the performance period by two years.
The performance of an SNF during the performance period is then compared to its performance
in the baseline period in order to determine rewards or penalties.
There are several steps in transforming performance, i.e. readmission rates, to changes in
payments. First, each SNF receives an achievement score. CMS uses a minimum “achievement
threshold” and a “benchmark” to set lower and upper bounds on achievement scores. Baseline
performance of all SNFs is used to calculate the achievement threshold and the benchmark. As
set by CMS, the achievement threshold is the 25th percentile of the performance distribution, and
the benchmark is the mean of the top decile. Depending on the SNFs’ performance in
performance period, their achievement scores can range from 0 to 100. If SNFs perform worse
than the achievement threshold, they receive a score of 0. If SNFs perform better than the
benchmark, they receive a score of 100. SNFs whose performance lies between the achievement
threshold and the benchmark receive scores greater than 0 but less than 100.
Second, each SNF also receives an improvement score. The improvement score is
calculated based on the change in performance, i.e., readmission rate, between the performance
period and the baseline period. Improvement scores range from 0 to 90 points. SNFs with no
improvement in performance receive an improvement score of 0. When SNFs show
improvement, they receive a score greater than 0, with higher scores for larger improvements.
Next, each SNF is given a total performance score which is higher of either the
achievement or the improvement scores. The total performance scores are then transformed
using the logit exchange function, which is S-shaped. This creates a distribution in which the
slopes around the middle are steeper than in the tails. Consequently, changes in total
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performance score towards the ends of the distribution are associated with only slight changes in
the transformed scores, whereas the change in total performance score around the middle leads to
larger changes in the transformed scores.
The transformed scores are then used to calculate the incentive payment multipliers.
Multipliers greater than one increase payments, whereas multipliers lower than one decrease
payments. A multiplier of one does not change payments. Other details are provided in Appendix
A, including exact mathematical formulas for all the terms discussed above.
Three things about the program should be noted. First, rewards or penalties in any year
account for past performance. So, an improvement in the performance of an SNF during any
given year impacts its future payments but does not impact the program’s current year payments.
Current penalties rely on past and not current performances, so current penalties may not be a
good measure for studying the program’s impact. Any changes in SNFs’ behavior would be due
to the expectation of future penalties/rewards rather than the current penalties/rewards. To
capture this incentive of the program, we calculate the MERRIPM. This incentive depends on the
expectation of incentive payment multiplier in the future and is not dependent on the current
incentive payment multipliers. Second, as discussed earlier, an SNFs performance is
transformed, using various functional forms, to estimate penalties or rewards. The MERRIPM
accounts for these transformations, which create non-linear incentives depending on the baseline
performance of the SNF. Third, since the SNF VBP rewards improvement in performance, it
might be subject to regression to the mean. Our empirical strategy addresses this concern.
Methods
Conceptual model
The SNF VBP has two potential sources by which it could incentivize a reduction in
readmissions. The first source is the MERRIPM. The second source is the Medicare share. SNFs
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with a larger share of Medicare patients would want to avoid the penalty since they would be
penalized on the larger share of their payments. Below, using a simple model, we show that the
interaction of MERRIPM and Medicare share can be used to study the SNF VBP program’s
impact.
The total revenue of a facility is the sum of Medicare payments and non-Medicare
payments. Due to the program, the Medicare payments are modified using an incentive payment
multiplier, which depends on performance (readmissions). As performance improves or the
readmission rate declines, the incentive payment multiplier increases. The percentage change in
total revenue due to the improvement in performance (decline in readmissions) is directly
proportional to the Medicare share and the MERRIPM. It is shown succinctly in the equations
below:
𝑇𝑜𝑡𝑎𝑙 𝑟𝑒𝑣𝑒𝑛𝑢𝑒 (𝑇𝑅 ) = 𝑀𝑒𝑑𝑖𝑐𝑎𝑟𝑒 𝑟𝑒𝑣𝑒𝑛𝑢𝑒 + 𝑛𝑜𝑛 − 𝑀𝑒𝑑𝑖𝑐𝑎𝑟𝑒 𝑟𝑒𝑣𝑒𝑛𝑢𝑒 (𝑛𝑀𝑅 )
With the program, the Medicare revenue is adjusted by the penalties and is given as
𝑇𝑅 = 𝑀𝑅 ∗ (𝐼𝑛𝑐𝑒𝑛𝑡𝑖𝑣𝑒 𝑃𝑎𝑦𝑚𝑒𝑛𝑡 𝑀𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑒 𝑟 (𝑝𝑒𝑟𝑓𝑜𝑟𝑚𝑎𝑛𝑐𝑒 )) + 𝑛𝑀𝑅
Taking the partial derivative with respect to performance results in:
𝜕𝑇𝑅 𝜕𝑅
= 𝑀𝑅 ∗
𝜕𝐼𝑃𝑀 𝜕𝑃𝑒𝑟
Dividing both sides by the total revenue we get:
𝜕𝑇𝑅 𝜕𝑃𝑒𝑟 𝑇𝑅
=
𝑀𝑅
𝑇𝑅
∗
𝜕𝑃
𝜕𝑃𝑒𝑟 = 𝑚𝑒𝑑𝑖𝑐𝑎𝑟𝑒 𝑠 ℎ𝑎𝑟𝑒 ∗ (
𝜕 𝐼𝑃𝑀 𝜕𝑃𝑒𝑟 )
= 𝑚𝑒𝑑𝑖𝑐𝑎𝑟𝑒 𝑠 ℎ𝑎𝑟𝑒 ∗ (
𝜕 𝑖𝑛𝑐𝑒𝑛𝑡𝑖𝑣𝑒 𝑝𝑎𝑦𝑚𝑒𝑛𝑡 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑒𝑟 𝜕 𝑝𝑒𝑟𝑓𝑜𝑟𝑚𝑎𝑛𝑐𝑒 )
This simple model shows that the percentage change in revenue due to change in
performance is directly related to the Medicare share of revenue and the change in incentive
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payment multiplier due to change in performance. In our analysis, we used the Medicare share of
patients as a proxy for the Medicare share of revenue for each SNFs. Assuming that the
Medicare share of revenue equals the prices times the Medicare share of patients, the Medicare
share of revenues are directly related to the Medicare share of patients. The second term captures
the increase in incentive payment multiplier due to an improvement in performance i.e.,
reduction in readmissions. It is the generalized form of the MERRIPM, which assumes that the
change in performance equals one standard deviation reduction in readmission rates (assuming
all other SNF readmission rates remain the same).
The program links the decline in readmission rate to the incentive payment multiplier.
The decline in readmission rate impacts the improvement and achievement scores, which affects
the total performance score. This total performance score affects the transformed score. This
transformed score affects the incentive payment multiplier. The sequence is given below:
𝑀𝑒𝑎𝑠𝑢𝑟𝑒 → 𝑃𝑒𝑟𝑓𝑜𝑟𝑚𝑎𝑛𝑐𝑒 𝑆𝑐𝑜𝑟𝑒 → 𝑇𝑟𝑎𝑛𝑠𝑓𝑜𝑟𝑚𝑒𝑑 𝑠𝑐𝑜𝑟𝑒 → 𝐼𝑛𝑐𝑒𝑛𝑡𝑖𝑣𝑒 𝑝𝑎𝑦𝑚𝑒𝑛𝑡 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑒𝑟 (𝐼𝑀 )
In this paper, we calculate the MERRIPM for each SNF as the change in incentive
payment multiplier due to a decline in readmission rate. We assume that an SNF reduces their
readmission rate by a fixed amount on its baseline readmission rate holding other SNFs’
readmission rates constant. This fixed amount is one standard deviation of the baseline
distribution of readmission rate. The ad hoc choice of one standard deviation simply scales the
MERRIPM measure and allows us to calculate the SNF incentive if the SNF were to improve by
one standard deviation, a sizeable yet plausible degree of improvement.
𝑀𝐸𝑅𝑅𝐼𝑃𝑀 =
Δ𝐼𝑀
Δ1𝑠𝑑

Conceptually, it is important to understand the need to interact the Medicare share and
MERRIPM to capture program incentives fully. SNFs with higher MERRIPM are more likely to
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reduce readmissions than SNFs with lower MERRIPM, even when the Medicare share is the
same, because the former have more to gain. Similarly, SNFs with higher Medicare shares would
likely try to reduce readmissions more than SNFs with lower Medicare shares, even when the
MERRIPM is the same.
Data sources
This study uses data from multiple sources. First, we downloaded the FY2020 SNF VBP
aggregate and facility-level data from the CMS website. For the main analysis, we used the
baseline period of FY2016 and the performance period of FY2018. To calculate MERRIPM, we
used the readmission data from FY2016 as SNFs were already receiving the information
confidentially from the CMS. Second, we took SNF-specific payment information from the
Medicare Public Use File payment data from calendar year (CY) 2017. Third, we downloaded
SNF facility-level characteristics from LTCfocus.org. We used information on the Medicare
share, for-profit status, government-owned, urban or rural location, average occupancy, and
average daily census from the data.
To show the outcomes of the SNF VBP program are subject to mean reversion, we used
the program data of FY2019 from the CMS website. The program uses past performance data for
the relevant fiscal year of the program data. The program data of FY2019 contains the
readmission rates for CY2015 and CY2017. A total of 14,972 SNFs were included in this
analysis.
Our main analysis had a total of 11,517 SNFs. Several SNFs were excluded for missing
various data elements from the public-use file. We excluded SNFs that had missing baseline
period performances (n=2513), performance period performances (n=651), payment data (n=5),
and facility-level characteristics (n=515).
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Marginal Effect of Performance Improvement on Penalties
We estimated the MERRIPM for each SNF. We calculated the MERRIPM by estimating
the incentive payment multiplier between two scenarios and extracting the difference. In the first
scenario, we calculated the payment incentive multiplier for each SNF by assuming that the
SNFs reduce their readmission rates by a fixed amount, one standard deviation of the baseline
readmission rates of all SNFs, assuming all of the other SNFs’ readmission rates remain the same
as in the baseline period. In the second scenario, we calculated the incentive payment multiplier
when there was no change in the readmission rates (i.e., performance and baseline period
readmission rates are the same) for all SNFs. The above method calculates the absolute increase
in incentive payment multiplier as the readmission rates declines. Since we calculated the
MERRIPM by assuming that SNFs reduced their readmission rate, MERRIPM was either
positive or zero. The MERRIPM was zero for SNFs that could not change their penalty and
rewards even with a decline in their readmission rates, which could happen when they were at
the tails of the baseline readmissions distribution. The top-performing SNFs would receive no
more rewards than they had already received. Similarly, for poor-performing SNFs, the decline
in readmission rate may not have been sufficient to change their penalties. Our estimate of
MERRIPM depended on the baseline readmission rate. Further details were given in Appendix
A.
Mean reversion of performance measures
We would like to understand whether SNFs with higher MERRIPM show a reduction in
their readmission rates. Our measure of MERRIPM is a function of the baseline readmission rate.
As such, at the SNF level, the readmission rate changes across periods can also be a function of
the baseline readmission rate when there is mean reversion. Mean reversion happens when units
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further away from the mean are likely to be measured closer to the mean in repeated
measurements by chance alone. In addition, the SNF VBP program compares readmission rate
across baseline and performance periods in calculating incentive payment multipliers. In the
program, the performance and baseline period cover a year, and the baseline period precedes the
performance period by two years. The same measure, i.e., readmission rate, is used in both
periods, so changes in readmission rate may be subject to mean reversion.
The impact of the program needs to adjust for the mean reversion of the readmission rate.
The outcomes, i.e., changes in the readmission rate, were adjusted using the method explained as
in Kelly and Price (2005). In this method, mean reversion is less likely to be a concern if the
correlation in readmission rate across different periods is high or if SNFs are near the mean in
the baseline period. We show the role of the mean reversion using the linear regression. The
linear regression uses changes in the readmission rate, adjusted and unadjusted for the mean
reversion, as the outcome variable and the baseline readmission rate as the independent variable.
Once adjusted for mean reversion, we should expect the coefficient on the baseline readmission
rate to be small in magnitude and insignificant. We use the readmission data of CY 2015 and CY
2017 as the baseline and performance periods. Given that these periods are before and
immediately after SNFs were provided data confidentially, they would not be subject to the
program and all the changes will be due to the mean reversion. Additional analyses are given in
Appendix B.
Empirical strategy
Our empirical strategy is to test if SNF VBP program incentives improve performance
i.e., reduce readmissions. We estimated multivariable regressions to study the relationship
between the program incentives (independent variable) and changes in the readmission rates
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(dependent variable). We used the interaction of the MERRIPM and the Medicare shares as the
measure of overall program incentives. We hypothesized that the decline in the readmission rate
would be greater for SNFs with a higher value of interaction of MERRIPM and Medicare share.
The empirical specification suggested by our conceptual model given earlier is given by:
Δ𝑅 𝑠 = 𝛽 0
+ 𝛽 1
∗ 𝑚𝑠 ∗ 𝑀𝐸𝑅𝑅 𝐼𝑃𝑀 𝑠 + 𝜖 𝑠
The outcome, Δ𝑅 𝑠 , is the change in readmissions for SNFs between the performance period,
FY2018, and the baseline period, FY2016. These periods are consistent with program data for
FY2020. Positive values suggest an increase in readmission rates, and negative values indicate a
decrease in readmission rates. 𝑀𝐸𝑅𝑅𝐼𝑃𝑀 is the marginal effect of readmissions reduction on
incentive payment multiplier and 𝑚𝑠 is the Medicare share. The key parameter of interest is 𝛽 1
,
the interaction of Medicare share and the MERRIPM, which captures the overall impact of the
SNF VBP program. This coefficient measures the changes in readmission rate given a one-unit
increase in the overall program incentives and is expected to be negative.
In our estimation, the MERRIPM and Medicare share are two sources of variation. As we
have explained earlier, MERRIPM is a function of baseline readmission rate. So, our sources of
variations are the baseline readmission rate and the Medicare share. However, the baseline
readmission rate is correlated with change in the readmission rate due to both the MERRIPM and
the mean reversion. So, our primary analysis accounts for the mean reversion by using adjusted
changes in the readmission rate. In our secondary analysis, we control for the baseline
readmission rate non-parametrically and use only the Medicare share to identify the effects of the
program incentives. We use decile dummies of the baseline readmission rate for this. As
sensitivity analyses, we drop SNFs that are in the tails of the baseline readmission rate
distribution. SNFs around the tails would be more likely to be the subject of random variation in
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readmission rate than SNFs around the mean. Given that the Medicare share might change with
the program itself, we use past Medicare shares in all the analyses. We control for SNF
characteristics in all our models, as they might be correlated with both the baseline readmission
rate and the Medicare share. We included an indicator for SNFs’ for-profit status, an indicator
for government-ownership, and an indicator for urban or rural location, average occupancy, and
average daily census. We used robust standard errors in all our analyses.
Results
SNF characteristics
Table 1 describes variables at the SNF level used in the main analysis. From the baseline
period (FY2016) to the performance period (FY2018), the readmission rate increased by 0.72
percentage points, from a mean (standard deviation) of 18.98 (1.91) to 19.70 (1.87). In our
sample of SNFs, 72.03% of SNFs were for-profit, and 4.28% were government-owned. Most of
the SNFs were located in non-rural areas with 71.76% in metropolitan areas and 12.41% of SNFs
in rural areas. The average occupancy rate was 73.27 per 100 beds. The average daily census was
85.63.

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Table 1: Characteristics of the Skilled Nursing Facilities in the Study Sample
Mean Standard Deviation
Baseline Period: FY2016 Risk-Standardized Readmission Rate
(%)
18.98 1.91
Performance Period: FY2018 Risk-Standardized Readmission
Rate (%)
19.70 1.87
Change in Risk-Standardized Readmission Rate (FY2016 -
FY2018)
-0.72 2.20
Medicare share (%) 16.03 13.82
Average occupancy rate (%) 73.27 14.99
Daily census 85.63 47.55

For-profit status (%) 72.03
Government-owned (%) 4.28
Non-profit (%) 22.54
Located in Micro areas 14.58
Located in Metropolitan areas (%) 71.76
Located in Rural areas (%) 12.41
Note: The total number of skilled nursing homes is 11,517. The baseline and performance periods are consistent with FY2020
value-based program data. These characteristics are taken from the LTCFocus.org dataset.

MERRIPM and baseline performance
Figure 1 shows the graph of MERRIPM as a function of the baseline readmission rate.
The values are positive since we estimated the MERRIPM with respect to a one-standard
deviation decline of the baseline readmission rate, equivalent to a 1.9 percentage-point reduction
in the readmission rate. By construction, this means that all SNFs reduced their readmission rate
compared to the baseline period. The graph shows that a reduction of readmission rate for a SNF,
conditional on all other SNFs’ performance being constant, does not reduce payments. The mean
of MERRIPM is 0.014. This means that for a 1.9 percentage point decline in readmission rate,
the average incentive payment multiplier improves by 0.014. For example, if the incentive
payment multiplier was 0.98 without a reduction in the readmission rate, with a decrease in the
readmission rate this is now 0.994 (0.98 + 0.014), which means that the incentive payment
multiplier increases by 1.4 percentage points. The value of MERRIPM ranges between 0 to 0.03
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units. So, the reduction in readmission rate impacts the payments by 0 to 3 percentage points
with less impact on tails and more in the middle.
Figure 1: The Distribution of the Marginal Effect of Readmissions Reduction on Incentive
Payment Multiplier (MERRIPM) on Baseline RSRR

Note: The above graph shows the marginal effect of readmissions reduction on incentive payment multiplier (MERRIPM) on
baseline risk-adjusted readmission rate (RSRR) when the Skilled Nursing Facilities (SNFs) reduce their readmissions by 1.9
percentage point assuming that all of the other SNFs’ readmission rates remain the same. The mean (standard deviation) and the
range of MERRIPM is 0.014 (0.01) and [0,.03] respectively.

Table 2 shows the different components of MERRIPM. We estimated the achievement
score, improvement score, total performance score, transformed performance score, and payment
incentive multiplier in two scenarios: (1) when there is a decrease in readmission rate from the
baseline by one standard deviation, that is 1.9 percentage points, and (2) when the readmission
rate does not change from the baseline. The mean achievement score is 67.94 when the
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readmissions decrease and 34.49 when there is no change in the readmission rate. The mean
improvement score is 65.50 when readmissions decrease. Since the improvement score is only
given when there is a decrease in the readmission rate, the improvement score is zero when there
is no change in the readmission rate. The means of total performance scores are 71.60 and 34.49
when there is a decline in readmission rate and no change in readmission rate respectively. Since
there is no improvement score when readmission rate remains the same, our total performance
score is just the achievement score. When total performance scores are transformed using the
logit exchange function, the means are 0.72 and 0.33 in the two aforementioned scenarios. The
mean payment incentive multiplier with improvement is 1.01 and 0.99 without changes in
performance. Finally, the mean of MERRIPM is 0.014, which is the mean of difference in
payment incentive multiplier between two scenarios, as described earlier, for each SNF.
Table 2: Intermediate Values in Estimation of the Marginal Effect of Readmissions Reduction on
Incentive Payment Multiplier (MERRIPM)
Mean Standard Deviation
Achievement score: decrease in readmission rate 67.94 33.63
Achievement score: no change in readmission rate 34.49 32.56
Improvement score: decrease in readmission rate 65.50 23.88
Improvement score: no change in readmission rate 0.00 0.00
Total performance score: decrease in readmission rate 71.60 27.53
Total performance score: no change in readmission rate 34.49 32.56
Transformed performance score: decrease in readmission rate 0.72 0.35
Transformed performance score: no change in readmission rate 0.33 0.38
Payment incentive multiplier: decrease in readmission rate 1.01 0.01
Payment incentive multiplier: no change in readmission rate 0.99 0.01
MERRIPM (difference in payment incentive payment multiplier) 0.014 0.011
Note: The table provides the mean and the standard deviation of values used for determining the marginal effect of readmissions
reduction on incentive payment multiplier (MERRIPM). The table provides estimates when skilled nursing facilities’ readmission
rates remain the same and when their readmission rates decrease from the baseline by a 1.9 percentage point, assuming that all of
the other SNFs’ readmission rates remain the same.

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Hospital readmissions and reversion to the mean
Table 3 shows the changes in the readmission rate across two periods, unadjusted and
adjusted for the mean reversion, on earlier period readmissions. Columns (1) and (2) compare the
changes in the readmission rates between CY2017 and CY2015. The coefficient on CY2015
without adjusting and adjusting for the mean reversion are -0.71 (se =0.008, P < 0.01) and -0.03
(se =0.008, P < 0.01) respectively. The unadjusted coefficient suggests that an SNF with a 1.0%
increase in readmission rate would see a 0.71 percentage point decrease in the readmission rate,
whereas the adjusted coefficient indicates only a 0.03 percentage point decrease. This means that
changes in the readmission rates across different periods show very little correlation once
adjusted for the mean reversion.
Table 3: The Association of Change in Risk-Standardized Readmission Rate Across Years with
the Baseline Risk-Standardized Readmission Rate (RSRR)
(1) (2)
VARIABLES
Change from CY15 and
CY17
RTM-Adjusted change from
CY15 and CY17
Baseline RSRR
CY2015, RSRR -0.71*** -0.03***

(0.008) (0.008)

Constant 0.14*** 0.01***

(0.002) (0.002)

Observations 14,972 14,972
R-squared 0.409 0.001
Note: This table provides results with both the mean reversion adjusted and unadjusted results. The outcomes are changes in risk-
adjusted readmission rate (RSRR) between two periods. The outcomes in column (1) are not adjusted for the mean reversion,
while the outcomes in column (2) are. CY stands for Calendar Year. RSRR is risk-standardized readmission rate and RTM is
regression to the mean. Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1.

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Relationship between program incentives and performance
Table 4 shows the impact of the SNF VBP program on changes in readmission rates
across FY2016 (baseline period) and FY2018 (performance period). In our primary analysis–
that adjusts for mean reversion – SNF VBP was associated with a 0.14 percentage point increase
in the readmission rate (se=0.067 p <.05) (column 1). In this model, SNF characteristics were
associated with changes in performance. For-profit status is associated with a 0.19 percentage
point increase in readmission rate (se=0.039, P < 0.01). Rural SNFs show a 0.17 percentage
point decrease in readmission rate (se=0.048, P < 0.01). In our secondary analysis, column 2,
which flexibly controls for the baseline readmission rate, the SNF VBP program shows no
statistically significant decrease in readmission rate. For-profit and rural SNFs are associated,
respectively, with increase and decrease in readmission rates as in the primary analysis.

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Table 4: Association of Changes in the Readmission Rate Between FY2018 and FY2016 and the
SNF VBP Program Incentives
(1) (2)
VARIABLES
RTM adjusted change in
readmission rate Changes in readmission rate

Program Incentives
(Medicare share X MERRIPM) 0.14** 0.12

(0.067) (0.080)
Non-profit (Reference)
For profit 0.19*** 0.19***

(0.039) (0.040)
Government owned -0.08 -0.10

(0.079) (0.080)
Non-rural (Reference)
Rural -0.17*** -0.18***

(0.048) (0.048)
Average occupancy -0.00*** -0.00***

(0.001) (0.001)
Average daily census -0.00** -0.00**

(0.000) (0.000)
Constant 0.91*** -1.61***

(0.093) (0.111)

Controls for baseline
readmissions using deciles No Yes

Observations 11,517 11,517
R-squared 0.006 0.342
Note: The outcome is the difference in risk-standardized readmission rate (RSRR) between Fiscal Year (FY) 2016 and FY2018.
Positive values of outcome imply increase in RSRR. For column (1) the outcome is adjusted for the regression to the mean
(RTM), and for column (3) the outcome is adjusted for the baseline readmission rate using deciles. The mean of the outcome is -
0.70. MERRIPM is the marginal effect of readmissions reduction on incentive payment multiplier. Robust standard errors are
given in parentheses. *** p<0.01, ** p<0.05, * p<0.1.

The increase in the readmission rate is not robust to dropping the SNFs that were at the
tails of baseline period readmission rate distribution. Table 5 shows the results where SNFs in
different deciles are dropped. Dropping the bottom and the top decile (column 1), the SNF VBP
was associated with a 0.06 percentage point increase in the readmission rate (se = 0.071, P >
0.10). Similarly, dropping the bottom two and top two deciles (column 2), the SNF VBP was
associated with a 0.03 percentage point increase in the readmission rate (se = 0.078, P > 0.10).

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Table 5: Association of Changes in the Readmission Rate Between FY2018 and FY2016 and the
SNF VBP Program Incentives, Dropping Poor Performing and Best Performing Deciles

(1)
Dropping SNFs in the Top
and Bottom Deciles of
Baseline Readmission Rates
(2)
Dropping Top Two and Bottom
Two Deciles of Baseline
Readmission Rates
VARIABLES Mean reversion adjusted changes in readmission rate

Program Incentives (Medicare share
X MERRIPM) 0.06 0.03

(0.071) (0.078)
Non-profit (Reference)
For profit 0.20*** 0.21***

(0.044) (0.051)
Government owned -0.15* -0.12

(0.088) (0.098)
Urban (Reference)
Rural -0.17*** -0.19***

(0.051) (0.059)
Average occupancy -0.00*** -0.00**

(0.001) (0.001)
Average daily census -0.00* -0.00**

(0.000) (0.001)
Constant 0.97*** 0.98***

(0.105) (0.123)

Observations 9,149 6,800
R-squared 0.007 0.007
Note: The outcome is the difference in risk-standardized readmission rate (RSRR) between Fiscal Year (FY) 2016 and FY2018.
Positive values of outcome imply increase in RSRR. The outcome is adjusted for mean reversion. In column (1) skilled nursing
facilities in the best and worst performing deciles are removed. In column (2) skilled nursing facilities in two deciles at each tail
of the distribution are removed. MERRIPM is the marginal effect of readmissions reduction on incentive payment multiplier.
Robust standard errors are given in parentheses. *** p<0.01, ** p<0.05, * p<0.1.

Discussion
Using the SNFs subject to the SNF VBP program, we found that greater exposure to
aggregate program incentives, as measured by the interaction of the MERRIPM and Medicare
share, was not associated with a decrease in readmission rate. In our primary specification we
found that the program was associated with an increase in readmission rate. In our secondary and
sensitivity analyses, we showed that the increase in readmission rate was not statistically
significant and also smaller in magnitude. We also found that the performances were correlated
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with SNF characteristics like for-profit status and rural locality. So, why did the SNFs appear not
to respond to program incentives under the SNF VBP program?
One reason could be using a single measure, measured by the risk-adjusted hospital
readmission rate, for program performance. Our analysis showed that risk-adjusted readmission
rates are subject to mean reversion. In the SNF VBP program, changes in readmissions are taken
to calculate the achievement and improvement score and to derive incentive payment multipliers.
Even though readmissions from SNFs are common and often avoidable (Mor, Intrator, Feng, &
Grabowski, 2010; Neuman et al., 2014; Ouslander et al., 2010; Rahman, Grabowski, Mor, &
Norton, 2016; Rahman, McHugh, Gozalo, Ackerly, & Mor, 2017), readmission rates could be a
poor measure of quality, such that changes in the quality of care across periods may not be
reflected in changes in the readmission rates. Mean reversion in hospital readmission rates were
also shown by earlier works in hospital settings (Joshi et al., 2019; Press et al., 2013).
Readmissions could be a poor measure for other reasons as well. Readmissions could be noisy
due to changing case mix of patients and not be a reliable measure for capturing year-to-year
changes. Readmission rates reflect both necessary readmissions and discretionary readmissions.
So, improvements in readmission rates can occur simply by cutting discretionary readmissions.
Necessary readmissions can occur as a result of poor care, but readmission as an outcome may
not be tightly coupled to care processes. If readmissions are not capturing the quality of care, use
of readmissions in SNF VBP program may be penalizing SNFs for issues that are not associated
with the quality of care.
Due to the lack of understanding of how their effort translates into payment rewards or
penalties, SNFs may not have changed their behavior or take longer to reduce readmissions. The
SNF VBP program, as we have discussed earlier, has a complex way of assigning rewards and
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penalties. Given the program's complexity, leaders of SNFs may be uncertain of the degree to
which a decrease in readmissions would translate into increased payments. The other reason for
the lack of changes in SNF behavior could be the size of the payments. The program withholds
2% of Medicare payments. Only 60% of the withheld amount is returned as program rewards.
Only a fraction of SNFs received positive payments every year (MEDPAC, 2021). In addition,
the payment adjustment has varied year to year for SNFs (MEDPAC, 2021). This would suggest
that it is difficult to clearly say that the program is consistently measuring the quality of care and
rewarding or penalizing good- or poor-quality care.
Finally, it could be very difficult to reduce readmissions. Prior literature using a
randomized control trial showed that programs that targeted reducing readmissions from SNF
have not been successful (Ouslander et al., 2021; Tappen et al., 2018). An earlier analysis of the
3-year voluntary Nursing Home Value-Based Purchasing demonstration showed little impact on
quality, and the observed savings likely reflected mean reversion rather than true savings
(Grabowski et al., 2017). They also found that participants engaged in few direct activities to
lower Medicare spending. Finally, to reduce readmissions, SNFs need to know which candidates
are more likely to be readmitted. Knowing which patient is likely to be readmitted ex-ante could
be difficult. All these factors may have contributed to the lack of improvement in performance
under the SNF VBP program.
Limitations
Our study has several limitations. Our main independent variable is a function of two
variables – the Medicare share of patients and the MERRIPM. There are several limitations to
this simple model. It assumes that there is no spillover due to changes in quality. This means that
there are no changes in Medicare and non-Medicare share due to changes in quality. In practice,
we can assume that an increase in quality may lead to an increase in non-Medicare share. Due to
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an increase in quality, the facility's ranking improves, attracting more non-Medicare patients and
increasing the non-Medicare share of patients. Similarly, the Medicare share could increase as
SNFs provide better care to Medicare patients. To overcome this, we used the past Medicare
share rather than the current share of the Medicare population for each SNF, but this may not
fully account for this spillover. The MERRIPM, as constructed, is a function of the baseline
readmission rate only, and the controls for the baseline may not have fully captured this.
Also, this analysis does not bring the cost into the calculation. Cost may not be an
important factor if there is an opportunity to improve the readmission rate as suggested by earlier
work. Our analysis controls outcomes for mean reversion since this depends on baseline
performance. Our controls may not have fully captured the independent effect of baseline
performance. We used a method that relies on normality assumption to correct for mean
reversion in our outcome variable. We also assumed that the correlation across baseline and
performance period was as observed in the data.
Our results are only for one year of the program data. So, this study precludes any
dynamic effects of the program. Our analysis also only uses facility-level data and does not say
anything about the individual-level data. Without individual-level data, we cannot differentiate
between necessary and discretionary readmissions. Finally, our analysis does not capture the
changes in processes that each SNF might have implemented to improve performance and
quality.
Conclusion
The SNF VBP embodies the idea that quality payment programs can create incentives to
improve the quality of care provided by SNFs to fee-for-service Medicare beneficiaries. We
found that SNFs have not yet reduced their readmission rates in response to the VBP’s financial
incentives. This could be due to several limitations of the program. The program relied on
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hospital readmissions, which are subject to mean reversion, to measure performance. Also, using
readmissions as a single measure for program performance may not have captured the
multidimensional nature of quality of care. The program's structure, which manipulates
performance using various functional forms may have diluted the incentives. These findings
imply that the program needs to reconsider how it provides incentives to skilled nursing
facilities.
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Chapter 3: Regression to the Mean in the Medicare Hospital Readmissions Reduction Program
2

Abstract
Importance: Excess 30-day readmissions have declined significantly in hospitals initially
penalized for high readmission rates under the Medicare Hospital Readmissions Reduction
Program (HRRP). Although a possible explanation is that the policy incentivized penalized
hospitals to improve care processes, another is regression to the mean (RTM), a statistical
phenomenon that predicts entities farther from the mean in one period are likely to fall closer to
the mean in subsequent (or preceding) periods due to random chance.
Objective: To quantify the contribution of RTM to declining readmission rates at hospitals
initially penalized under the HRRP.
Design, Setting, and Participants: This study analyzed data from Medicare Provider and Analysis
Review files to assess changes in readmissions going forward and backward in time at hospitals
with high and low readmission rates during the measurement window for the first year of the
HRRP (fiscal year [FY] 2013) and for a measurement window that predated the FY2013
measurement window for the HRRP among hospitals participating in the HRRP. Hospital
characteristics are based on the 2012 survey by the American Hospital Association. The analysis
included fee-for-service Medicare beneficiaries 65 years or older with an index hospitalization
for 1 of the 3 target conditions of heart failure, acute myocardial infarction, or pneumonia or
chronic obstructive pulmonary disease and who were discharged alive from February 1, 2006,
through June 30, 2014, with follow-up completed by July 30, 2014. Data were analyzed from
January 23, 2018, through March 29, 2019.

2
This is a joint work with Teryl Nuckols, Jose Escarce, Peter Huckfeldt, Ioana Popescu, and Neeraj Sood. This chapter is
published as “Regression to the Mean in the Medicare Hospital Readmissions Reduction Program” in JAMA Internal Medicine
(Joshi et al., 2019).
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Exposure: Hospital Readmissions Reduction Program penalties.
Main Outcome and Measures: The excess readmission ratio (ERR), calculated as the ratio of a
hospital’s readmissions to the readmissions that would be expected based on an average hospital
with similar patients. Hospitals with ERRs greater than 1.0 were penalized.
Results: A total of 3258 hospitals were included in the study. For the 3 target conditions,
hospitals with ERRs of greater than 1.0 during the FY2013 measurement window exhibited
decreases in ERRs in the subsequent 3 years, whereas hospitals with ERRs of no greater than 1.0
exhibited increases. For example, for patients with heart failure, mean ERRs declined from 1.086
to 1.038 (−0.048; 95% CI, −0.053 to −0.043; P < 0.001) at hospitals with ERRs of greater than
1.0 and increased from 0.917 to 0.957 (0.040; 95% CI, 0.036 - 0.044; P < 0.001) at hospitals
with ERRs of no greater than 1.0. The same results, with ERR changes of similar magnitude,
were found when the analyses were repeated using an alternate measurement window that
predated the HRRP and followed up hospitals for 3 years (for patients with heart failure, mean
ERRs declined from 1.089 to 1.044 (−0.045; 95% CI, −0.050 to −0.040; P < 0.001) at hospitals
with below-mean performance and increased from 0.915 to 0.948 (0.033; 95% CI, 0.029 to
0.037; P < 0.001) at hospitals with above-mean performance). By comparing actual changes in
ERRs with expected changes due to RTM, 74.3% to 86.5% of the improvement in ERRs for
penalized hospitals was explained by RTM.
Conclusions and Relevance: Most of the decline in readmission rates in hospitals with high rates
during the measurement window for first year of the HRRP was due to RTM. These findings call
into question the notion of an HRRP policy effect on readmissions.

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Introduction
The Medicare Hospital Readmissions Reduction Program (HRRP), enacted under the
Affordable Care Act in March 2010 (Centers for Medicare & Medicaid Services (CMS), 2019),
imposes financial penalties on hospitals with excess 30-day readmission rates. Excess
readmissions measure whether risk adjusted admissions for a particular condition at a hospital
during a preceding reference measurement window exceed the national average. Beginning in
fiscal year (FY) 2013, Medicare penalized hospitals with excess readmissions for heart failure
(HF), acute myocardial infarction (AMI), and pneumonia during a reference measurement
window from July 2008 through June 2011 (Centers for Medicare & Medicaid Services (CMS),
2019). In particular, Medicare measured excess readmissions using the excess readmissions ratio
(ERR) – calculated by taking the ratio of a hospital’s predicted 30-day readmissions by the
number that would be expected based on an average hospital with similar patients. Only
hospitals with ERRs greater than 1.0 for targeted conditions are penalized.
Risk-adjusted readmissions for targeted conditions started to decline in 2011, shortly after
the announcement of the HRRP, and the reductions were larger at penalized than non-penalized
hospitals (Desai et al., 2016; Wasfy et al., 2017). Some interpreted this evidence as suggesting
that the HRRP’s financial penalties incentivized hospitals to improve transitions of care and
implement other strategies that resulted in declines in readmissions (Desai et al., 2016; Wasfy et
al., 2017). However, most changes in excess readmissions at penalized hospitals may be
explained by regression to the mean (RTM), a statistical phenomenon that occurs when an
outcome for an entity is measured repeatedly and the outcome is a random variable (Atkinson,
Loenneke, Fahs, Abe, & Rossow, 2015; Barnett, van der Pols, & Dobson, 2005; J M Bland &
Altman, 1994; J Martin Bland & Altman, 1994; Kelly & Price, 2005; Linden, 2013; Yudkin &
Stratton, 1996). With repeated measurements over time, outcomes for entities with outcomes
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further away from the mean in one period are likely to be recorded closer to the mean in
subsequent or preceding periods simply by chance, because more extreme values have a lower
probability of occurring than do values near the mean. Therefore, RTM has the potential to
produce the appearance of improvement among initially low performers and deterioration among
initially high performers. Given that hospitals’ excess readmissions involve randomness,
hospitals with excess readmissions before the HRRP—that is, penalized hospitals—would be
more likely to exhibit subsequent reductions in excess readmissions due to chance alone. Chance
or random events might play an important in determining excess readmissions as readmissions
are not only a function of care processes and treatment provided to patients but also of random
biological variation in treatment efficacy or adverse effects and random events such as poor
outcomes due to severe weather or falls due to hazardous living conditions.
The objective of this analysis was to describe and quantify the role of RTM in explaining
improvements in performance, relative to national averages, at hospitals initially classified as
below-average performers under the HRRP. First, we tested whether hospitals with below
average baseline performance during the initial HRRP measurement window experienced
subsequent improvements in performance after announcement and implementation of HRRP and
inversely whether hospitals with above average performance experienced subsequent declines in
performance after announcement and implementation of HRRP.
Next, we tested two hypotheses to examine whether RTM rather than HRRP policy
effects played a major role in explaining the above trends in excess readmissions. First if RTM
played a major role, then hospitals with worse than mean baseline performance during an earlier
alternate reference measurement window that predates the implementation of HRRP would
exhibit subsequent declines in ERRs. These declines would be qualitatively similar to those
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observed at hospitals with low performance after the implementation of HRRP. Second, if RTM
played a major role, then hospitals with worse than mean baseline performance during the HRRP
would exhibit declines in ERRs going backward in time just as they do going forward in time.
Finally, for hospitals with below-mean baseline performance, we used established methods to
calculate the percentage of the subsequent improvements in excess readmissions that were
attributable to RTM.
Methods
Population and setting
The study was done at the hospital level. We included fee-for-service Medicare
beneficiaries 65 years or older with an index hospitalization for 1 of the 3 target conditions (HF,
AMI, and pneumonia) and chronic obstructive pulmonary disease (COPD) that resulted in
discharge alive from February 1, 2006, through June 30, 2014. We excluded index
hospitalizations when the patient was admitted with the same condition during the prior 30 days.
Study hospitals had at least 25 eligible index hospitalizations for a target condition in the excess
readmission measurement period.
Data sources
We used data from Medicare Provider and Analysis Review files from February 1, 2006,
through June 30, 2014, to identify index hospitalizations and 30-day readmissions to July 30,
2014. Information on patient characteristics came from Master Beneficiary Summary Files.
Hospital characteristics were based on the 2012 Medicare Provider of Services files and 2012
American Hospital Association Annual Survey.
Measures
Following the HRRP methods, we calculated ERRs for each hospital and study period by
using linear regression to estimate the predicted number of readmissions (based on patient
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characteristics and hospital-level random effects) and the expected number (based only on
patient characteristics), and then dividing the predicted by the expected number. In these
regression models, patient characteristics included age group (65-69, 70-74, 75-79, 80-84, 85-89
years and a single group >=90 years), sex, and condition-specific comorbidities documented
during the index hospitalization. We used the ERR to measure performance because it reflected
how Medicare assigned HRRP penalties and accounted for trends in mean readmission rates,
whether owing to the policy or other factors.
Based on the reference-period ERRs, we stratified eligible hospitals into 2 groups
reflecting below-average (ERR > 1.0) or above-average (ERR <= 1.0) performance. These group
variables were the main independent variables in the analyses. The main outcome variable was
the change in the ERR from the reference period to the subsequent or preceding period.
Statistical Analysis
First, we summarized the characteristics of hospitals used in the analyses. Next, we
conducted three sets of analyses, described below, with three analyses per set (HF, AMI, and
pneumonia). In each analysis, we performed linear regression to examine whether the ERRs for a
reference period predicted changes in ERRs from the reference period to a subsequent or
preceding period.
Analysis 1: Baseline Performance during Initial HRRP Measurement Window
We examined changes in ERRs from the FY2013 measurement window (July 1, 2008
through June 30, 2011) to the subsequent three-year period (July 1, 2011 through June 30, 2014)
after the announcement and implementation of HRRP. We expected that for targeted conditions,
hospitals with below-mean performance (ERR > 1.0) would experience a decrease in ERRs, and
hospitals with above-mean performance (ERR <= 1.0) would experience an increase in ERRs.
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These effects are consistent with RTM and HRRP policy effects (Figure 2). In 1 alternate
specification, we repeated this analysis by examining trends in readmissions for hospitals with
ERRs greater than 1.07 (75
th
percentile of the ERR distribution). Hospitals in the right tail of the
ERR distribution had limited incentives to respond to HRRP because the policy capped
penalties; therefore, the hospitals would have to achieve substantial declines in readmissions to
reduce the size of the penalties, and substantial declines might have been infeasible. We
considered index hospitalizations for COPD in another alternate specification because the HRRP
did not create incentives to lower COPD readmissions until FY2015.
Figure 2: Periods Relevant to Analyses 1 to 3
2006 2007 2008 2009 2010 2011 2012 2013 2014
Policy
Events
ACA Announced HRRP Penalties
Imposed
Analysis
1
Measurement Window for
Penalties in FY2013
Subsequent Period
Analysis
2
Alternative Measurement
Period
Alternate Subsequent Period

Analysis
3
Preceding Period
Measurement Window for
Penalties in FY2013

Note: Analysis 1: Changes in Excess Readmissions Rates Are Inversely Associated with Baseline ERRs. In hospitals with worse
(or better) than average performance during the HRRP measurement period for FY2013, excess readmissions rates decline (or
increase) during the three years post-measurement. Analysis 2: Hospitals with Low Performance During an Alternate
Measurement Period Exhibit Subsequent Declines in Excess Readmissions Rates. In hospitals with worse (or better) than average
performance during an alternate measurement period, declines (or increases) in excess readmissions rates occur during the three
years post-measurement i.e. during FY2013 measurement period. Analysis 3: Hospitals with Low Performance During the HRRP
Measurement Period for FY2013 Exhibit Declines in Excess Readmissions Rates When Going Backward in Time. In hospitals
with worse (or better) than average performance during the HRRP measurement period for FY2013, declines (or increases) in
excess readmissions rates occur in reverse chronological order during the alternate measurement period.

Analysis 2: Alternate Measurement Period
We hypothesized that with RTM, hospitals with below-mean performance during a
different measurement window predating the HRRP would also exhibit subsequent
improvements despite the absence of policy incentives, and performance would deteriorate at
hospitals with above-mean performance. To test this hypothesis, we examined changes in ERRs
from an alternate measurement period that immediately preceded the FY2013 measurement
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window (February 1, 2006, through June 30, 2008; data from before 2006 were not available) to
the FY2013 measurement window.
Analysis 3: Reverse Chronological Trends
Regression to the mean suggests that hospitals with below-mean performance during the
FY2013 measurement window would exhibit improvement going backward in time, just as they
do going forward in time. Hospitals that are above-mean performers would exhibit deterioration
going backward in time. To test this hypothesis, we examined changes in ERRs in reverse-
chronological order from the FY2013 measurement window to the preceding alternate
measurement period (February 1, 2006, through June 30, 2008).
Quantifying Regression to the Mean
For hospitals that performed below average during the FY2013 measurement window, we
quantified the percentage of the subsequent improvement in performance that was due to RTM
(Linden, 2013). The formula, which is explained in detail in the Appendix C, captures the three
phenomena that influence the size of the RTM effect and are easily understood intuitively. First,
the expected RTM effect is greater when the outcome in the baseline period is more extreme
(i.e., farther from the mean of the distribution), because extreme outcomes rarely occur and
consequently are very unlikely to be repeated. Second, other things equal, the expected RTM
effect is greater when the variance of the outcome in the baseline period is greater, because a
greater variance means that the outcome distribution is more spread out. Consequently, any
movement from the tail of the distribution at baseline to the mean in the post period represents a
greater difference in the outcome. Third, the RTM effect is smaller when the correlation in the
outcome between the baseline and post periods is higher, because a high correlation means that
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outcomes tend to be more persistent over time. We used methods described in Linden (Linden,
2013) to estimate the expected RTM effect.
Results
Descriptive analyses
Our analyses of eligible hospitals included 3,116 for HF, 2,196 for AMI, and 3,233 for
pneumonia. Medicare beneficiaries comprised about half of patients in these hospitals (Table 6).
For each condition, more than 60% of hospitals were non-profit, and more than 70% were
located in Metropolitan areas.
Table 6: Hospital Characteristics, by Target’s Summary Statistics by Conditions

Heart
Failure
Acute Myocardial
Infarction Pneumonia
Number of Hospitals Included in Analysis 3,116 2,196 3,233
Missing Hospital Characteristics (N) 128 41 219
Number of Hospital Beds per Hospital, Mean 227.54 281.68 226.11
Percentage of Inpatients with Medicare 51.01 51.13 50.79
Percentage of Inpatients with Medicaid 19.66 19.22 19.60
Hospital Type

Non-profit, % 63.39 68.82 63.11
For-profit, % 20.75 20.00 20.57
Government, % 15.86 11.18 16.32
Teaching Status

Major Teaching, % 8.13 10.90 8.10
Minor Teaching, % 29.35 35.03 29.33
Non-teaching, % 62.52 54.06 62.57
Location

Metropolitan Area, % 70.75 80.79 70.31
Micropolitan Area, % 19.65 16.38 19.74
Rural Area, % 9.61 2.83 9.95
Note: This includes all hospitals that are used to analyze the changes in Excess Readmissions Rates (ERRs). Individual hospitals
may be listed for more than one target condition. Hospital characteristics are based on the 2012 survey by the American Hospital
Association.

Changes in ERRs between contiguous non-overlapping measurement periods
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Analysis 1: Baseline Performance During Initial HRRP Measurement Window Predicts
Changes in Excess Readmissions after Announcement of HRRP. For all 3 target conditions,
hospitals with below-mean performance (ERR > 1.0) in the FY2013 measurement window
exhibited improvements (decreases in ERRs) in the subsequent 3 years, whereas hospitals with
above-mean (ERR <= 1.0) performance exhibited deterioration (Figure 3). For HF, the mean
ERRs declined from 1.086 to 1.038 (-0.048, 95% CI, -0.053 to -0.043, P<0.001) at hospitals with
below-mean performance and increased from 0.917 to 0.957 (0.040, 95% CI, 0.036 to 0.044,
P<0.001) at hospitals with above-mean performance. Similarly, for AMI, the mean ERRs
declined from 1.106 to 1.043 (-0.063, 95% CI, -0.070 to -0.057, P<0.001) at lower-performing
hospitals and increased from 0.899 to 0.963 (0.063, 95% CI, 0.057 to 0.070, P<0.001) at higher-
performing hospitals. For pneumonia, the mean ERRs declined from 1.112 to 1.041 (-0.071, 95%
CI, -0.077 to -0.066, P<0.001) and increased from 0.898 to 0.955 (0.057, 95% CI, 0.052 to
0.062, P<0.001), respectively. Results were qualitatively similar for hospitals with ERRs greater
than 1.07 and for COPD patients (Tables 7 and 8, and Figure 4).

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Figure 3: Changes in Excess Readmissions Rate (ERRs) from FY2013 Measurement Period to 3-
years Post-measurement.

Note: Data from analysis 1 (described in Figure 2) are stratified by condition.

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Table 7: Change in Excess Readmissions Rates (ERRs) Explained by Regression to the Mean
(RTM) for Hospitals in Right Tail of ERR Distribution
Heart Failure
Acute Myocardial
Infarction
Pneumonia

Change in
ERR
% due to
RTM
Change in
ERR
% due to
RTM
Change in
ERR
% due to
RTM
a) Change in
ERR (3-years
Post-
Measurement
minus
FY2013) on
FY2013

ERR > 1.07 -0.0710*** 90.66 -0.0955*** 83.67 -0.101*** 75.18

(-0.0779 - -
0.0640)
(85.59-
95.73)
(-0.104 - -
0.0868)
(78.13-
89.2)
(-0.108 - -
0.0933)
(71.03-
79.33)
ERR > 1 -0.0482*** 85.8 -0.0632*** 86.45 -0.0712*** 74.34

(-0.0530 - -
0.0434)
(80.57-
91.02)
(-0.0699 - -
0.0565)
(80.25-
92.65)
(-0.0766 - -
0.0657)
(70.12-
78.55)
Number of
Hospitals
2965 2064 3013
Note: The % due to RTM is calculated by dividing the RTM effect by the actual change in ERR multiplied by 100. RTM effects
were calculated using rtmci command in Stata with cutoff of 1.07 (Linden (2013)). The cutoff of 1.07 is around the 75
th

percentile. Confidence interval in parentheses *** p<0.001, ** p<0.01, * p<0.05.

Table 8: Change in Excess Readmissions Rates (ERRs) Explained by Regression to the Mean
(RTM) for COPD
COPD

Change in ERR % due to RTM
a) Change in ERR (3-years Post-
Measurement minus FY2013) on FY2013

ERR > 1 -0.0595*** 80.93

(-0.0641 - -0.0550) (76.03-85.82)
ERR <= 1 0.0411*** 92.98

(0.0373 - 0.0448) (87.31-98.65)
Number of Hospitals 2926
Note: The % due to RTM is calculated by dividing the RTM effect by the actual change in ERR multiplied by 100. RTM effects
were calculated using rtmci command in Stata with cutoff of 1 (Linden (2013)). COPD stands for chronic obstructive pulmonary
disease. Confidence interval in parentheses *** p<0.001, ** p<0.01, * p<0.05.

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Figure 4: Changes in Excess Readmissions Rate (ERRs) for COPD prior to inclusion of COPD
in the HRRP

Note: Post-measurement period is in reference to the fiscal year 2013 measurement period. COPD stands for chronic obstructive
pulmonary disease.

Analysis 2: Alternate Measurement Period. For all 3 target conditions, performance
improved at hospitals with below-mean performance during an alternate measurement period
predating the HRRP and deteriorated at hospitals with above-mean performance (Figure 5). For
HF, mean ERRs declined from 1.089 to 1.044 (-0.045, 95% CI, -0.050 to -0.040, P<0.001) at
hospitals with below-mean performance and increased from 0.915 to 0.948 (0.033, 95% CI,
0.029 to 0.037, P<0.001) at hospitals with above-mean performance. Results were similar for
AMI and pneumonia.
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Figure 5: Changes in Excess Readmissions Rates (ERRs) from an Alternate Measurement Period
to 3-years Post-measurement (i.e. FY2013 Measurement Period).

Note: Post-measurement period is in reference to the fiscal year 2013 measurement period. Data from analysis 2 (described in
Figure 2) are stratified by condition.

Analysis 3: Reverse Chronological Trends. Results reveal an inverse relationship between
performance during the FY2013 measurement window and reverse chronological changes in
performance from that window to the preceding time period. For HF, hospitals with ERRs greater
than 1.0 saw mean ERRs decline from 1.086 to 1.051 (-0.035, 95% CI, -0.040 to -0.030, P<0.001),
whereas hospitals with mean ERRs equal to or below 1.0 exhibited mean increases from 0.918 to
0.951 (0.033, 95% CI, 0.029 to 0.038, P<0.001). Results were similar for AMI and pneumonia
(Figure 6).
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Figure 6: Changes in Excess Readmissions Rates (ERRs) from FY2013 Measurement Period to
Pre-measurement Period.
Note: Post-measurement period is in reference to the fiscal year 2013 measurement period. Data from analysis 3 (described in
Figure 2) are stratified by condition.

Quantifying Regression to the Mean
Among hospitals with below-mean baseline performance during the FY2013
measurement window, 74.3% to 86.5% of the improvement observed from that window to the
subsequent 3-year period was explained by RTM (Table 9). Similarly, 83.6% to 91.8% of the
decline in performance among hospitals with above-mean baseline performance was explained
by RTM.
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Table 9: Changes in Excess Readmissions Rates (ERRs) Explained by Regression to the Mean
(RTM)
Heart Failure
Acute Myocardial
Infarction
Pneumonia

Change in
ERR
% due to
RTM
Change in
ERR
% due to
RTM
Change in
ERR
% due to
RTM
Change in ERR
(3-years Post-
Measurement
minus FY2013
Measurement
Period)

FY2013
Measurement
Period ERR > 1
-0.0482*** 85.8 -0.0632*** 86.45 -0.0712*** 74.34

(-0.0530 - -
0.0434)
(80.57-
91.02)
(-0.0699 - -
0.0565)
(80.25-
92.65)
(-0.0766 - -
0.0657)
(70.12-
78.55)
FY2013
Measurement
Period ERR <=
1
0.0399*** 91.84 0.0633*** 87.45 0.0569***
83.62

(0.0356 -
0.0442)
(85.80-
97.88)
(0.0567 -
0.0699)
(80.51-
94.39)
(0.0521 -
0.0616)
(78.22-
89.03)
Number of
Hospitals
2965 2064 3013
Note: The % due to RTM is calculated by dividing the RTM effect by the actual change in ERR multiplied by 100. RTM effects
were calculated using rtmci command in Stata with cutoff of 1 (Linden (2013)). Confidence interval in parentheses *** p<0.001,
** p<0.01, * p<0.05.

Discussion
This analysis found that hospitals with below-mean performance in the measurement
window for first year of HRRP penalties experienced a decline of 4.8 to 7.1 percentage points in
excess readmissions over the subsequent 3 years. However, we found strong evidence suggesting
that most of this improvement was due to RTM rather than HRRP policy effects. The evidence
supporting this conclusion includes the fact that we observed similar changes in excess
readmissions at below-mean and above-mean performing hospitals when we defined
performance during an alternative measurement period predating the HRRP and when we
examined changes in performance going backward rather than forward in time. These
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observations held for all 3 target conditions, including HF, AMI, and pneumonia. Furthermore,
readmissions for patients with COPD and for hospitals in the right tail of the ERR distribution,
where there was no incentive to improve performance, show a similar trend across time. Finally,
quantitative analyses indicated that at least three-fourths of the improvement observed at
hospitals with below-mean performance during the FY2013 measurement window was explained
by RTM.
Regression to the mean was first conceived by Sir Francis Dalton in 1886 to explain why
tall parents have children shorter than themselves and short parents have children taller than
themselves. Despite its long history, RTM remains an overlooked statistical phenomenon.
Observers often erroneously ascribe improvements among low performers to an intervention of
interest when the true cause is RTM. Consistent with our findings of RTM, Press et al. (Press et
al., 2013) detected decreases in readmissions from 2009 (the year before the HRRP was
announced) to 2011 (the year before it was implemented) at hospitals with initially high rates and
increases at hospitals with initially low rates. Our results expand on these prior findings by
examining a longer time frame including after the HRRP was implemented, using multiple
strategies to document the effects of RTM, and quantifying the size of that effect.
The fact that RTM had such a large effect on trends in hospital performance has 3
important implications. First, it suggests that the HRRP explains at most a small portion of the
more favorable trends in readmissions that occurred at penalized as compared with non-
penalized hospitals. Hospitals that were penalized in FY2013 experienced a financial shock due
to excess readmissions, but our results imply that this did not result in greater declines in excess
readmissions. However, this does not mean that HRRP did not lead to a decline in readmissions.
Other researchers (Gupta, 2018; Zuckerman, Sheingold, Orav, Ruhter, & Epstein, 2016) have
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evaluated the HRRP using analytical strategies that are not biased by RTM and have found that
the policy was associated with a decline in readmissions. Others investigators (Ibrahim et al.,
2018; Ody, Msall, Dafny, Grabowski, & Cutler, 2019) have suggested that the decline in risk-
adjusted readmissions across all hospitals might have been inflated due to nationwide changes in
coding practices.
The second implication of our findings is that hospital performance and the assignment of
penalties under the HRRP is more strongly influenced by chance. The results suggest that
hospitals that were penalized based on their ERRs in the baseline period converged to the mean
in the post-measurement period. This possibility suggest that bad luck rather than poor-quality
care explains the poor performance in the baseline period. Moreover, if hospitals have limited
abilities to control their performance, they may be less likely to sustain efforts to improve
transition-related care and reduce readmissions during the long term.
The third implication of our findings pertains to the ability to detect associations between
trends in readmissions and mortality. Dharmarajan et al. (Dharmarajan et al., 2017) found
hospital-level improvements in readmissions were only weakly associated with declines in
mortality. Our findings suggest that chance may have played such a large role in changes in
readmissions that the ability to detect a true association with mortality was limited—this is an
example of regression dilution bias (Barnett et al., 2005).
Limitations
The results of our analysis should be viewed in light of its limitations. This study
analyzes observational data on trends in readmissions at high-and low-performing hospitals after
the implementation of HRRP. Ideally, we would have preferred having data from a control group
of hospitals that were unaffected by HRRP; however, that was not possible given that the policy
was implemented nationally. The study would also have been stronger if we had richer data on
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care processes at hospitals. With such data we could directly analyze changes in care processes at
high- and low-performing hospitals and more definitively assess the extent to which RTM or
changes in care processes explain trends in readmissions at these hospitals. In addition, the
analysis focuses on low-and high-performing hospitals as a group. We cannot conclude whether
declines in readmissions at individual hospitals were due to RTM, favorable changes in
transition-related care, or other factors.
Conclusion
Hospitals with poor baseline performance during the first year of HRRP penalties
appeared to exhibit substantial improvement relative to other hospitals nationally during the
subsequent years. This analysis found that three-fourths of the relative improvement was due to
RTM rather than the policy. Modifications to the HRRP that better account for the role of
chance, such as excluding small hospitals with greater variability in readmissions from HRRP or
mean readmissions across multiple conditions when estimating excess readmissions, might
enhance its fairness and possibly also its effectiveness.
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Chapter 4: Staffing Shortages, Staffing Hours, and Resident Deaths in U.S. Nursing Homes
During the COVID-19 Pandemic
3

Abstract
Importance: Staffing shortages at nursing homes during the COVID-19 pandemic may have
impacted care providers’ staffing hours and affected residents’ care and outcomes.
Objective: To study the association of staffing shortages with staffing hours and resident deaths
in nursing homes during the COVID-19 pandemic.
Design, Setting, and Participants: This study used daily staffing payroll data to create a weekly
measure of staffing hours per resident for registered nurses, licensed practical nurses, and
certified nursing assistants between May 31, 2020, and March 27, 2022. The study also used
total weekly resident deaths and self-reported staffing shortages by nursing homes to the Centers
for Disease Control and Prevention’s National Healthcare Safety Network (NHSN) between May
31, 2020, and May 15, 2022. Multivariate linear regressions with facility and county-week fixed
effects were used to investigate the association of staffing shortages with staffing hours and
resident deaths due to COVID-19 and other causes.
Exposure: Weekly measured self-reported staffing shortages at nursing homes.
Main Outcomes and Measures: The primary outcomes included staffing hours per resident of
registered nurses, licensed practical nurses, and certified nursing assistants (further divided into
employee and contract hours) and deaths per 100 residents (due to COVID-19 and non-COVID-
19 deaths) at the weekly level for each nursing home.
Results: In the weeks ending between May 31, 2020 and May 15, 2022, 18.4 to 33.3 percent of
nursing homes reported staffing shortages during any week. Self-reported staffing shortages were

3
I would like to acknowledge the comments and suggestions of my committee members Alice Chen, Teryl Nuckols, and Neeraj
Sood.
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associated with lower staffing hours per resident with a 0.009 decrease in registered nurse hours
per resident (95% CI, 0.005 to 0.014), a 0.014 decrease in licensed practical nurse hours per
resident (95% CI, 0.010 to 0.018), and a 0.050 decrease in certified nursing assistant hours per
resident (95% CI, 0.043 to 0.057). These are equivalent to a 1.8%, 1.7%, and 2.4% decline
respectively. The decrease was driven primarily by the reduction in employee hours. Some of
this decrease in employee hours per resident was compensated by an increase in contract hours.
There was a positive association between staffing shortages and resident deaths with a 0.049
(95% CI, 0.041 to 0.058) and 0.026 (95% CI, 0.001 to 0.036) increase in deaths per 100 residents
due to COVID-19 and non-COVID-19, respectively.
Conclusion and Relevance: Our results showed that self-reported staffing shortages were
associated with a statistically significant decrease in staffing hours per resident for registered
nurses, licensed practical nurses, and certified nursing assistants. Staffing shortages were also
associated with a statistically significant increase in resident deaths per 100 residents due to
COVID-19 and non-COVID-19 causes. These results suggest that staffing played a vital role in
resident health outcomes during the pandemic, and policies should target minimizing staffing
issues in nursing homes.

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Introduction
The COVID-19 pandemic has had an unprecedented and disproportionate impact on
nursing homes in the U.S. As of May 2022, there were more than a million confirmed COVID-
19 cases and more than 150,000 COVID-19 deaths of nursing home residents (Centers for
Medicare & Medicaid Services (CMS), 2022a). The COVID-19 pandemic also put significant
stress on nursing home staff, with more than a million recorded COVID-19 cases and around
2,500 recorded deaths among the staff (Centers for Medicare & Medicaid Services (CMS),
2022a). More than 25 percent of nursing homes reported shortages of some staff, including
critical staff like registered nurses, licensed practical nurses, and certified nursing assistants in
any given week between May 2020 and May 2022 (Centers for Medicare & Medicaid Services
(CMS), 2022a; Ochieng, Chidambaram, & Musumeci, 2022).
Adequate staffing is critical to providing care to nursing home residents. Prior research
has shown that nursing homes with higher staffing levels provide better quality of care (Boscart
et al., 2018; Bostick, Rantz, Flesner, & Riggs, 2006; Harrington, Dellefield, Halifax, Fleming, &
Bakerjian, 2020; Min & Hong, 2019). Even before the pandemic, staffing has been a long-term
concern in nursing homes. Nursing homes were plagued with high staff turnover, low retention,
staffing below CMS suggested levels, and low wages (Gandhi, Yu, & Grabowski, 2021; Geng,
Stevenson, & Grabowski, 2019; The White House, 2022; Wagner, Bates, & Spetz, 2021). The
pandemic put additional strain on nursing homes, and staffing problems have only become worse
(Gibson & Greene, 2020; Harrington, Ross, et al., 2020; Kirkham & Lesser, 2020; McGarry,
Grabowski, & Barnett, 2020; Moe, 2022; Ochieng et al., 2022; Ouslander & Grabowski, 2020;
Quinton, 2020; White, Wetle, Reddy, & Baier, 2021; Xu, Intrator, & Bowblis, 2020). In addition,
employment in nursing homes declined during the pandemic and continues to remain low even
when employment in other health sectors like physicians’ offices and hospitals has already
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reached the pre-pandemic level (Buerhaus, Staiger, Auerbach, Yates, & Donelan, 2022; Wager,
Telesford, Hughes-Cromwick, Amin, & Cox, 2022).
Previous studies have shown the association between COVID-19 cases and COVID-19-
related deaths in nursing homes, controlling for facility characteristics, including past quality
measures like star ratings (Ochieng, Chidambaram, Garfield, & Newman, 2021). A study noted
that deaths due to COVID-19 and non-COVID-19 were associated with past quality
measurements but did not include contemporaneous staffing issues (Cronin & Evans, 2022).
Studies have investigated the change in staffing hours among nursing home staff because of the
COVID-19 pandemic. A prior study found that staff hours per patient day did not decrease in the
first nine months of 2020 compared to a similar period in 2019 (Werner and Coe 2021).
Researchers using a sample of nursing homes also found that severe COVID-19 outbreaks were
associated with lower staffing hours due to absences and departures (Shen et al. 2022). There are
no studies on staffing shortages and deaths in nursing homes.
This study aimed to fill these knowledge gaps by examining the association of self-
reported staffing shortages with staffing hours and resident deaths due to COVID-19 and non-
COVID-19 causes in nursing homes during the COVID-19 pandemic. The main research
questions were: (1) whether self-reported staffing shortages were associated with changes in the
staffing hours of registered nurses (RNs), licensed practical nurses (LPNs), and certified nursing
assistants (CNAs); (2) whether the staffing shortages on hours per resident had any impact on
contract and employee hours; and (3) whether staffing shortages during any week were
associated with an increase in deaths due to COVID-19 and other causes during that specific
week.

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Methods
Data sources
This study uses multiple publicly available datasets. We used data reported by nursing
homes to the Centers for Disease Control and Prevention’s (CDC’s) National Healthcare Safety
Network (NHSN) Long Term Care Facility (LTCF) COVID-19 Module: Surveillance Reporting
Pathways and COVID-19 Vaccinations (Centers for Medicare & Medicaid Services (CMS),
2022a). We obtained data reported any week between May 31, 2020, and May 15, 2022. We
used information on residents’ weekly deaths due to COVID-19 and total deaths, weekly
residents confirmed COVID-19 cases, and self-reported shortages of nursing staff, aides, and
other staff.
We used the Payroll Based Journal (PBJ) Public Use Files that have daily data on nursing
home staffing levels based on data submitted by nursing homes to CMS through the PBJ system
(Centers for Medicare & Medicaid Services (CMS), 2022b). The data includes the staffing
information each day for each facility submitted by nursing homes quarterly. Our analysis
focused on nursing staff (RNs, LPNs, and CNAs) because they provide most of the direct care to
residents in nursing homes. The daily data was aggregated weekly and merged with the NHSN
data. We used data for the week ending between May 31, 2020, and March 27, 2022.
We obtained nursing home characteristics by downloading the data from the Nursing
Home Compare website (Centers for Medicare & Medicaid Services, 2020). We used
information on ownership (Profit, Non-Profit, and Government), in-hospital location, and the
number of certified beds. The Nursing Home Compare data included Social Security
Administration (SSA) state and county codes. We used the cross-walk file downloaded from the
National Bureau of Economic Research to get Federal Information Processing System (FIPS)
state and county codes (National Bureau of Economic Research, 2018). Finally, we used the
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2010 Rural-Urban Commuting Areas Codes (RUCAs) data to match FIPS zip codes to location
(Metro, Micro, and Rural) (Economic Research Service U.S. Department of Agriculture, 2020).
Our study included nursing homes that reported data to NHSN between May 31, 2020,
and May 15, 2022. We dropped nursing homes for the reporting week if they failed to pass the
data quality assurance check performed by CDC and CMS. We also excluded observations if
nursing homes reported higher deaths due to COVID-19 than total deaths in any week.
Variables
Staff Shortages
Shortages of any staff, a dummy variable, was defined based on whether nursing homes
reported a shortage of nursing staff, nursing aides, or other staff. Nursing staff included
registered nurses and licensed practical nurses or vocational nurses. Aides included certified
nursing assistants, nurse aides, medication aides, and medication technicians. Other staff
included other facility personnel not included in the categories above, regardless of clinical
responsibility or resident contact (for example, environmental services). We also created lagged
values of shortage of any staff going back up to three weeks to capture the impact of persistent
shortages on resident outcomes. In NHSN data, registered nurses and licensed practical nurses
are categorized under nursing staff, and certified nursing assistants are categorized under aides.
Outcome Variables
Staff hours. We used the staff hours of registered nurses, licensed practical nurses, and
certified nursing assistants (total hours and divided by employee hours and contract hours). We
calculated the total hours per resident per day for each staffing category and took an average for
that week.
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Resident deaths. All resident deaths for the week were categorized as deaths due to
COVID-19 and non-COVID-19 causes. Deaths due to non-COVID-19 causes were derived by
subtracting the deaths due to COVID-19 from the total deaths reported for the week. We
estimated deaths due to COVID-19 and non-COVID-19 causes per 100 residents.
Additional variables
The weekly number of residents with new laboratory-confirmed COVID-19 cases and its
one-week lagged values were included in the analyses as additional explanatory variables in
multivariate linear regression models. Past COVID-19 cases may impact future deaths in
addition to the staffing shortages. We used nursing home information on ownership, geographic
location, the total number of certified beds, in-hospital location, and occupancy rate.
Analysis
We first conducted descriptive analysis that graphed the fraction of nursing homes that
reported staffing shortages, total deaths due to COVID-19, and total deaths due to non-COVID-
19 causes for each week during the study period. In addition, we summarized the nursing home
characteristics that were included in the analysis.
We conducted multivariable linear regressions with nursing home and county-week fixed
effects to examine the association of staffing shortages with staffing hours and resident deaths
with standard errors clustered at the facility level. The nursing home fixed effects control for any
time-invariant facility-specific variables that may be correlated to staffing shortages, staffing
hours, and resident deaths (e.g., this could be the process of care that is facility specific). In
addition, to control for bias due to region-specific (e.g., local labor market conditions or
neighborhood COVID-19 cases) shocks that may affect all facilities in a particular week we
included county-week fixed effects in all multivariable regressions. In our regression models, we
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included current week and one-week lagged resident confirmed COVID-19 cases among
residents as additional covariates. If past COVID-19 cases impact current deaths, not controlling
for them would bias the estimate of staffing shortages.
First, we estimated the association between staffing shortages and staffing hours. We
used staffing hours of registered nurses, licensed practical nurses, and certified nursing assistants
per resident as dependent variables and the self-reported shortages of nursing staff and aides as
the main independent variables. We further divided the staffing hours into employee and contract
hours, estimating the models for them individually.
Second, we estimated the association between staffing shortages and resident deaths. Our
models included weekly deaths due to COVID-19 and non-COVID-19 causes per 100 residents
as outcomes and shortages of any staff as the primary explanatory variable.
Third, we estimated the association between staffing shortages and resident deaths using
lagged variables for shortages of any staff. Using lagged values for shortages would capture not
only contemporaneous staffing shortages and their impact on resident deaths but also the impact
of past shortages on current resident deaths. Our models included weekly deaths due to COVID-
19 and non-COVID-19 causes per 100 residents as outcomes and the shortages of any staff and
their lagged values up to three weeks as explanatory variables. We ran separate regression
models by the number of lags and calculated the cumulative of the coefficient of lagged values to
get the point estimates for long-term effects of staffing shortages on COVID-19 and non-
COVID-19 deaths.
Fourth, we divided the sample into multiple periods and ran separate models for each
period. We split the data into six periods that captured different waves of the pandemic.
Published by Pew Research (Jones, 2022), the dates of each period are delineated as follows: the
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initial period: 03/15/2020 - 06/30/2020; the second wave: 07/01/2020 - 09/30/2020; the third
wave (vaccine rollout): 10/01/2020 - 03/31/2021; spring and summer of 2021: 04/01/2021 -
07/31/2021; the fourth wave (delta variant surge): 08/01/2021 - 11/30/2021;, and the fifth wave
(including omicron surge): 12/01/2021 and later. We estimated the models using weekly deaths
due to COVID-19 and non-COVID-19 causes per 100 residents as outcomes and the shortages of
any staff as the primary explanatory variable for each period separately.
Sensitivity analysis
We conducted sensitivity analyses using the same set of methods described earlier. For
the sensitivity analysis, we estimated the association of staffing shortages with staffing hours and
resident deaths for nursing homes using complete panel data. For staffing hours, we also dropped
the last quarter of 2021 since there was a cyber-attack in several nursing homes, and their data
were not reported to CMS.
Results
Trends in staffing shortages and summary statistics
Figure 7 reports weekly fractions of nursing homes that reported staffing shortages to
CMS from the weeks between May 30, 2020 through May 15, 2022. The fraction of nursing
homes reporting shortages of any staff ranged from 18% during the week ending on March 21,
2021 to 33% during the week ending on January 23, 2022. Figure 7 also reports the total weekly
deaths of nursing home residents for the same period. Total deaths due to COVID-19 ranged
from 43 during the week ending on June 20, 2021 to 5,928 during the week ending on December
20, 2020. Similarly, deaths due to non-COVID-19 causes ranged from 4,783 during the week
ending on May 8, 2022 to 7,001 during the week ending on May 31, 2020. The correlation co-
efficient between deaths due to COVID-19 and deaths due to non-COVID-19 causes was 0.84.

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Figure 7: Staffing Shortages and Resident Deaths in Nursing Homes, Week Ending on May 31,
2020 to Week Ending on May 15, 2022

Note: This figure reports the fraction of nursing homes with staff shortages and total resident deaths due to COVID-19 and other
causes by week ending, from May 31, 2020 to May 15, 2022. Shortages of any staff include shortages of aides, nursing staff, or
other staff. Nursing staff includes registered nurses, licensed practical nurses, and vocational nurses. Aides includes certified
nursing assistants, nurse aides, medication aides, and medication technicians. Other staff includes other facility personnel not
included in the categories above, regardless of clinical responsibility or resident contact (for example, environmental services).
The total deaths are divided into deaths due to COVID-19 and those due to non-COVID-19 causes. This figure uses nursing
home COVID-19 data from the Centers for Medicare and Medicaid Services.

Table 10 summarizes the variables used in the analysis. The mean of shortages of any
staff, aides, nursing staff, and other staff were 23.7%, 21%, 19%, and 11%, respectively. The
mean RN hours per resident were 0.50. Of these hours, 0.48 were employee hours, and 0.02 were
contract hours. The mean LPN hours per resident were 0.84. Of these hours, 0.79 were employee
hours and 0.05 were contract hours. The mean CNA hours per resident were 2.11. Of these
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hours, 1.99 are employee hours and 0.12 were contract hours. The mean of weekly resident
deaths per 100 residents due to COVID-19 and non-COVID-19 causes were 0.13 and 0.53,
respectively. The mean of weekly confirmed COVID-19 cases among residents was 0.67. In our
sample of 15,212 nursing homes, 70.1% of the nursing homes were for-profits, 23.6% were non-
profits, and the remaining 6.3% were government owned. Nursing homes in metro areas
accounted for 68.9% of all nursing homes, with the remaining 31.1% located in micro or rural
areas. Only 4% of nursing homes were located inside hospitals. The mean number of certified
beds was 106.7, and the occupancy rate was 72.1%.

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Table 10: Nursing Home Characteristics, Week and Facility Level
Variables Mean Standard deviation N

Nursing home week level

Shortage of Any Staff (%) 23.71 42.53 1,538,364
Shortage of Aides (%) 21.03 40.75 1,538,364
Shortage of Nursing Staff (%) 19.03 39.25 1,538,364
Shortage of Other Staff (%) 11.02 31.32 1,538,364

Total Hours for RN per resident 0.50 0.50 1,390,995
Employee Hours 0.48 0.49 1,390,995
Contract Hours 0.02 0.09 1,390,995
Total Hours for LPN per resident 0.84 0.42 1,390,995
Employee Hours 0.79 0.42 1,390,995
Contract Hours 0.05 0.13 1,390,995
Total Hours for CNA per resident 2.11 0.73 1,390,995
Employee Hours 1.99 0.75 1,390,995
Contract Hours 0.12 0.28 1,390,995

Residents Weekly Deaths due to COVID-19 per 100
residents
0.13 0.95
1,538,364
Residents Weekly Deaths due to non-COVID-19
Deaths per 100 residents
0.53 2.16
1,538,364

Residents Weekly Confirmed COVID-19 cases 0.61 2.80
1,538,364

Nursing home level

For Profit (%) 70.12 45.78 15,212
Non- Profit (%) 23.55 42.43 15,212
Government (%) 6.34 24.36 15,212

Located in Metro areas (%) 68.81 46.33 15,212
Located in Micro areas (%) 13.82 34.51 15,212
Located in Rural areas (%) 17.37 37.89 15,212
Located In-hospital (%) 3.95 19.48 15,212

Number of Certified Beds 106.69 60.76 15,212
Occupancy Rate (%) 72.11 30.81 15,212
Note: The shortages of staff are self-reported by the skilled nursing facilities. Shortages of any staff include shortages of aides,
nursing staff, or other staff. Nursing staff includes registered nurses, licensed practical nurses, and vocational nurses. Aides
include certified nursing assistants, nurse aides, medication aides, and medication technicians. Other staff includes other facility
personnel not included in the categories above, regardless of clinical responsibility or resident contact (for example,
environmental services). Staffing hours are calculated for each day per resident and then averaged over a week to match with
staffing shortages and deaths data.
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Association of staffing shortages with staff hours per resident
Table 11 shows the association between the registered nurse hours and the licensed
practical nurse hours per resident and the self-reported shortage of nursing staff. Self-reported
shortage of nursing staff was associated with a decline of 0.009 (95% CI, 0.004-0.013) in
registered nurse hours per resident (equivalent to a 1.8%decrease). When divided into employee
and contract hours per resident, self-reported shortages of nursing staff were associated with a
decrease in employee hours by 0.013 (95% CI, 0.009-0.018) and an increase in contract hours by
0.005 (95% CI,0.003-0.006) for registered nurses (equivalent to 2.9% decline and 20.0%
increase respectively). Self-reported shortage of nursing staff was associated with a decline of
0.014 (95% CI, 0.010-0.018) in the licensed practical nurse hours per resident (equivalent to
1.7% decline). When divided into employee and contract hours per resident, self-reported
shortage of nursing staff was associated with a decline in employee hours per resident by 0.025
(95% CI, 0.021-0.030) and an increase in contract hours by 0.011 (95% CI, 0.009-0.014) of
licensed practical nurses (equivalent to a 3.3% decrease and a 21.1% increase, respectively).
Table 11 also shows the negative association between certified nursing assistant hours per
resident and shortages of aides. Self-reported shortages of aides were associated with a decrease
of 0.048 (95% CI, 0.042-0.055) in certified nursing assistant hours per resident (equivalent to a
2.4% decrease). When divided into employee and contract hours per resident, self-reported
shortage of aides was associated with a decrease in employee hours by 0.067 (95% CI, 0.060-
0.075) and an increase in contract hours by 0.019 (95% CI, 0.014-0.024) of certified nursing
assistants (equivalent to 3.6% decline and 15.2% increase respectively). While these reductions
may seem small, we note that there are an average of 77 residents (106.7*72) in an SNF, with the
total reductions in RNs, LPNs, and CNAs hours summing up to 5.6 hours on average.
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Table 11: Association Between Nursing Staff Shortages and Nurse Staffing Hours per Resident
Registered Nurse

Total Hours Employee Hours Contract Hours

Shortage of Nursing Staff -0.009*** -0.013*** 0.005***
(-0.013 - -0.004) (-0.018 - -0.009) (0.003 - 0.006)

1.8% change,
mean=0.501
2.9% change,
mean=0.476
20.0% change,
mean=0.025
Licensed Practical Nurse
Total Hours Employee Hours Contract Hours

Shortage of Nursing Staff -0.014*** -0.025*** 0.011***
(-0.018 - -0.010) (-0.030 - -0.021) (0.009 - 0.014)

1.7% change,
mean=0.838
3.3% change,
mean=0.780
21.1% change,
mean=0.057

Certified Nursing Assistant
Total Hours Employee Hours Contract Hours

Shortage of Nursing Aides -0.048*** -0.067*** 0.019***
(-0.055 - -0.042) (-0.075 - -0.060) (0.014 - 0.024)

2.4% change,
mean=2.098
3.6% change,
mean=1.967
15.2% change,
mean=0.132
Note: The shortages of staff are self-reported by the skilled nursing facilities. Nursing staff includes registered nurses, licensed
practical nurses, and vocational nurses. Aides includes certified nursing assistants, nurse aides, medication aides, and medication
technicians. All analyses control for facility and county-week fixed effects. Confidence interval in parentheses. Standard errors
are clustered at the facility level. *** p<0.01, ** p<0.05, * p<0.1. N= 1,306,918.

Association of staffing shortages with resident deaths
Table 12 shows the association between resident weekly deaths and shortages of any
staff. The results show that staffing shortages are positively associated with resident deaths due
to COVID-19 and non-COVID-19 causes. Shortages of any staff were associated with a 0.049
(95% CI, 0.041-0.058) increase in resident deaths per 100 residents due to COVID-19 and 0.019
(95% CI, 0.001-0.036) increase in resident deaths due to non-COVID-19 causes per 100
residents (equivalent to 39.8% and 3.6%, respectively).
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Table 12: Association Between Staffing Shortage and Deaths Due to COVID-19 and Other
Causes
(1) (2)

Weekly Deaths due to Covid-19 per
100 Residents
Weekly Deaths due to non-Covid-19 per
100 Residents
Any shortages of
staff 0.049*** 0.019**
(0.041 - 0.058) (0.001 - 0.036)

39.8% change,
mean=0.123
3.6% change,
mean=0.527
Note: The shortages of staff are self-reported by the skilled nursing facilities. Shortages of any staff include shortages of aides or
nursing staff or other staff. Nursing staff includes registered nurses, licensed practical nurses, and vocational nurses. Aides
include certified nursing assistants, nurse aides, medication aides, and medication technicians. Other staff includes other facility
personnel not included in the categories above, regardless of clinical responsibility or resident contact (for example,
environmental services). All analyses control for facility and county-week fixed effects. Confidence interval in parentheses.
Standard errors are clustered at the facility level. *** p<0.01, ** p<0.05, * p<0.1. N= 1,423,698.

Association of staffing shortages with resident deaths (lagged shortages)
Table 13 top panel shows the association of resident weekly deaths due to COVID-19 and
shortages of any staff and its lagged values. The cumulative estimate when including shortages
of any staff lagged one week was associated with a 0.075 (95% CI, 0.065 - 0.085) increase in
resident deaths per 100 residents due to COVID-19. Similarly, when shortages of any staff were
lagged by two and three weeks it was associated with 0.087 (95% CI, 0.076- 0.097) and 0.086
(95% CI, 0.076 - 0.096) increases in resident deaths per 100 residents due to COVID-19,
respectively. The bottom panel in Table 13 shows the association of resident weekly deaths due
to non-COVID-19 and shortages of any staff and their lagged values. The cumulative estimate
when including shortages of any staff lagged one week was associated with a 0.022 (95% CI,
0.002 - 0.043) increase in resident deaths per 100 residents due to non-COVID-19 causes.
Similarly, when shortage of any staff was lagged by two and three weeks, it was associated with
a 0.026 (95% CI, 0.004 - 0.048) and 0.024 (95% CI, 0.001 - 0.048) increase in resident deaths
per 100 residents due to non-COVID-19 causes, respectively.
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Table 13: Association Between Long-Term Staffing Shortages and Resident Deaths in Nursing
Homes
Cumulative estimate N
Deaths due to COVID-19 per 100 residents
Shortages of any staff lagged one week 0.075*** 1,423,698
(0.065 - 0.085)
Shortages of any staff lagged one and two
weeks 0.087***

1,403,096
(0.076 - 0.097)
Shortages of any staff lagged one, two, and
three weeks 0.086***

1,382,903
(0.076 - 0.096)
Deaths due to non-COVID-19 per 100
residents

Shortages of any staff lagged one week 0.022** 1,423,698
(0.002 - 0.043)
Shortages of any staff lagged one and two
weeks 0.026**

1,403,096
(0.004 - 0.048)
Shortages of any staff lagged one, two, and
three weeks 0.024**

1,382,903
(0.001 - 0.048)
Note: The shortages of staff are self-reported by the skilled nursing facilities. Shortages of any staff include shortages of aides,
nursing staff, or other staff. Nursing staff includes registered nurses, licensed practical nurses, and vocational nurses. Aides
include certified nursing assistants, nurse aides, medication aides, and medication technicians. Other staff includes other facility
personnel not included in the categories above, regardless of clinical responsibility or resident contact (for example,
environmental services). All analyses control for facility and county-week fixed effects along shortages of any staff, number of
residents new confirmed COVID-19 cases among residents and their lagged values. Confidence interval in parentheses. Standard
errors are clustered at the facility level. *** p<0.01, ** p<0.05, * p<0.1.

Association of staffing shortages with resident deaths during different periods in the
pandemic
Table 14 shows the association between resident weekly deaths per 100 residents due to
COVID-19 and non-COVID-19 causes and the shortages of any staff during different periods.
The results show that staffing shortages matter in some periods and not in other periods for
deaths per 100 residents due to both COVID-19 and non-COVID-19 causes. Shortages of any
staff were positively associated with deaths due to COVID-19 during the second wave, third
wave, and fourth wave (delta variant surge). Shortages of any staff were associated with 0.069
(95% CI, 0.043 - 0.096), 0.139 (95% CI, 0.107-0.171), and 0.021 (95% CI, 0.010-0.032)
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increases in resident deaths per 100 residents due to COVID-19 during the second wave, third
wave, and fourth wave (delta variant surge), respectively (equivalent to 45.7%, 46.6%, and
45.7% respectively). Shortages of any staff were positively associated with deaths due to non-
COVID-19 during the third wave, the spring and summer of 2021, and the fifth wave (including
the omicron surge). Shortages of any staff were associated with 0.029 (95% CI, -0.004 - 0.063),
0.038 (95% CI, 0.006 - 0.071), and 0.039 (95% CI, 0.017 - 0.060) increases in resident deaths
per 100 residents due to non-COVID-19 during the third wave, the spring and summer of 2021,
and the fifth wave (including the omicron surge), respectively (equivalent to 5.0%, 8.1%, and
7.8% respectively).
Table 14: Association of Resident Deaths with Staffing Shortages During Different Periods of
the COVID-19 Pandemic

Deaths due to
COVID-19 per
100 residents

% of
the
Mean

Mean Deaths due to
non-COVID-19
per 100 residents

% of the
mean

Mean
N

Initial period -0.002 -1.2% 0.168 0.167 27.7% 0.602 55,792
(-0.059 - 0.055) (-0.093 - 0.428)
Second wave 0.069*** 45.7% 0.151 -0.008 -1.4% 0.559 184,263
(0.043 - 0.096) (-0.056 - 0.040)
Third wave
(vaccine rollout) 0.139***

46.6%

0.298 0.029*

5.0%

0.585

365,651
(0.107 - 0.171) (-0.004 - 0.063)
Spring/Summer 2021 -0.009 -75.0% 0.012 0.038** 8.1% 0.469 235,661
(-0.026 - 0.009) (0.006 - 0.071)
Fourth wave (delta
variant surge) 0.021***

45.7%

0.046 -0.026*

-5.3%

0.494

249,589
(0.010 - 0.032) (-0.053 - 0.000)
Fifth wave (including
omicron surge) 0.006

13.3%

0.045 0.039***

7.8%

0.498

332,654
(-0.002 - 0.013) (0.017 - 0.060)
Note: Initial period: 03/15/2020 - 06/30/2020; second wave: 07/01/2020 - 09/30/2020; third wave (vaccine rollout); 10/01/2020 -
03/31/2021; spring and summer of 2021: 04/01/2021 - 07/31/2021; fourth wave (delta variant surge): 08/01/2021 - 11/30/2021;
fifth wave (including omicron surge): 12/01/2021 and later. The shortages of staff are self-reported by the skilled nursing
facilities. Shortages of any staff include shortages of aides, nursing staff, or other staff. Nursing staff includes registered nurses,
licensed practical nurses, and vocational nurses. Aides include certified nursing assistants, nurse aides, medication aides, and
medication technicians. Other staff includes other facility personnel not included in the categories above, regardless of clinical
responsibility or resident contact (for example, environmental services). All analyses control for facility and county-week fixed
effects along with the number of new confirmed COVID-19 cases among residents and their lagged values. Confidence interval
in parentheses. Standard errors are clustered at the facility level. *** p<0.01, ** p<0.05, * p<0.1.
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Sensitivity analysis
Using the same estimation methods, we estimated the association between staffing
shortages and staffing hours using only the complete panel data of nursing homes. Like before,
we find that the total hours per resident decreased for RNs, LPNs, and CNAs (Tables 15 and 16).
This decrease was concentrated among employee hours (Tables 15 and 16). There was
statistically significant positive association between staffing shortages and resident deaths per
100 residents when including only nursing homes with complete panel data (Table 17).
However, the positive association of staffing shortages with deaths due to non-COVID-19 causes
per 100 residents was not statistically significant (Table 17).
Table 15: Association Between Nursing Staff Shortages and Nurse Staffing Hours per Resident
(Complete Panel Only)
Registered Nurse Licensed Practical Nurse

Total
Hours
Employee
Hours
Contract
Hours
Total
Hours
Employee
Hours
Contract
Hours
Shortage of
Nursing Staff
-
0.007**
* -0.011*** 0.004*** -0.013*** -0.025*** 0.012***

(-0.011 -
-0.003)
(-0.016 - -
0.007) (0.003 - 0.006)
(-0.018 - -
0.008)
(-0.030 - -
0.020) (0.009 - 0.015)

1.4%
change,
mean=0.
502
2.3% change,
mean=0.479
17.4% change,
mean=0.023
1.5% change,
mean=0.842
3.2% change,
mean=0.789
23.1% change,
mean=0.052
Note: The shortages of staff are self-reported by the skilled nursing facilities. Nursing staff includes registered nurses, licensed
practical nurses, and vocational nurses. All analyses control for facility and county-week fixed effects. Confidence interval in
parentheses. Standard errors are clustered at the facility level. *** p<0.01, ** p<0.05, * p<0.1. N=752,644.

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Table 16: Association Between Nursing Staff Shortages and Nurse Staffing Hours per Resident
(Complete Panel Only)
Certified Nursing Assistant

Total Hours Employee Hours Contract Hours
Shortage of Nursing Aides -0.045*** -0.066*** 0.021***
(-0.054 - -0.037) (-0.076 - -0.057) (0.015 - 0.027)

2.1% change,
mean= 2.112
3.3% change,
mean=1.992
17.5% change,
mean=0.120
Note: The shortages of staff are self-reported by the skilled nursing facilities. Aides include certified nursing assistants, nurse
aides, medication aides, and medication technicians. All analyses control for facility and county-week fixed effects. Confidence
interval in parentheses. Standard errors are clustered at the facility level. *** p<0.01, ** p<0.05, * p<0.1. N=752,644.

Table 17: Association Between Nursing Staff Shortages and Resident Deaths in Nursing Homes
(Complete Panel Only)
(1) (2)

Deaths due to COVID-19
per 100 residents
Deaths due to non-COVID-19
per 100 residents

Any shortages of staff 0.047*** 0.012
(0.037 - 0.057) (-0.008 - 0.031)

38.8% change,
mean = 0.121
2.23% change,
mean = 0.538
Note: Note: The shortages of staff are self-reported by the skilled nursing facilities. Shortages of any staff include shortages of
aides, nursing staff, or other staff. Nursing staff includes registered nurses, licensed practical nurses, and vocational nurses. Aides
include certified nursing assistants, nurse aides, medication aides, and medication technicians. Other staff includes other facility
personnel not included in the categories above, regardless of clinical responsibility or resident contact (for example,
environmental services). All analyses control for facility and county-week fixed effects. Confidence interval in parentheses.
Standard errors are clustered at the facility level. *** p<0.01, ** p<0.05, * p<0.1. N=977,716.

Discussion
Within the context of the COVID-19 pandemic, this study examined the association
between staffing shortages and resident deaths in nursing homes and the association between
staffing shortages and staff hours in nursing homes. We found that self-reported staffing
shortages were associated with declining staffing hours for RNs, LPNs, and CNAs. The decrease
was concentrated on the employee hours rather than the contract hours. Our results also showed a
slight increase in contract hours associated with staffing shortages. Recent work has found that
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overall per-resident staffing levels were not lower than pre-pandemic levels (Shen, McGarry,
Grabowski, Gruber, & Gandhi, 2022; Werner & Coe, 2021). However, overall trends may hide
variations across nursing homes. We found that staffing hours decreased for nursing homes with
reported shortages. This finding also raises the question of the suitability of per-resident staffing
hours for capturing staffing problems during the pandemic, as they may not accurately capture
the stress and pressure placed on staffing.
Our study also found that the self-reported staffing shortages were associated with an
increase in deaths due to COVID-19 and non-COVID-19 causes in nursing homes. Using lagged
values of staffing shortages, we found that past staffing shortages were associated with resident
deaths, suggesting that long-term staffing shortages lead to poor outcomes for residents. Dividing
into different periods, we found that staff shortages were associated with an increased number of
deaths due to COVID-19 during the second wave, third wave, and fourth wave (delta variant
surge) and an increased number of deaths due to non-COVID-19 causes during the third wave,
the spring and summer of 2021, and the fifth wave (including the omicron surge). This suggests
that the stress of staffing and its association with resident deaths fluctuated during the pandemic.
While using only nursing homes that had data for every week in the study period, we found that
the association of staffing shortages with deaths due to COVID-19 per 100 residents was positive
and statistically significant. However, deaths due to non-COVID-19 causes per 100 residents
were not statistically significant. Nursing homes that reported data for every week of the study
period had different characteristics than nursing home that did not. This may explain the
difference in results when we only used nursing homes that reported weekly data for all the
weeks in the study period. Overall, results suggest that staffing shortages were associated with
increased deaths among residents.
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A positive association between staffing shortages and deaths due to non-COVID-19
causes suggests that the quantity and quality of care in nursing homes may have decreased
during the pandemic. Previous work has shown that CNAs tend to provide most of the direct care
in nursing homes (Harrington, Dellefield, et al., 2020). We found that staffing hours per resident
were the largest for CNAs compared to RNs and LPNs, and the decrease was also the largest for
CNAs. This finding implies that the shortage of CNAs may have impacted not only the care for
residents who tested positive for COVID-19 but for all residents in nursing homes. So, the
association between staffing shortages and resident deaths due to non-COVID-19 causes could
be consistent with the overall worsened resident health owing to inadequate staffing.
To fully understand the impact of self-reported shortages in nursing homes, future work
needs to determine how the staffing shortages impacted the day-to-day care of residents. This
work will also need to account for how informal care changed during the pandemic, as nursing
homes severely limited resident interaction with family members living in the community who
may have provided some help before the pandemic.
Limitations
This study has limitations. First, our measure of staffing shortages is self-reported.
Nursing homes might report shortages if their residents had poor outcomes to deflect poor
quality of care to staffing shortages. However, since we found that self-reported staffing
shortages were consistent with separately-reported daily staffing hours, this may not be a
concern. Second, our outcomes of deaths due to COVID-19 and non-COVID-19 causes may be
misclassified. Since we found an increase in both types of deaths, this misclassification should
not be an issue per se. Third, we did not have complete weekly data for all nursing homes since
some of the nursing homes did not provide reports or the reported data did not pass the CDC and
CMS quality check. However, our results were similar when we used only nursing homes that
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had complete weekly data. Finally, this research does not study the number of staff changes but
only the hours worked per resident by staffing category. It is therefore not possible for us to
disentangle whether the hours worked decreased due to absences or due to departures.
Conclusion
In this study of nursing homes during the COVID-19 pandemic, self-reported staffing
shortages were associated with declining staffing hours for registered nurses, licensed practical
nurses, and certified nursing assistants and with increased deaths due to COVID-19 and non-
COVID-19 causes. Policies aimed at improving access and quality of care in nursing homes,
especially in times of major health crises such as the COVID-19 pandemic, must consider ways
to increase staffing, either through interventions aimed at retaining the existing staff or by
attracting additional staff.

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Appendix
Appendix A: Steps in Calculation of Incentive Payment Multiplier and MERRIPM
Part 1 provides details on calculation incentive payment multiplier. Part 2 provides details on
the calculations of marginal effect of readmissions reduction on incentive payment multiplier
(MERRIPM).
Part 1: Incentive Payment Multiplier
Performance measure is given as 1 minus risk-adjusted 30-day all cause readmissions. The
performance is measured in two periods: performance period (pp) and baseline period (bp)).
Given the distribution of baseline performance we can estimate the benchmark and the
achievement threshold. The benchmark (bm) is the mean of the tenth decile (national) of the
baseline performance. These are the best performing SNFs (national) during baseline period. The
achievement threshold (at) is the 25
th
percentile of the performance distribution (national) of the
baseline performance distribution. This demarcates the lowest 25
th
percent performing SNFs
(national) during baseline period.
Given the baseline period performance, performance period performance, benchmark,
and the achievement threshold we can calculate the achievement score and improvement score.
For achievement score (𝑎𝑠 ), performance period performance is compared to the national
performance measures (i.e. benchmark and achievement threshold) in the baseline period.
• Achievement Score ranges from 0 to 100
• 100 if 𝑝𝑝 ≥ 𝑏𝑚
• ([9 ∗ (
𝑝𝑝 −𝑎𝑡
𝑏𝑚 −𝑎𝑡
)] + 0.5) ∗ 10 if 𝑏𝑚 > 𝑝𝑝 ≥ 𝑎𝑡
• 0 if 𝑝𝑝 < 𝑎𝑡
For improvement score (is) performance period measure is compared to its own baseline
performance.
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• Improvement score ranges from 0 to 90
• 90 if 𝑝𝑝 ≥ 𝑏𝑚 & 𝑝𝑝 > 𝑏𝑝
• ([10 ∗ (
𝑝𝑝 −𝑏𝑝
𝑏𝑚 −𝑏𝑝
)] − 0.5) ∗ 10 if 𝑏𝑝 < 𝑝𝑝 < 𝑏𝑚
• 0 if 𝑝𝑝 ≤ 𝑏𝑝
Given the achievement and improvement score performance score (ps) are calculated by
taking the higher of achievement score and improvement score i.e. 𝑝𝑠 = max {𝑎𝑠 , 𝑖𝑠 }
This performance score is translated using the equation:
𝑙 (𝑝𝑠
𝑖 ) =
1
1 + 𝑒 −0.1(𝑝 𝑠 𝑖 −50)
𝑤 ℎ𝑒𝑟𝑒 𝑝𝑠
𝑖 𝑖𝑠 𝑡 ℎ𝑒 𝑝𝑒𝑟𝑓𝑜𝑟𝑚𝑎𝑛𝑐𝑒 𝑠𝑐𝑜𝑟𝑒
This transformed score is used to calculate the adjustment rate. To calculate the adjustment rate,
the payment data for each SNF and the total payments are needed. The exact formula is given
below.
𝐴𝑑𝑗𝑢𝑠𝑡𝑚𝑒𝑛 𝑡 𝑖 = 𝑙 𝑖 ∗
𝑤 𝑝 ∑𝑝 𝑖 ∑(𝑙 𝑖 ∗𝑝 𝑖 )
where,
• 𝑤 is the proportion of dollars withheld (0.02, i.e. hold 2%)
• 𝑝 is the proportion of dollars to create pool (0.6, i.e. return 60%)
• 𝑝 𝑖 is the overall payments to SNF 𝑖 .
𝐼𝑛𝑐𝑒𝑛𝑡𝑖𝑣𝑒 𝑃𝑎𝑦𝑚𝑒𝑛𝑡 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑒𝑟 (𝑖𝑚 ) is 0.98 plus the adjustment rate. If incentive payment
multiplier is greater than 1 it means that the SNF is rewarded. SNF would earn more than the 2%
withheld for the program. If the incentive payment multiplier is less than 1 it means that the SNF
is penalized. SNF would receive less than the 2 % withheld for the program. If incentive
payment multiplier is 1 then the SNF receives the 2% withheld amount.
Let us go over an example to see how each of these terms are calculated. Assume a SNF
with baseline RSRR = .21 and performance period RSRR = .18 and has the required minimum
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number of eligible stays. If there are less than 25 eligible stays in the performance period, the
SNF automatically receives a net-neutral incentive payment multiplier of 1. This means that the
SNF reduced its readmissions and improved its performance. Given this the baseline and
performance period RSRR the baseline (bp) and performance period (pp) performance are:
𝑏𝑝 = 1 − .21 = .79
𝑝𝑝 = 1 − .18 = .82
Assume the benchmark and achievement threshold are: 𝑎 𝑡 = .79, 𝑏𝑚 = .83. This would be
calculated from the baseline performance of all SNFs.
Since 𝑝𝑝 < 𝑏𝑚 and 𝑝𝑝 ≥ 𝑎𝑡 ,
𝑎𝑐 ℎ𝑖𝑣𝑒𝑚𝑒𝑛𝑡 𝑠𝑐𝑜𝑟𝑒 (𝑎𝑠 ) = ([9 ∗ (
𝑝𝑝 − 𝑎𝑡
𝑏𝑚 − 𝑎𝑡
)] + 0.5) ∗ 10
= ([9 (
0.3
0.4
)] + 0.5) ∗ 10
= 72.5
If 𝑝𝑝 ≥ .83 the 𝑎𝑠 would have been 100 and if 𝑝𝑝 < .79 the 𝑎𝑠 would have been 0.
Since 𝑏𝑝 < 𝑝𝑝 < 𝑏𝑚 ,
𝑖𝑚𝑝𝑟𝑜𝑣𝑒𝑚𝑒𝑛𝑡 𝑠𝑐𝑜𝑟𝑒 (𝑖𝑠 ) = ([10 ∗ (
𝑝𝑝 − 𝑏𝑝
𝑏𝑚 − 𝑏𝑝
)] − 0.5) ∗ 10
= ([10 (
0.3
0.4
)] − 0.5) ∗ 10
= 70
If 𝑝𝑝 ≥ .83 & 𝑝𝑝 > .79 then is would have been 90 and if 𝑝𝑝 ≤ . 79 then is would have been
0.
The higher value of the achievement and improvement score is the performance score.
Since the achievement score is 72.5 and improvement score is 70, the performance score (𝑝𝑠 ) is
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72.5. The logit transformation of this score is .904651. Next, we calculate the adjustment rate.
For this we need the payment data. Assume that the total SNF payment is 25 billion dollars. The
incentive payment pool is 0.3 (25*.6*.02) billion dollars or 300 million dollars.
The adjustment rate has two parts, one common to all SNFs and the other that is specific
to each SNF. The common part is
𝑤 𝑝 ∑𝑝 𝑖 ∑(𝑙 𝑖 ∗𝑝 𝑖 )
and the specific part is 𝑙 𝑖 . Given the 𝑙 𝑖 and 𝑝 𝑖 for all
SNF we can calculate the common part. Let the common part be 0.0416. So, for the above SNF,
the adjustment rate is = .904651*0.0416=0.037633462. So, the incentive payment multiplier
(𝑖𝑚 ) for this SNF is =0.98+0.037633462= 1.017633462. Since im is greater than 1 this SNF
receives more than its contribution to the incentive pool.

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Part 2: The Marginal Effect of Readmissions Reduction on Incentive Payment Multiplier
(MERRIPM)
In this section we provide in detail how each term and the final value of MERRIPM is
calculated. As described in the main text, MERRIPM is calculated as the difference in incentive
multiplier in two scenarios. The first scenario is when the performance improves by a fixed
amount between baseline and performance period and in the second scenario the performance
does not change across periods. We graph improvement in performance, achievement score,
improvement score, performance score, logit transformed performance score, and the incentive
multiplier for both scenarios. This is calculated using the program data for FY2020 (baseline
FY2016 and performance FY2018). The payment data is from CY2017. Figure 8 plots the
improvement in performance on baseline. We have assumed that all SNFs improve by their
performance by the same amount. Figures 9, 10, and 11 shows that the when the baseline
performance is poor, the increase in performance is mostly driven by improvement score and
when the baseline performance is better the performance score is mostly driven by achievement
score. Figure 12 shows how the logit transformation introduces non-linearity. It also shows how
logit transformations dampens the impact by squeezing values that were between 0 and 100 to 0
to 1. Also, most of the SNFs would be in the portion of the graph where small changes would
produce large change in incentives. The difference between the two lines in Figure 13 would be
the MERRIPM. This is shown in the main text in Figure 1.

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Figure 8: Improvement in Performance on Baseline Performance

Note: We assume that that the SNFs improve by 0.19 that i.e. reduce risk-adjusted readmissions by 1.9 percentage points. The
graph shows that irrespective of where the SNF performs during baseline they are able to improve by the same amount.

Figure 9: Distribution of Achievement Score

Note: The graph plots the achievement score on baseline performance for two scenarios: when the performance (i.e. quality)
improves and when the performance does not change. This shows that the achievement score improves for some SNFs when their
performance improves but not for others (mostly in the tails).

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Figure 10: Distribution of Improvement Score

Note: The graph plots the improvement score on baseline performance for two scenarios: when the performance (i.e. quality)
improves and when the performance does not change. In contrast to achievement score, improvement score is improved for all
SNFs when their performance improves.

Figure 11: Distribution of Performance Score

Note: The graph plots the performance score on baseline performance for two scenarios: when the performance i.e. quality
improves and when the performance does not change. The figure shows that except for very high performing SNFs, they are able
to improve their performance score by improving their quality.
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Figure 12: Distribution of Logit Transformed Performance Score

Note: The graph plots the logit transformed performance on baseline performance for two scenarios: when the performance i.e.
quality improves and when the performance does not change. The figure shows that the once the transformation is done, small
change changes in performance for SNFs around the middle has large impact on their transformed score. Improvement around
the tails are dampened by this transformation.

Figure 13: Distribution of Incentive Payment Multiplier

Note: The graph plots the incentive multiplier on baseline performance for two scenarios: when the performance i.e. quality
improves and when the performance does not change. The difference in above two values is the financial incentive and given in
Figure 1 (in the text).
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Appendix B: Regression to the Mean Additional Analysis
This section provides additional analysis to show the mean reversion of the outcome
measure (i.e. RSRR) used in the SNF VBP program. Here we conduct three analyses. In the first
analysis, we divide the readmissions into quartiles and show what fraction of SNFs move across
different quartiles between the baseline and performance periods. In the second analysis, we
graph the change in readmissions on the baseline readmissions. Finally, we adjust the outcome
for mean reversion and graph the results. The regression results are given in the main text.
We used program data from FY2019 of the SNF VBP program. The performance period
and baseline period are CY2017 and CY2015 respectively. In the first analysis, we divide
baseline and performance period readmissions for each year of program data into quartiles. Then
we find out what fraction of SNFs remain in the same quartiles or improve/decline to other
quartiles. The results are given in Figures 14.
In Figure 14, the blue bar shows the percent of SNFs in different quartile in CY2017 that
were in the Lowest quartile in CY2015. We find that 39 percent of SNFs in Lowest quartile in
CY2015 are in the Lowest quartile in CY2017. Similarly, 40 percent of SNFs in the Highest
quartile in CY2015 are in the Highest quartile in CY2017. For Low and High quartiles only
around 25 percent of SNFs are in the same quartile.
In conclusion, we find that SNFs in Lowest and Highest quartiles are more likely to
remain in the same quartiles than SNFs in Low and High quartiles. At the same time, it also
shows that SNFs are less likely to be in the same quartile across different years. This suggests
that there is a strong possibility that SNF readmissions are subject to random variation.

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Figure 14: Movement Across Quartiles Between CY2015 and CY2017

Note: The figure shows the distribution of SNFs into different quartiles in CY2017 given the performance quartile in CY2015.
For example, the blue bar shows 39 percent of SNFs that were in Lowest quartile in CY2015 were in lowest quartile in CY2017.
27 percent of SNFs moved to Low, 20 percent to high and even 14 percent moved to the highest performing quartile. Data using
FY2019 program data.

The second analysis shows the change in outcome between baseline and performance
period readmissions on baseline period readmissions for FY2019 program data. The Figures 15
shows the change in readmissions across baseline and performance period on baseline
readmissions. The graphs clearly show a negative relationship between changes in readmissions
and baseline readmissions. This means that SNFs with low readmissions worsened their
readmissions and SNFs with high readmissions improved their readmissions. We expect this to
happen when there is mean reversion.
The third analysis shows the change in readmissions between baseline and performance
period on baseline period readmissions adjusted for mean reversion. Figure 16 plots the scatter
39
27
20
14
27
25
27
20
21
27
26
27
13
20
27
40
Lowest (CY 2017) Low (CY 2017) High (CY 2017) Highest (CY 2017)
Percentage of SNFs
Lowest (CY 2015) Low (CY 2015) High (CY 2015) Highest (CY 2015)
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plot and linear fit. We adjust for mean reversion by first calculating what is the expected change
in readmissions and adjusting for this. The method is explained in detail in the main text.
Adjusted for mean reversion, the relationship between baseline readmissions and change in
readmissions is non-existent. The main text discusses the regression results.
Figure 15: Change in RSRR and Baseline RSRR Between CY2015 and CY2017
3
Note: This is a scatter plot of change in readmissions between CY2017 and CY2015 on readmissions of CY2015. The graph also
includes linear fit. This is the program data from FY2019. RSRR is the risk-standardized readmission rate.

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Figure 16: Adjusted Change in RSRR and Baseline RSRR Between CY2015 and CY2017

Note: This is a scatter plot of adjusted change in readmissions between CY2017 and CY2015 on readmissions of CY2015. The
graph also includes linear fit. This is the program data from FY2019. The outcomes have been adjusted to account for the mean
reversion. RSRR is the risk-standardized readmission rate and RTM is regression to the mean.

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Appendix C: Calculation of Regression to the Mean
We explain here how the expected regression to the mean (RTM) effect is calculated as
given in Linden (Linden, 2013). For normally distributed data, the classic formula to estimate
RTM requires four inputs: the population mean at baseline (𝜇 ), the population variance at
baseline (𝜎 2
), the correlation coefficient between the baseline and the post period (𝜌 ), and the
cut-off for selection of group at baseline (𝜅 ). Given this information the expected RTM effect is:
=
𝛾 2
√𝛾 2
+𝛿 2
𝐶 (𝑧 ) where 𝛾 2
is the within-subject variance (i.e. 𝜎 2
− 𝛿 2
), 𝛿 2
is the between-subject
variance (i.e. 𝜌 𝜎 2
). The denominator is the square root of total variance (i.e. 𝜎 ). 𝐶 (𝑧 ) =
𝜙 (𝑧 )
1−Φ(𝑧 )
,
where 𝜙 (𝑧 ) is the probability density function and Φ(𝑧 ) is the cumulative distribution function
of the standard normal distribution. The 𝑧 -score is given by: 𝑧 =
𝜅 −𝜇 𝜎 if the selection is done
when baseline measurement are greater than 𝜅 and 𝑧 =
𝜇 −𝜅 𝜎 if the selection is done when the
baseline measurement are less than 𝜅 .
Given the above setup, the expected mean values for both baseline and post-period for
the selected group based on a cut-off is given as follows:
Expected pre−test mean = 𝜇 ± 𝐶 𝜎
Expected post−test mean = 𝜇 ± 𝐶𝜌𝜎
The difference in expected mean, i.e. 𝐶 (1 − 𝜌 )𝜎 , is the expected RTM effect and is identical to
formula given earlier. If there is high a correlation between the baseline and post-period, the
expected mean will be similar across periods. Also, if the population standard errors are small,
the mean of the baseline and post-period will not deviate further away from the population mean
and RTM effect will be muted. Linden (Linden, 2013), using simulation, shows that the “actual”
and “calculated” RTM effects are similar when data is normally distributed. “Actual” is the
effect derived directly from data and the “calculated” is the effect derived using above formula.
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We used a statistical package, rtmci in Stata, to estimate the expected RTM effect. This
package not only provides expected RTM effects but also confidence interval using bootstrap
simulation (Linden, 2013).

Abstract (if available)

Abstract This dissertation studies topics in U.S. healthcare. In Chapters 2 and 3, I study Center for Medicare & Medicaid Services (CMS) value-based programs. CMS implements value-based programs to improve the quality of care provided to patients as well as lower the cost of healthcare by rewarding healthcare providers for delivering better quality of care. Chapter 2 shows that a nationally implemented skilled nursing value-based purchasing program (SNF VBP) did not reduce hospital readmissions of nursing home residents. In chapter 3, in joint work with Teryl Nuckols, Jose Escarce, Peter Huckfeldt, Ioana Popescu, and Neeraj Sood, we study the mean reversion of hospital readmissions in one of the largest value-based programs for hospitals, hospital readmissions reduction program (HRRP). We found that not accounting for mean reversion over-states the decline in hospital readmissions due to the program. In chapter 4, I study the impact of staffing shortages on nursing homes during the COVID-19 pandemic. As staffing is crucial in providing quality care to residents in nursing homes, I find that staffing shortages were associated with declining staffing hours and increasing resident deaths.

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School School of Policy, Planning and Development

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Degree Program Public Policy and Management

Degree Conferral Date 2022-12

Publication Date 10/31/2023

Defense Date 10/18/2022

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