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Application of random effects models to a clinical retrospective hierarchical database
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Application of random effects models to a clinical retrospective hierarchical database
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Content
APPLICATION OF RANDOM EFFECTS MODELS TO A CLINICAL
RETROSPECTIVE HIERARCHICAL DATABASE
by
Choo Phei Wee
A Thesis Presented to the
FACULTY OF THE KECK SCHOOL OF MEDICINE
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
MASTER OF SCIENCE
(BIOSTATISTICS)
August 2008
Copyright 2008 Choo Phei Wee
ii
Acknowledgements
I would like to thank my co-chair, Dr. Frederick Dorey, under whose
supervision I chose this topic and began the thesis. This paper would not have been
possible without his guidance, instruction, and encouragement. This work was
supported by funds awarded to Dr. Upperman from the Robert Wood Johnson
Foundation SU401 and the National Institutes of Health K08 GM00696 grants. I am
very grateful for Dr. David Conti, my co-chair, and Dr. Wendy Mack, my committee
member in the final stages of the work, have also been incredibly helpful, and have
assisted me in numerous ways, including reviewing and offering invaluable suggestions
on this paper. I would also like to thank Dr. Kimberly Siegmund, who has provided
ideas and valuable advice during the process of writing this paper.
I cannot conclude without speaking of the gratitude I possess for my family, my
fellow roommates, and my mentor, on whose constant encouragement and love I have
relied upon throughout my studies at the University of Southern California. I am
especially grateful for the example of my mentor, Dr. Sharon Chen. Her constant
courage and conviction will continue to inspire me as I carry on that spirit in my own
way.
iii
Table of Contents
Acknowledgments ii
List of Tables iv
Abbreviations v
Abstract vi
Introduction 1
Research Design and Methods 2
Background of the study 2
Data description 4
Inclusion criteria 5
Exclusion criteria 6
Explanatory criteria 7
Limitations of the data 8
Statistical analyses 9
Results 11
Population characteristics 11
Patient factors 13
Hospital specific factors 15
Mortality associated with surgery 16
Discussion 19
References 25
iv
List of Tables
Table 1: Demographic characteristics 12
Table 2: Random effects model of mortality adjusted for birth
weight with hospital effect treated as random effect 14
Table 3: Multivariate random effects model of mortality
with hospital treated as random effect 15
Table 4: PDA in relation to mortality stratified by birthweight
category 17
Table 5: Model comparisons 17
Table 6: NEC surgery estimates in relation to mortality
stratified by NICU levels 18
v
Abbreviations
AAP American Academy of Pediatrics
g Gram
HMO Health Maintenance Organization
ICD-9-CM International Classification of Disease, 9
th
Revision Clinical
Modification
NEC Necrotizing Enterocolitis
NICUs Neonatal Intensive Care Units
OR Odds ratio
OSHPD Office of Statewide Health Planning and Development
PDA Patent Ductus Arteriosus
vi
Abstract
The NEC study is a retrospective study exploring factors related to mortality and
evaluating if surgical treatment for NEC results in less mortality in at-risk neonates after
adjusting for all risk factors. Based on OSHPD inpatient hospital discharge data from
the NEC study, we initially found that the surgery did not decrease the risk of mortality
before any adjustment (OR=3.37, 95%CI=2.85-4.88, p<0.001). NEC surgery remained
a significant risk factor after adjusting for NICU levels and other risk factors while
using hospitals as a random effect (OR=2.40, 95%CI=1.72-3.36, p<0.001). Thus, after
adjusting for all available risk factors, surgery was association with a doubling in the
likelihood of death. Due to the variation of mortality amongst the hospitals, and the
correlation of outcomes within the hospitals, it is preferable to use a random effects
model to adjust for NICU levels with hospitals treated as a random effect.
1
Introduction
Regression analysis and analysis of variance have served as the fundamental
methods for statistical modeling for the past decades. These methods have some
common assumptions that the residual of error terms are independently and identically
normally distributed. In medical and social sciences as well as marketing applications,
multiple logistic regression is used extensively. The use of multiple logistic regression
in biomedical research and the recognition that it could be applied to case-control data
has led to the widespread use of this methodology
19
. Random effects models have
become an important new approach to modeling, which allows relaxation of the
independence assumption and takes into account more complex data structures in a
flexible way
13
. Benefits of the random effects models include an increase in the
precision of our estimates, and a more appropriate modeling of complex data
structures.
Random effects models are used when the difference across groups or other
class variable is treated as a random, rather than a fixed effect
27
. For example, when
subjects are nested within neighborhoods, a model testing neighborhood differences as
a fixed effect would include all neighborhoods in the sample as a set of dummy
variables in a regression equation with individuals as the unit of analysis. A random
effects model would treat neighborhood differences as realizations from a probability
distribution; that is, neighborhood intercepts would be allowed to vary randomly
across neighborhoods following a probability distribution. An underlying assumption
is that the neighborhoods in the study are a random sample from a larger population of
2
neighborhoods about which inferences are to be made
11
. Random effects models can
be thought of as a particular case of the more general multilevel models in which only
intercepts are allowed to vary randomly across groups
11,13
. The term, “random effects
models,” is sometimes used more broadly to refer to multilevel models in general; that
is, models that allow for both random intercept and random covariate effects. In a
hierarchical database, for instance, a multi-center study is conducted at several centers
due to the small number of patients available at any one center, or with the deliberate
intention of assessing the effectiveness of treatments in several settings. In this case,
there will be extra variability in treatment effect estimates which may be related to
differences between the centers caused by different investigators, patient populations,
and other factors. Including centers and center-specific treatment effects as random
effects in the model can account for the extra variation. Such variation is likely to be
most noticeable in trials that do not compare drugs
19,27
. For instance, in a trial to
compare surgical procedures, there may be some degree of variation in levels of
experience at each center with the different procedures. Hence, this would lead to a
positive variance component for the center-treatment effects
19
. The following study
will illustrate how a random effects model is incorporated into a hierarchical clinical
database where data is collected from multiple hospitals.
Research Design and Methods
Background of the study
Necrotizing enterocolitis (NEC) is one of the leading causes of neonatal
mortality
7
and the most common reason for emergency gastrointestinal surgery during
3
the neonatal period
20,30
. The rising rates of preterm and low birthweight deliveries
are the most common risk factors
18,39
. Despite decades of NEC research, many
unanswered questions remain regarding its pathogenesis
1,4,44,59
, treatment
43
,
prevention
47
and epidemiology
37,38
. Each neonatal NEC-associated hospitalization
costs approximately $300,000 and an infant requiring surgical care adds nearly
$200,000 to the cost of neonatal care in comparison to other premature infants.
Furthermore, the initial cost and care is only the tip of the iceberg because survivors
are prone to future gastrointestinal and neurodevelopmental morbidities
22,31,42,46,53,57
.
Given the burden NEC imposes on the families and institutions caring for these
infants, it is vital to determine strategies to improve outcomes associated with this
condition.
Prematurity is the most important condition that leads to NEC
25,38,54
.
Therefore, intensive care management is required for premature infants or those with
low birthweight, intrauterine growth retardation, congenital malformations (birth
defects), sepsis, birth asphyxia, or pulmonary insufficiency. A common condition also
associated with prematurity is patent ductus arteriosus (PDA), which is a type of
congenital heart defect that is present at birth. Infants with PDAs are at risk for
development of NEC
10,15,21,46,54
. Not only is the presence of PDA itself a risk factor
for NEC, but the medical treatment of PDA with indomethacin is also associated with
the development of NEC
10
. Though the link between PDA and NEC is well
established, the PDA contribution to mortality is not well characterized.
4
NEC treatment and prevention continue to challenge neonatalogists and
pediatric surgeons through active research efforts. The ever-increasing healthcare
costs and growing momentum for State-based universal healthcare coverage makes it
imperative to understand neonatal ailments that may lead to costly chronic conditions.
Since California is a hugely diverse population, it is an ideal setting to determine the
patient-specific and institutional-based factors associated with NEC. Disparities in
infant mortality are primarily determined by differential access to specialized health
care
60
. Such disparities have been demonstrated in the adult population where recent
evidence from California showed that differences in adult patient characteristics, such
as race/ethnicity and insurance status, are associated with surgical care received at
high volume hospitals
34
.
Data description
The California Office of Statewide Health Planning and Development
(OSHPD) inpatient hospital discharge database was used in this study. Numerous
investigators have analyzed this database to investigate various health
conditions
17,33,34,36,45,48,49,52
. Administrators in California licensed hospitals submit
information regarding every discharge from their respective facilities to the State. The
study period covered hospital discharges from January 1, 1999 to December 31, 2004.
Neonatal intensive care units (NICUs) were categorized based on the American
Academy of Pediatrics (AAP) California Directory of Neonatal Intensive Care Units,
Neonatalogist & Perinatalogists (October 2006 version) by OSHPD hospital
identification numbers assigned to each institution, a method that has been used by
5
other investigators
32-34,39
. NICUs were defined and grouped as follows: Level I
(institution with a nursery but without a neonatal intensive care unit); Level IIA (no
mechanical ventilation); Level IIB (brief duration of mechanical ventilation); Level
IIIA (able to care for infants with birthweight > 1000 g and gestational age > 28 weeks
and only capable of conventional mechanical ventilation); Level IIIB (able to provide
comprehensive to care for infants with extremely low birthweight or infants of 28 or
fewer weeks’ gestation); and the highest level designation Level IIIC (able to provide
extracorporeal membrane oxygenation also known as ECMO and surgical repair of
serious congenital cardiac malformations that require cardiopulmonary bypass)
58
.
With regards to NEC-specific outcomes, the OSHPD dataset was analyzed rather than
a national dataset to capture local disparity paradigms
23-25,35
. With the hypothesis that
NEC outcome is affected by patient-specific and/or institution-specific factors, the
data was analyzed in an exploratory manner. The contribution of patient-specific
factors to mortality including gender, race/ethnicity, socioeconomic status, and patient
co-morbidities (patent ductus arteriosus, PDA) were first determined. The data was
then analyzed by health care-specific factors including NICU levels of care, treatment
type (surgical or medical), and admission status (inborn or outborn).
Inclusion Criteria
All birth hospitalizations were extracted from the database using the OSHPD-
specific newborn code and examined according to the International Classification of
Disease, 9th Revision Clinical Modification (ICD-9-CM) for relevant procedure and
diagnosis codes. The NEC cohort was determined using the diagnosis code 777.5.
6
Surgically-treated NEC patients were identified with procedure codes 45.0-46.99.
From this range of procedure codes, we excluded codes that would not be part of an
operative procedure for NEC. Procedure codes that were included in the range of
45.0-46.99 were restricted to include exploratory laparatomy (45.0, 45.00), bowel
resection (45.02-3, 45.1, 45.29, 45.3-4, 45.41, 45.49, 45.50-2, 45.6-63, 45.7-79, 45.8,
46.99), stoma creation (46.0-46.64) and intestinal anastomosis (45.9-94, 46.73-79,
46.93-4). PDA was identified with diagnostic code 747.0 and the PDA-ligation with
procedure code 38.85. Low birthweight was identified with the following ICD-9-CM
codes: 764.0-764.99, 765.01-765.19 and V21.31-21.35.
Exclusion Criteria
Analysis of total mortality and demographic descriptions includes the whole
NEC cohort without excluding any patients (N=3328). Random effects model
analyses were limited to only those neonates whose birthweight codes were entered
(N=2318) since birthweight is one of the most common risk factors for NEC. Only 27
patients were admitted into the hospital for less than 24 hours. Among these patients,
21 died, 4 were transferred, and 2 patients had unknown dispositions. Since these
subjects had insufficient information and follow-up, they were excluded from our
analyses. The final patient total was 2318. According to the California Center for
Health Statistics and Office of Health Information and Research, total live births for
1999-2004 numbered 3,191,486 as opposed to 3,102,621 infants that were identified
from the OSHPD database for the same years. The 2.70% difference is likely due to
7
those uncomplicated home births which were not included in this study as these
patients were never admitted to hospitals in California.
Explanatory Variables
The primary outcome of interest is in-patient mortality; 13.29% of the neonates
died and 86.71% neonates survived. OSHPD categorizes ethnicity as Hispanic, non-
Hispanic, or Unknown. Race was coded as White, Black, Native
(American/Eskimo/Aleut), Asian, Other, and Unknown. As commonly done in
literature
9,17,25,34,52
, race and ethnicity were treated as a single variable and
subcategorized as Hispanic White (Hispanic), non-Hispanic White (White), Black, and
Asian. Hispanic Asian, Hispanic Black, Pacific Islander and Native groups were
included in the “Others” category since the sample size was less than 1% of the overall
NEC data. To identify economic and institutional healthcare factors, mortality was
analyzed in relation to insurance status (State based funding such as Medi-Cal vs.
HMO/Private Coverage), level of NICU care and admission source defined as either
inborn (preterm infants born in tertiary care center) or outborn (preterm infants born in
a level I or level II and then transferred to a tertiary care center within the first 4 days
of age for further treatment). In addition, the relationship of parental income and
mortality was investigated. Household income was categorized at the quartiles of the
sample as <$30,000, $30,000-$39,999, $40,000-$49,000, and ≥$50,000. Because the
database did not include any measure of severity of NEC, a variable summarizing the
number of ICD-9-CM diagnoses assigned to each patient was included as a surrogate
measure of severity
26,41
. This variable was found to be correlated with in-patient
8
mortality
26
and was categorized as 1-8, 9-20, >20 diagnoses based on the tertile
distribution of the sample. The number of diagnosis variables represents the number
of ICD-9-CM diagnoses that administrators assigned at the time of patient disposition,
and substantially increases with mortality of the NEC neonates. The non-surgical
PDA group was not defined as medical treatment (with indomethacin or ibuprofen)
because the number of patients who received indomethacin or ibuprofen prior to
undergoing PDA-ligation and/or the number of neonates in whom PDA may have
possibly been treated with volume restriction could not be determined.
Limitations of the Data
One limitation of the OSHPD dataset is possible coding errors and/or missing
codes. The dataset does not include clinical information, such as medications or
physiological parameters. The OSHPD database does not allow consideration of the
order in which treatments were given. Thus, for example, we cannot determine what
treatments were given prior to surgery. There is only one ICD-9-CM code for NEC,
which prevents determination of the clinical stage of NEC
3
. It was also not possible to
determine the number of patients who may have failed medication-based treatment
and proceeded to PDA-ligation from this database, as medication-based treatment
codes do not exist. Since household income was not available, the median household
income based on zip codes
5,30
was used as an approximation in order to apply some
socioeconomic factors to the analysis.
9
Statistical Analyses
Analysis of these hierarchical clinical data was addressed by a random effects
model, which account for the correlations within hospitals and the variation of
hospitals related to mortality. Random effects models are an extension of generalized
linear models to incorporate dependent data; that is, patients’ mortality data may be
correlated due to treatments within the same hospital associated with mortality. In-
hospital death was the dependent variable while NEC surgery was the primary
independent variable of interest. To determine whether the association of NEC with
mortality varies among hospitals, the interaction terms of hospital and NEC surgery
were tested using the likelihood ratio test.
Basic descriptive statistical approaches were used to summarize the
demographic characteristics of the study sample, stratified by patients’ surviving to
discharge versus death in the hospital. Continuous variables were summarized using
means and standard deviations. Annual median household income was initially
treated as a continuous variable. The variable was then categorized into <$30,000,
$30,000-$39,999, $40,000-$49,000, and ≥$50,000 based on the quartile distribution of
the data and treated as categorical. Categorical (nominal/ordinal) variables were
described by the frequencies and the percentages of each category. Categorical
variable were: number of ICD-9-CM diagnoses, gender, race/ethnicity, birthweight,
NICU levels, admission type, PDA, ligation with PDA, and insurance status.
Birthweight was categorized as <1000g, 1000-1500g, and >1500g. The higher
10
birthweight category is then treated as reference group to assess the effect of low
birthweight.
For parsimonious analyses, subjects of Black and Asian race were combined
with “Others” as they did not provide enough information to separately describe the
mortality as they had small numbers of death. Annual median household income was
also dichotomized into <$30,000 and >$30,000 in an attempt to capture information in
regards to socioeconomic status that might relate to mortality.
Since the data were collected from multiple hospitals, the mortality varied
among the hospitals. Hence, the variation of mortality among hospitals was assessed
with the loneway procedure in STATA which fits large one-way analysis of variance
models on datasets with many levels of a class variable. The means and standard
deviations of the number of diagnoses by NICU levels were computed to illustrate the
trend of the number of diagnoses by NICU levels.
A multivariable logistic regression analysis with hospital treated as a random
effect was used to estimate and test associations with mortality. In general, the main
random effect model applied in this study can be written as
€
logit(Pr(Y =1)) =α +βX +γZ +π
h
where Y is our outcome of interest(mortality), represents population mean,
represents the log odds ratio associated with NEC surgery, X represents NEC surgery
(0=no, 1=yes), represents log odds ratios associated with other covariates, Z
represents other covariates, represents hospital as a random effect where we
assumed that are independent random variables that are normally distributed with
11
means 0 and with a common variances σ
2
. A random effects model was used in the
analyses to account for the variation of the hospitals due to the mortality differences
among the hospitals and the correlation in mortality outcomes within the hospitals.
Birthweight was included as an adjustment variable as it is a well-known risk factor
for NEC. Likelihood ratio tests were used to assess whether the association of NEC
surgery with mortality varies by NICU levels. Associations were summarized as ORs
(odds ratios) as the estimators of relative risk, with a 95% confidence interval.
In multivariate modeling, we considered a variable to be a confounder based
on previous literature and whether or not its inclusion altered the ORs of the
association of interest by 15% or more compared to the unadjusted value. These
confounders were included in the final model. The model, which included the
interaction term of PDA and birthweight, was compared to another model without the
interaction to assess whether the association of PDA with mortality varies with
birthweight by the likelihood ratio test.
Statistical significance was set at a 2-sided 5% level. These methods were
implemented using Intercooled Stata, version 9.2 (StatCrop LP, College Station,
Texas).
Results
Population characteristics
During 1999-2004, 3,102,621 hospitalized live births were identified in
California. The incidence of NEC was 1 per 1000 live births from the initial sample
population (N=3328). The in-hospital NEC cohort mortality was 12.5% (n=415) and
12
the overall mortality rate was 13.4 deaths per 100,000 live births. In this study,
there was no significant correlation between the calendar years of the study and
mortality (p=0.33).
Table 1. Demographic characteristics
Characteristics Total
(N=2318)
%
Number of ICD-9-CM diagnosis
1 - 8 695 30
9 - 20 1367 59
> 20 256 11
Gender
Female 926 40
Male 1217 52
Missing 175 7
Ethnicity
White 645 28
Hispanic 526 23
Black 257 11
Asian 108 5
Others 369 16
Missing 413 18
Birthweight
< 1000 g 890 38
1000-1500 g 728 31
>1500 g 700 30
NICU Levels
I, IIA, IIB, IIIA 579 25
IIIB 976 42
IIIC 763 33
Admission Type
Outborn 555 24
Inborn 1763 76
PDA
Yes 860 37
No 1458 63
PDA – Ligation
Yes 115 13
No 745 87
Annual median household income
< $30,000 458 20
$30,000 - $39,000 694 30
$40,000 - $49,000 495 21
≥ $50,000 628 27
Missing 43 2
Insurance status
State Funded 1343 58
HMO/Private 975 42
Remark:
Others include unknown, Hispanic Asian, Hispanic Black and Native Americans.
13
Table 1 summarizes the characteristics of the NEC study population from
California after excluding those who were missing birthweight (N=2318). The
characteristics yielded similar results from the initial sample population; therefore, we
excluded those without birthweight from our analyses.
As expected, 38% of the neonates had birthweight less than 1000 grams as
birthweight is an important risk factor for NEC in neonates. In this study sample, 40%
of the neonates were female, 52% were male, and about 7% were missing gender.
Ethnic composition of the study was 28% White, 23% Hispanic, 11% Black, and 5%
Asian. 1343 (58%) of the subjects with State-based healthcare coverage compared to
975 (42%) of the subjects with HMO/private health care coverage. Within this NEC
cohort, about 75% of neonates were admitted to NICU levels IIIB and IIIC, and 70%
of neonates had more than 9 diagnoses. Sicker neonates were therefore more likely to
be admitted to NICU levels IIIB and IIIC as these higher level healthcare hospitals
have the facilities to provide comprehensive care and treatment for the sicker
neonates.
Patient Factors
There was a statistically significant relationship between mortality risk and low
birthweight; for every 250g decrease in birthweight, neonates with NEC were 1.51
times more likely to die (95% CI = 1.38-1.66, p<0.001). Males were significantly
more likely to die than females after adjustment for birthweight and the variation of
the hospitals (Table 2). The mortality rate was higher among Hispanic neonates
compared to White, Black or Asian neonates; however, it was marginally significant
14
after adjustment (Table 2). Neither insurance status nor median household incomes
were risk factors of increased mortality (Table 2).
Table 2. Random effects model for NEC mortality adjusted for birthweight with hospital treated
as random effect
Death (%)
Odds Ratio (95% CI) SE P-value
Number of ICD-9 diagnosis
1-8 (Ref) 7.63 1.00 - -
9-20 14.70 1.20 (0.84, 1.74) 0.22 0.32
>20 21.09 0.95 (0.57, 1.55) 0.24 0.81
Gender
Female (Ref) 10.91 1.00 - -
Male 15.20 1.53 (1.15, 2.03) 0.22 0.003
Race/Ethnicity
White 13.33 1.08 (0.72, 1.62) 0.22 0.71
Hispanic 18.06 1.52 (1.01, 2.29) 0.32 0.05
Others (Ref) 9.13 1.00 - -
NEC surgery
No (Ref) 10.26 1.00 - -
Yes 29.89 2.26 (1.66, 3.08) 0.36 <0.001
PDA
No (Ref) 9.60 1.00 - -
Yes 19.53 1.41 (1.06, 1.87) 0.20 0.02
PDA-Ligation
No (Ref) 18.26 1.00 -
Yes 27.83 1.38 (0.83, 2.31) 0.36 0.22
NICU Levels
I, IIA, IIB, IIIA (Ref) 3.80 1.00 - -
IIIB 11.48 2.21 (1.16, 4.24) 0.73 0.02
IIIC 22.80 5.19 (2.53, 10.67) 1.91 <0.001
Admission Type
Inborn (Ref) 11.23 1.00 - -
Outborn 19.82 1.22 (0.83, 1.79) 0.24 0.31
Median Household Income
< $30,000 8.95 1.48 (0.97, 2.25) 0.32 0.07
> $30,000 (Ref) 14.5 1.00 - -
Insurance
HMO/Private (Ref) 13.44 1.00 -
State Funded 13.18 1.10 (0.82, 1.47) 0.16 0.54
Remark:
Ref denotes reference group.
CI denotes confidence interval.
SE denotes standard error.
Others include Black, Asian, unknown, and others.
Income dichotomized at $30,000(the lower 25th percentile of the income distribution
of the study cohort) was not significantly associated with mortality, although the
15
association indicated an almost 50% increased mortality risk among subjects with
less than $30,000 of median household incomes (OR=1.48, 95%CI=0.97-2.25,
p=0.07).
Hospital-specific Factors
The majority of the NEC-associated hospitalizations were at institutions with
Level IIIB and IIIC designations (Table 1). The highest mortality was at Level IIIC
followed by IIIB units (Table 2). We found the number of diagnoses increased with
higher level of NICU care. The mean (± standard deviation) number of diagnoses per
NICU levels were as follows: Level IIA (5 ± 2.3), Level IIB (7.5 ± 3.7), Level IIIA
(8.6 ± 3.9), Level IIIB (11.2 ± 5.2), level IIIC (13.1 ± 6.7). In general, the most ill
neonates were cared at level IIIC of NICUs as evidenced by the highest mortality rates
(Tables 2 & 3). In this NEC data, 23% of the neonates were inborn and 76% were
outborn.
Table 3. Multivariate random effect model of mortality and hospital treated as random effect
Odds Ratio (95% CI) Standard Error P-value
Birthweight
*
2.41 (1.95, 3.00) 0.27 <0.001
Number of diagnoses
1-8 (Ref) 1.00 - -
9-20 0.99 (0.67,1.47) 0.20 0.98
>20 0.54 (0.31, 0.93) 0.15 0.03
Gender 1.48 (1.11, 1.97) 0.22 0.01
NICU levels** 2.10 (1.48, 3.00) 0.38 <0.001
PDA 1.38 (1.02, 1.88) 0.22 0.04
NEC Surgery 2.40 (1.72, 3.36) 0.41 <0.001
Remark:
The analysis is adjusted for birth weight, number of diagnoses, gender, PDA, NICU level and hospital
treated as random.
CI denotes confidence interval.
Ref denotes reference group
*Birth weight is treated as ordinal variable and is coded as 1(Ref) = >2000; 2=1000-1500; 3= <1000
**NICU levels are treated as ordinal variable and is coded as 3 (Ref)= I, IIA, IIB, IIIA ; 4 = IIIB; 5 =
IIIC
16
There was no difference in mortality between the inborn and outborn neonates after
adjusting for birthweight and the variation of the hospitals (Table 2).
Mortality associated with surgery
Since the sicker neonates were given surgery, NEC surgery was associated
with a greater mortality than no NEC surgery (Table 2), which is consistent with other
reports
3,22,25
. The mortality rate of the NEC surgery cohort was 29.89%. NEC surgery
remained significantly positively associated with mortality after the adjustment for
other factors (Table 3). To evaluate the possible differences in association of NEC
surgery with mortality, patients were stratified by the PDA diagnosis (yes, no). PDA
is a condition that has been linked to the development of NEC
10,15,21,46,54
. The
presence of PDA was greater in neonates with lower birthweight as expected, such
that for every 250g decrease in birthweight, neonates were 2.27 times more likely to
have the diagnosis of PDA (95%CI = 1.97-2.61, p<0.001). After adjusting for
birthweight and the variation of the hospitals, NEC neonates with PDA were more
likely to die compared to neonates without PDA (Table 2). Although neonates with
PDA were 1.23 times more likely to have surgery compared to neonates without PDA
after adjusting for all possible risk factors and the variation of the hospitals (95% CI =
0.91-1.67, p=0.18), neonates with PDA was not significantly associated with NEC
surgery. However, after adjusting for gender, birthweight, the number of diagnoses,
and the variation of the hospitals, the effect of PDA on mortality still remained
significant as shown in Table 3.
17
Table 4. PDA in relation to mortality stratified by birthweight catergory
Birthweight category
PDA
< 1000 g
(n = 890)
1000-1500g
(n = 728)
> 1500 g
(n = 700)
Test of
heterogeneity*
Odds Ratio 1.47 1.04 1.49
Standard Error 0.29 0.34 0.68
95% CI (1.01, 2.16) (0.56, 1.96) (0.61, 3.65)
P-value 0.04 0.90 0.38 0.53
Remark:
CI denotes confidence interval.
n denotes number of sample size of each group.
The odds ratios of PDA by birthweight were adjusted for gender, number of diagnoses, NICU levels,
NEC surgery with hospital as a random effect.
* Test of heterogeneity is test of equivalence of PDA odds ratios across birthweight groups.
Table 4 illustrates the association of PDA with mortality by birthweight category.
Although PDA was associated with increased risk of mortality in neonates with
birthweight <1000g (OR=1.47, 95%CI=1.01-2.16, p=0.04), there was no strong
evidence to indicated that the association of PDA with mortality varied by birthweight
(likelihood ratio test = 1.26 on 2 degress of freedom, p=0.53).
Table 5. Model comparisons
NEC surgery
Model Odds Ratio Standard Error 95% CI P-value
Unadjusted* 3.37 0.51 (2.85, 4.88) <0.001
Logistic Regression** 2.53 0.41 (1.85, 3.46) <0.001
Random Effects*** 2.40 0.41 (1.72, 3.36) <0.001
Remark:
CI denotes confidence interval.
*Unadjusted model is without any adjustment.
**Logistic model is adjusted for birthweight, number of diagnoses, gender, PDA, and NICU levels.
The within hospital correlation is ignored.
***Random effect model is adjusted for birthweight, number of diagnoses, gender, PDA, NICU levels
with hospital as a random effect.
Table 5 shows model comparisons using 3 different approaches. The NEC
surgery estimates from the 3 models were significant (all p<0.001). The standard
error estimate in the unadjusted model was large, suggesting there is some variability
in the data. Although the standard logistic regression and random effects model
18
yielded similar results, the random effects model was preferred as it accounts for the
variation of the hospitals and the correlation within the hospitals.
Table 6. NEC surgery estimates in relation to mortality stratified by NICU levels
NICU levels
NEC surgery
I, IIA, IIB, IIIA
(n = 579)
IIIB
(n = 976)
IIIC
(n = 763)
Test of
heterogeneity*
Overall**
(N = 2318)
Odds Ratio 2.79 2.95 2.10 2.40
Standard Error 5.60
¥
0.82 0.45 0.41
95% CI (0.06, 141.51) (1.71, 5.09) (1.38, 3.21) (1.72, 3.36)
P-value 0.61 <0.001 0.001 0.58 <0.001
Remark:
CI denotes confidence interval.
n denotes number of sample size of each group.
The odds ratios of NEC surgery by NICU levels were adjusted for birthweight, number of diagnoses,
gender, and PDA with hospital treated as a random effect.
* Test of heterogeneity is test of equivalence of NEC surgery odds ratios across NICU levels.
** Overall denotes the same random effects model from table 5.
¥ The large standard error is due to very small proportion of death rates in the group.
Table 6 illustrates the association between the surgery and mortality stratified
by NICU levels. The standard error estimate in NICU levels of I, IIA, IIB, and IIIA
was incredibly large compared to NICU levels IIIB and IIIC as there were only about
22 (3%) of deaths in that NICU level (data not shown). After stratification by NICU
levels, NEC surgery is not a significant risk factor for mortality in NICU levels of I,
IIA, IIB, and IIIA. However, neonates receiving surgery in NICU levels of IIIB and
IIIC appeared to be a risk factor for mortality as presented in Table 6. Regardless,
there was no evidence to indicate the association of NEC surgery with mortality
significantly varied across NICU levels (likelihood ratio test=1.96 on 3 degree of
freedom, p=0.58).
19
Discussion
Based on our data, the mortality rates associated with NEC have not
significantly changed over the study period of 1999-2004 (data not shown). Based on
previous literature, the presence of PDA not only has been linked to NEC, but also its
treatment
10
. In this data, PDA ligation was performed in 115 of the 860 neonates with
PDA. 28% of neonates with PDA who underwent PDA ligation died. However,
PDA ligation was not associated with an additional increased risk of mortality when
compared to neonates whose PDA was treated non-surgically after adjusting for
birthweight and the variation of hospitals (Table 2). PDA was significantly associated
with mortality after adjusting for birthweight, number of diagnoses, gender, NICU
levels, and with hospitals treated as a random effect (OR=1.38, 95%CI=1.02-1.88,
p=0.04). NEC surgery was statistically significantly associated with higher mortality
after adjustment (Table 3).
To assess the potential contribution of socioeconomic status to infant
mortality, insurance status and parental median household income were evaluated.
The data in this study did not provide any strong evidence indicating that
socioeconomic status is a risk factor for NEC mortality after adjusting for birthweight
and the variation of the hospitals. However, Joseph et al. showed that lower income
was associated with an increase in preterm birth
28
. Based on this, since the greatest
risk factor for NEC is low birthweight, we initially hypothesized that low income
would be associated with preterm delivery, and that income and mortality should be
correlated. In our data, there was no evidence to indicate that low birthweight was
20
associated with low income. Socioeconomic status was not significantly associated
with mortality before and after all the adjustments. However, since median household
income was defined based on zip code, it might not be an accurate measure of
individual income and therefore might not accurately estimate the effect of
socioeconomic status on mortality. Regardless, the fact that insurance status and
median household income were not determinants of increased infant mortality within
the NEC data suggests socioeconomic status is not related to neonatal mortality in
these data.
Using a random effects model to analyze a hierarchical dataset is a preferable
approach as sometimes there will be extra variability in treatment effect estimates,
which can be due to differences between hospitals. This extra variation can be taken
into account by including hospital effects as random effects in the model; we might
otherwise draw an incorrect inference by ignoring the variation. For instance, the
principal investigator of this study believed that outborn infants had a higher risk of
mortality as he believed that the neonates who transferred to another NICU level
would be sicker and therefore would be another factor related to mortality. Indeed, a
standard logistic regression analysis approach indicated that there is a higher risk of
death for the outborns compared to the inborns (OR=1.95, 95%CI=1.51-2.52,
p<0.001). However, after including hospital as a random effect, there was no strong
evidence suggesting that outborn is a risk factor of mortality (OR=1.22, 95%CI=0.83-
1.79, p=0.31). Thus, there was some variability in the outborn effect due to the
difference in mortality between hospitals.
21
Previous reports suggest that institution-based health care discrepancies
affect infant mortality
2,9,49
. Goodman et al. demonstrated that outcomes improved in
communities with a greater number of neonatalogists
14
. Other population-based
studies showed that risk-adjusted neonatal mortality (for all causes) are lower in high
volume institutions with level III designated units
49
. In table 2, the mortality rate was
higher in level IIIC-designated hospitals after adjusting for birthweight and the
variation of the hospitals, this contradicted other studies in mortality. However, they
included more than just NEC in their studies. Thus, it may not be conflicting.
Before concluding NEC surgery is a risk factor for mortality, we investigated
all the possible factors that might inflate our results. In Table 5, neonates with NEC
surgery were 3.37 times more likely to die compared to those not having surgery
without any adjustments (95%CI=2.85-4.88, p<0.001). However, after stratifying by
the NICU levels, the odds ratio associated with NEC surgery decreased by 29% in
NICU level IIIC from NICU level IIIB even though surgery still remained a
significant risk in death (Table 6). Therefore, NICU levels are another important
covariate in estimating the relationship between NEC surgery and mortality. NICU
levels were included in the final multivariate random effects model.
Since NICU levels are correlated with mortality; we hypothesized that it might
be sufficient to account for NICU levels in the final model without also adjusting for
the nesting of the data. By fitting hospitals as a random effect, allowance is made for
some of the variability in the magnitude of the risk factor effects between hospitals as
well as taking account for differences in mortality rates among the hospitals.
22
Although adjusting only for NICU levels may seem sufficient for estimating the
relationship between NEC surgery and death, it does not fully account for the within-
hospital correlation of mortality. Treating hospitals as a random effect accounts for
the variability of NEC mortality related to differences in hospital mortality rates.
Some hospitals had only 1 death compared to other hospitals having as much as 30 or
more deaths. In fact, the variability due to hospitals remains significantly large even
when stratified by NICU levels. Hence, even though NICU levels and hospitals are
highly correlated, they serve different purposes in model fitting.
Deciding whether hospital and hospital-treatment effects should be fixed or
random is often subjective. To obtain global effect estimates, hospital and hospital-
treatment effects should be fitted as random as it reflects the heterogeneity of the
treatment effects across hospitals. But, in practice, the choice will depend on whether
treatment estimates are relating only to the set of hospitals used in the study or, more
widely, to circumstances and locations of which the hospitals can be regarded as a
sample
19
. In this example, hospital effects were treated as random as it increases the
accuracy of NEC surgery estimates, since information from the center error factor is
used in addition to that from the residual factor
19
.
Initially, we found that NEC surgery showed some trends in reducing the risk
of mortality from NICU level IIIB to IIIC. However, after the interaction between
NICU levels and NEC surgery were tested, the results did not provide any strong
evidence that the relationship between NEC surgery mortality was modified by NICU
levels as presented in Table 6. Since the final model adjusted for NICU levels and
23
treated hospital as a random effect, it is reasonable that a hospital-specific effect of
NEC surgery has no additional role in estimating mortality. Therefore, hospital-
specific effects of NEC surgery were not included in the final model.
Despite our final results showing that NEC surgery is statistically significantly
positively associated with mortality after adjusting for birthweight, number of
diagnoses, gender, race, PDA, NICU levels, and the variation of hospital, the relative
risk decreased compared to the unadjusted model (Table 5). Birthweight, number of
diagnoses, and PDA are known for their association with severity of NEC and lack of
adjustment for these factors might inflate the effect of NEC surgery on mortality.
Before any adjustment was made, the neonates who had NEC surgery were 3.37 times
more likely to die compared to the neonates without NEC surgery, suggesting that
NEC surgery is not an ideal treatment in reducing the risk of mortality for neonates.
But, after adjusting for all the factors associated with severity of NEC, the neonates
who had NEC surgery were 2.40 times more likely to die compared to the neonates
without NEC surgery. Even though the NEC surgery still remained as a positive risk
factor of mortality, the relative risk of NEC surgery was reduced by 29%. Therefore,
it is difficult to conclude whether or not undergoing NEC surgery actually increased
the risk of mortality. We certainly cannot rule out the possibility of unmeasured
confounding factors that biased this association.
This hierarchical clinical database showed that NEC surgery does not improve
survival from NEC after adjusting for all the risk factors and the variation among
hospitals. Even though we adjusted for hospital and other risk factors available in our
24
multivariate model, we still should not conclude that NEC surgery is a risk factor
for death. Neonates who received surgery very likely could have other unmeasured
risk factors that led to the surgery that were not adjusted for. In this case, it is of
course unethical to perform a randomized controlled trial. This analysis did show that
the adjustment for other measured risk factors reduced the relationship between NEC
surgery and death.
In practice, generalization of results from random effects model needs to be by
degree and will always to some extent involve subjective judgments
19
. However,
these results can be generalized since our study sample has been taken at random from
the whole population of interest
19
. Random effects models are often preferred and are
appropriate approaches when a study sample represents a multilevel clustering and
where there are differences in outcome of interests across groups (or clusters).
Choosing an appropriate statistical approach and getting the appropriate estimates
depends on what research question is being addressed
11
. The results of this data
analysis however must be regarded as preliminary; further data is required to confirm
or refute the findings.
25
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Creator
Wee, Choo Phei
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Core Title
Application of random effects models to a clinical retrospective hierarchical database
School
Keck School of Medicine
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Master of Science
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Biostatistics
Publication Date
07/21/2008
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OAI-PMH Harvest,random effects models
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Conti, David (
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), Dorey, Frederick (
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), Mack, Wendy J. (
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