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Essays on the equitable distribution of healthcare

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ESSAYS ON THE EQUITABLE DISTRIBUTION OF HEALTHCARE

by

Adam Turpcu

________________________________________________________________________

A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(PHARMACEUTICAL ECONOMICS AND POLICY)

December 2010

Copyright 2010 Adam Turpcu
ii

Table of Contents

List of Tables iii

List of Figures iv

Abstract v

Chapter 1: The QALY Distribution Problem: Equity Concepts and Their Place in Health
Economics 1
Chapter 1 References 12

Chapter 2: The Effect of Framing on Preferences for Equality 14
Chapter 2 References 33

Chapter 3: The Equity-Efficiency Tradeoff and Cumulative Prospect Theory: Extending
the Rank-Dependent QALY Model to Reference Dependence 35
Chapter 3 References 63

Bibliography 64

Appendices:
Appendix A: The Sure Thing Principle and Additive Welfare Functions 67
Appendix B: Sample Elicitation Questions 68

iii

List of Tables

Table 1-1: Opportunity for health vs. final health outcomes 3
Table 1-2: Equality of current health status 4
Table 1-3: Equality of lifetime health 4
Table 1-4: Equity concept attributes by paper 5
Table 1-5: The book-making principle – decision 1 5
Table 1-6: The book-making principle – decision 2 5
Table 1-7: The book-making principle – decisions 1&2 (the book) 6
Table 1-8: The utility model vs. the dual model 8
Table 2-1: Violations of the sure thing principle by frame – Experiment 1 27
Table 2-2: Violations of the sure thing principle by frame – Experiment 2 27
Table 3-1: Scenarios used in Elicitation of Utility Function 42
Table 3-2: Scenarios used in Elicitation of Weighting Function 43
Table 3-3: Demographics 47
Table 3-4: Median constant allocation equivalents (in years) for gain scenarios 48
Table 3-5: Median constant allocation equivalents (in years) for loss scenarios 48
Table 3-6: Median Gonzales and Wu Parameters for Gains and Losses Before r adjustment 50
Table 3-7: Median Values for r 50
Table 3-8: Median Gonzales and Wu Parameters for Gains and Losses After r adjustment 52
Table 3-9: Distribution of QALYs and Equity Weights 55
Table 3-10: Equity-adjusted cost-utility ratios 58
Table 3-11: Ranking comparison between studies 59

iv

List of Figures

Figure 2-1: Questions asked in experiment 1 and experiment 2 32
Figure 3-1: Median W(p) by p - assuming r=1 49
Figure 3-2: Elicited Marginal Social Utility Function for QALYs 51
Figure 3-3: Median W(p) by p - adjusting for r 52

v

Abstract
This dissertation investigates methods to incorporate societal preferences for equity in health
economic decision making. Cost –effectiveness analysis (CEA) solves the problem of how to
prioritize health programs so as to maximize health. However, CEA may not always agree with
our social preferences for prioritizing health programs. For example, suppose for a cohort of
persons, two health programs deliver at the same cost, the same aggregate health gain.
However, the first program gives the health gain mostly to those poor in health and the second
program gives it mostly to those rich in health. Individuals may strictly prefer the first health
program to the second, yet CEA would consider these health programs equivalent. We call this
preference behavior ‘inequality aversion’. Inequality aversion may explain, in part, why there is
sometimes negative reaction to policies prescribed by CEA.

In this dissertation, existing equity models are reviewed, potential framing problems in the
elicitation process are analyzed, and finally a new model is proposed which extends the Rank-
Dependent QALY model to reference dependence. Results of the framing study suggest that
preferences for equality are volatile and the common way of asking for preferences for equality
tends to violate the sure thing principle. When an additive social utility model is assumed,
question frames that occasion preferences consistent with the sure thing principle are desirable
because they are more likely valid when this is the case. Results of the reference-dependent
equity study suggest that preferences for equity vary depending upon whether a policy maker is
looking to expand existing health coverage or to curtail it. Respondents exhibited stronger
preferences for equity in “loss” scenarios that curtailed existing health coverage. Two model
types are incorporated: a power utility model and an equity weighting model. Results indicate
vi

that respondents have a diminishing marginal utility function for health. After adjusting for
utility curvature, the median equity weighting function for both gains and losses were linear.
Our results suggest that preferences for equity can be sufficiently measured by a utility function
and that the equity weighting function adds little value.

1

Chapter 1. The QALY Distribution Problem: Equity Concepts and Their Place in Health
Economics
The founders of modern economic thought neglected the altruistic aspects of human nature in
creating “Homo economicus,” the rational and self interested economic man (see Mill, 1863;
1874). Edgeworth wrote that “the first principle of Economics is that every agent is actuated
only by self interest” (1881). The principle advantage of this characterization is not in its
accurate portrayal of individual preference (it is widely accepted that the economic man is a
crude over simplification of human behavior), but in its parsimony. As Persky observed, “The
message to derive from Mill's Homo economicus is not that humans are greedy, not that man is
rational, but that social science works best when it ruthlessly limits its range” (1995).

The simplifying characterizations of man as rational and self interested may be justifiable in war
and contracts (Edgeworth’s areas of study), but in health they are not. In Rational Fools Sen
asserted that “the purely economic man is indeed close to being a social moron” (1977). A
study by Bleichrodt, Doctor, and Stolk (2005) found that members of the general public in the
Netherlands were willing to sacrifice some health to obtain a more equitable distribution of
health. Dolan et al. (2005) reviewed several earlier papers and conclude also that persons
exhibit some preference for equity over efficiency. People appear to have altruistic tendencies,
especially when it comes to the distribution of health, and policy makers that choose to ignore
those tendencies may make decisions that are not satisfactory to their constituents.

Recently, economic models in health have been subject to public criticism and derision. These
criticisms may reflect short-comings in economists’ reliance on Homo Economicus as a means of
studying health preferences. For example, Viagra™ has been shown to be more cost-effective
than lung transplant, yet legislative and public reaction to its purported value as formulary drug
has been remonstrative (Stolk et al., 2003). This may be because Viagra™ confers a health
benefit to many otherwise healthy persons. More recently, the Department of Health and
Human Services panel on mammography recommended, based on six cost-effectiveness and
decision models, that women should no longer receive mammography at age 40 years, but
rather wait until age 50 years (Madelblatt et al., 2009). Public reaction to this recommendation
has also been negative and strong with 76% of women saying they disagree or strongly disagree
2

with the recommendations (Szabo, 2009). This negative reaction may, in part, be because those
persons with breast cancer that are the worst-off are young women who die from the disease,
and these individuals benefit the most from early screening. Hence, this new recommendation
may have been perceived as one that forsakes the worse-off patients. Consideration of
inequality aversion in economic modeling may reduce the frequency and intensity of negative
public reaction to model results.

For the remainder of this paper we review equity concepts and the proposed methods to
incorporate those concepts into health economic analysis. In doing so, we seek to sharpen the
debate surrounding the merits of the use of equity models in health economic modeling.

2. Equity Concepts

In this section we review different equity concepts that have appeared in the QALY literature, as
not all definitions of equity have been the same.

To help classify the equity concepts we define them according to two attributes:
1) Is the study concerned with the equality of current health status or lifetime health?
2) Is the study concerned with fairness in the opportunity for health or in the equality of the
final health outcomes?

It’s important that we first clarify what we mean by each of the attributes above.

Fairness in the opportunity for health or fairness of final outcomes?

Bleichrodt (1997) carefully and formally characterizes the distinction between fairness in
opportunity for health and fairness in final health outcomes. He used allocations of quality-
adjusted life years. A QALY is a year of life adjusted for quality of health. For example, two
years living in health condition that reduces one’s utility to ½, is worth 1 QALY, as is 1 year in full
health. Consider the following three health programs each resulting in different QALY
allocations. There is a 50% chance that State s
1
will occur and a 50% chance state s
2
will occur.
3

The first number listed in a set is the amount of utility gained for the first individual and the
second number is the amount of utility gained for the second individual.
Table 1-1. Opportunity for health vs. final health outcomes
Program State s
1
(p=.5) State s
2
(p=.5) Expected Utility
1 (1, 0) (1, 0) 1
2 (1, 0) (0,1) 1
3 (1, 1) (0, 0) 1

A decision maker who is only interested in maximizing expected utility will be indifferent
between the three programs. Indifference between any pair of the programs is consistent with
equity neutrality, that is, “A QALY is a QALY no matter who gets it.” A decision maker who is
interested in the fairness of opportunity for health will be indifferent between Programs 2 and 3
because they both offer each individual a 50% chance of gaining a QALY (even though the final
outcomes for the two individuals will be different in Program 2). A decision maker who is
interested in the fairness of final outcomes will prefer Program 3 because both individuals will
have the same outcome in both s
1
and s
2
. In summary, a policy maker who desires program
recipients achieve equal health status will favor Program 3, equal expected health (opportunity
for health) will favor Program 2 and 3 over 1, and if concerned only with total health produced
by the program will indicate indifference between any two of the three health programs.
Though in the aforementioned example, Program 3, dominates when opportunity for health and
equal health status are of concern, there are practical issues around this program. Program 3
leads to a “high variance” all or nothing health policy, whereby everyone wins or everybody
loses. Despite concerns for equality of health status, a policy maker may not want his policy to
be a total failure and Program 3 offers this possibility.

Equality of current health status or equality of lifetime health

The last example dealt with marginal improvements in health, but did not consider prior accrual
of health or one’s current health circumstances. One way to consider prior accrual is to examine
lifetime (expected) QALYs. An approach to considering one’s current health circumstances is to
evaluate how a program will change health. Consider the following two health programs:

4

Table 1-2. Equality of current health status
Program
Before
Treatment After Treatment
Individual QALY
Gain
Societal QALY
Gain
1 (0.3, 0.7) (0.3, 0.9) (0.0, 0.2) 0.2
2 (0.3, 0.7) (0.5, 0.7) (0.2, 0.0) 0.2

First, notice that the societal QALY gain in each of the two programs is 0.2 QALYs (5
th
column).
Therefore, an equity neutral decision maker seeking to only maximize QALYs would be
indifferent between programs 1 and 2. Notice also (4
th
column) that the programs are
symmetric in opportunity for health, with each giving one individual a 0.2 QALY gain above the
other. Therefore, a QALY maximizer and a policy maker concerned primarily with opportunity
for health would find these programs equally desirable. However, a policy maker who is
interested in the equality of current health status would prefer program 2 which would give .2
QALYs to the worse off patient as opposed to program 1 which would give 0.2 QALYs to the
better off patient.

The last example dealt only with current health and improvements from one’s current health.
This type of analysis does not consider lifetime health. Persons in temporary severe conditions
may in some cases still expect to accrue a large number of lifetime QALYs as compared to others
who are currently well off in QALYs, but may fall ill or die at an early age without intervention.
To evaluate programs with respect to lifetime QALYs, consider the following health programs:

Table 1-3. Equality of lifetime health
Program
Lifetime QALYs
w/o Treatment
Lifetime QALYs
w Treatment
Individual QALY
Gain
Societal QALY
Gain
1 (60, 70) (60, 75) (0, 5) 5
2 (60, 70) (65, 70) (5, 0) 5

A policy maker who has a preference for equality of lifetime health would prefer Program 2,
which gives 5 QALYs to the person with less QALYs over the course of their life to Program 1
which gives 5 QALYs to the person with more lifetime QALYs. Again, in this example a QALY
maximizer as well as a policy maker concerned with (marginal) opportunity for health would be
indifferent between these two programs.
5

Table 1-4. Equity concept attributes by paper

Equality of current
health status
Equality of lifetime
health
Fairness in the
opportunity for
health Bleichrodt (1997)
Fairness of final
health outcomes Dolan (1998)
Wagstaff (1991),
Williams (1997),
Bleichrodt (1997),
Bleichrodt (2004),
Stolk (2004)

As table 4 indicates, the majority of published equity models are concerned with the fairness of
final health outcomes over individuals’ lifetimes.

The book-making principle

The book-making principle is an important consistency condition that underlies most equity
models. This principle states that if we evaluate a sequence of decisions and find each decision
(each page) to be good individually, then when we evaluate the set of decisions as a whole (the
book), the book must also be considered good collectively. This assumption is not as trivial as it
may seem. Consider the following examples:
Table 1-5: The book-making principle - decision 1
Program
Lifetime QALYs
w/o Treatment
Lifetime QALYs
w Treatment
Individual QALY
Gain
Societal QALY
Gain
1 (50, 50) (50, 70) (0, 20) 20
2 (50, 50) (59, 59) (9, 9) 18

In Table 5 above, a policy maker will make the first of two decisions. Let’s suppose that the
policy maker is inequity averse and thus chooses program 2 because the outcomes are more
equitable. After making this decision he proceeds to decision 2.
Table 1-6: The book-making principle - decision 2
Program
Lifetime QALYs
w/o Treatment
Lifetime QALYs
w Treatment
Individual QALY
Gain
Societal QALY
Gain
3 (50, 50) (70, 50) (20, 0) 20
4 (50, 50) (59, 59) (9, 9) 18

6

In decision 2, the policy maker picks program 4 over program 3 because the outcomes are
likewise more equitable.

Table 1-7: The book-making principle - decisions 1 & 2 (the book)
Program
Lifetime QALYs
w/o Treatment
Lifetime QALYs
w Treatment
Individual QALY
Gain
Societal QALY
Gain
1 & 3 (50, 50) (70, 70) (20, 20) 40
2 & 4 (50, 50) (68, 68) (18, 18) 36

After making decision 2, the decision-maker considers the overall results of his decisions and to
his dismay he finds that he is not happy with his results. Were he to have ignored equity and
made the efficient choice in both decisions (1&3), both individuals would have been better off.
The book-making principle assumes that the above situation will not happen. A collection of
individual good decisions must also be good collectively or the book-making principle (along
with the equity models that assume it) will be violated. Only QALY maximization will always
satisfy the bookmaking principle.

3. Equity Models

So far we have argued that there are legitimate concerns with the QALY is a QALY is a QALY
principle and that society may have preferences for equity. We have also described what some
of those equity preferences may entail. However, none of this matters unless there is a simple,
parsimonious way to incorporate these concepts into health economic models. The fact
remains that, despite its inherent problems, the QALY is a QALY is a QALY principle leads to
simple parsimonious models. Adding equity into the fray will make things more complicated.
The only way equity will become more widely acceptable is if these additional complications are
easy to understand and easy to incorporate. Furthermore, equity models will need to
demonstrate that policy decisions based on these models are more palatable to society when
compared to their unadjusted counterparts. In this section we will review currently available
methods to incorporate equity into cost-effectiveness analysis.

7

3.1 Utility Models

The traditional method for modeling equity is through a social utility function for health. These
functions are typically found to be concave indicating a diminishing marginal utility for health.
Utility models for health have considered both current health status (Dolan 1998) as well as
lifetime QALYs (Wagstaff 1991, Williams 1997). In the former, a QALY is worth more for those
in poorer current health states. In other words, the U(.4)-U(.3) > U(.9) – U(.8). In the latter
framework, an additional QALY for a child with a terminal disease would be would be worth
more than an additional QALY to someone who has had a chance to live their life. For example,
the U(10 QALYs)-U(9 QALYs) > U(80 QALYs) – U(79 QALYs). The value of a policy measured by
the utility model is as follows:

∑
=
n
i
i
q U
1
) (

The utility function for health is frequently modeled using either a power utility function or an
exponential utility function (Cher, Miyamoto & Lenert 1997). The attitude towards equity
described by the utility function has been described as one that “reflects an attitude towards
health (extra health is more desirable when in poor health than when in close to perfect
health).”(Bleichrodt, Crainich, and Eeckhoudt 2008).

3.2 Dual Models

Dual Models were first introduced in 2004 with the rank dependent model (Bleichrodt, Diecidue
& Quiggin 2004). Dual models generate explicit equity weights which are used to adjust cost-
effectiveness ratios. In the case of the Rank Dependent Model, these weights are based on the
ranking of individuals in terms of their expected lifetime QALYs. Individuals with a small
expected number of lifetime QALYs (eg. A child with a terminal disease) will receive a higher
equity weight than those who can expect to live a full healthy life. The value of a policy in this
model can be seen in the following function:
8

∑
=
n
i
i i
q
1
π

Note that there is no transformation of health (q
i
) as there was in the utility model. Instead the
health of each individual is weighted by an equity weight, which again is based on an individual’s
rank. To make the model tractable, individuals are grouped into categories with those who are
in similar health states. For example, the rank dependent model elicited by Bleichrodt, Doctor
and Stolk (2005) groups individuals with less than 10 years of expected lifetime QALYs, 10-20
expected lifetime QALYs, and so forth. So in practice, it’s the proportions of these groups that
are transformed based on their relative health ranking.

Bleichrodt, Crainich, and Eeckhoudt describe the attitude towards the distribution of health
measured by the dual function as “an attitude towards inequality (inequality is undesirable).”
This is in direct contrast to the attitude measured by the utility function, which is concerned
with the marginal utility of health. To further explicate the differences between these two,
consider the following example:

Table 1-8: The utility model vs. The dual model
Program
Lifetime QALYs
w/o Treatment
Lifetime QALYs
w Treatment
Individual QALY
Gain
Societal QALY
Gain
1 (10, 10) (13, 17) (3, 7) 10
2 (10, 10) (14, 16) (4, 6) 10

A policy maker may prefer program 2 over program 1 for two reasons:

1) The utility a policy maker receives from moving the first individual from 13 QALYs (policy 1) to
14 QALYs (policy 2) is greater than the utility he loses by moving the second individual from 17
QALYs (policy 1) to 16 QALYs (policy 2). This is what is measured by the utility function.

2) The policy maker prefers to have a more equitable end distribution of QALYs (eg 14 and 16 is
closer together than 13 and 17. This is what is measured by the dual function.

9

3. Combination Models (Utility Models + Dual Models)
Combination models incorporate both utility models and dual models into one model. An
example of this is the Rank Dependent QALY model by Bleichrodt, Doctor, and Stolk (2005). The
value of a health policy in a combination model is shown below:

∑
=
n
i
i i
q U
1
) ( π

These models measure both the marginal utility of health (U(q
i
)) and a dual function π
i
. The
obvious advantage of this approach is that it considers both the diminishing marginal utility of
health as well as attitudes towards inequality. It is a more complicated model, however, and it
is consequently more difficult to elicit equity preferences in this model relative to the stand
alone utility and dual models. During the elicitation process, respondents must answer several
more questions to estimate the model parameters. This additional responder burden can only
be justified if it can be shown that this model offers a substantially better picture of societal
preferences for equity relative to the previous models. The Bleichrodt, Doctor, and Stolk (2005)
paper found the social utility function for QALYs to be linear on average across respondents
indicating that the stand alone dual model may be sufficient to measure preferences for equity.
However, preliminary findings of a separate study the current authors have conducted run
counter to those found in the Bleichrodt, Doctor, and Stolk study. These findings indicate that
the average social utility function for QALYs is concave. We would recommend against assuming
a linear social utility function for QALYs until more evidence becomes available.

10

3.4 Reference Dependent Combination Models.

Reference dependent combination models take combination models one step further by
incorporating attitudes towards gains and losses when measuring preferences for equity. The
motivation behind these models is that preferences for equity may change based on whether a
policy maker is considering expanding existing coverage or curtailing existing coverage. The
value of a policy in these models can be measured by the following formula:

∑

∑

These models incorporate separate dual models and utility models for gains and losses. This
model is the subject of a working paper by the current authors.

4. Discussion

In this paper we have argued that traditional cost-effectiveness analysis, which assumes a QALY
is a QALY is a QALY regardless of who gets it, can lead to policy decisions that are not reflective
of societal preferences for distributions of health. We then discussed various equity concepts
which attempt to relax the QALY is a QALY is a QALY principle. We found that most of the equity
literature considers equity in terms of lifetime QALYs and not current health status. We then
reviewed methods to model these equity concepts including traditional utility models, dual
models, combination models, and reference-dependent combination models. Combination
models are more powerful but are more difficult to estimate (in terms of responder burden).
One of the problems with equity models that have been generated so far is that they only
consider one equity concept at a time. The Rank-Dependent QALY model, for example, only
ranks individuals by how disadvantaged they are in terms of lifetime QALYs and does not
incorporate other equity concepts such as the current health status of individuals. In the future,
equity models may want to consider creating a multi-attribute equity index that ranks
individuals based on more than just one dimension of equity.

11

Future studies may also want to evaluate how well various equity models predict actual policy
decisions. It has been shown that unadjusted cost-effectiveness ratios are often a poor indicator
of whether or not a treatment will be covered by a health plan (Stolk 2003). Equity models may
become more readily acceptable if it can be shown that they better align with actual formulary
decisions that are made. Such a study could also identify discrepancies between what equity
models predict will be covered and what is actually covered. This could elucidate what else
policy makers care about that currently isn’t being reflected in equity models.

Some might argue that it is hard enough to get policy makers to understand traditional cost-
effectiveness analysis and considering equity will only further complicate things. Admittedly,
whenever you have a new idea or a new model, there is going to be a lack of understanding and
a fair amount of skepticism to go along with it. However, we believe that equity models appeal
to decision makers’ preferences for distributions of health in society and that decision makers
already take several of these concepts into account when making their decisions. Equity models
can help make that decision making process transparent.

12

Chapter 1 References

Bleichrodt H. 1997. Health utility indices and equity considerations. Journal of Health Economics
16: 65-91.

Bleichrodt H, Diecidue E, Quiggin J. 2004. Equity Weights in the Allocation of Health Care: the
Rank-Dependent QALY Model. Journal of Health Economics 23: 157–171.

Bleichrodt H, Doctor JN, Stolk E. 2005. A nonparametric elicitation of the equity-efficiency
tradeoff in cost-utility analysis. Journal of Health Economics 24: 655-678.

Bleichrodt H, Crainich D, Eeckhoudt L. 2008. Aversion to health inequalities and priority setting
in health care. Journal of Health Economics 27:1594-1604

Cher, DJ, Miyamoto J, Lenert LA. 1997. Incorporating risk attitude into Markov-process decision
models: Importance for individual decision making. Medical Decision Making 17(3): 340-350.

Dolan P. 1998. The measurement of individual utility and social welfare. Journal of Health
Economics 17:39-52.

Dolan P, Shaw R, Tsuchiya A, Williams A. 2005. QALY Maximisation and people’s preferences: a
methodological review of the literature. Health Economics 14: 197-208.

Edgeworth FY. 1881. Mathematical Physics: An essay on the Application of Mathematics to the
Moral Sciences. 16.

Mandelblatt J. 2009. Effects of mammography screening under different screening schedules:
model estimates of potential benefits and harms. Annals of Internal Medicine 151: 738-747.

Mill J. 1836. On the Definition of Political Economy, and on the Method of Investigation Proper
to It. London and Westminster Review.

Mill J. 1874. Essays on Some Unsettled Questions of Political Economy. 2nd ed. Longmans,
Green,Reader &Dyer. Essay 5.

Persky J. 1995. Retrospectives: The Ethology of Homo Economicus. The Journal of Economic
Perspectives 9(2): 221-231

Sen AK. 1997. Rational fools: A critique of the behavioural foundations of economic theory.
Philosophy and Public Affairs 6:317-344.

Stolk EA. 2003. Are patients and the general public like-minded about the effect of erectile
dysfunction on quality of life. Urology 61: 810-815.

Stolk EA. 2004. Reconciliation of economic concerns and health policy: Illustration of an equity
adjustment procedure using proportional shortfall. Pharmacoeconomics 22(17): 1097-1107.
13

Szabo L. 2009. Women are insistent on mammograms, poll shows. USA Today. 23 Nov.

Wagstaff A. 1991. QALYs and the equity-efficiency trade-off. Journal of Health Economics 10:
21–41.

Williams A. 1997. Intergenerational equity: An exploration of the ‘Fair Innings’ argument.
Health Economics 6: 117-132.

14

Chapter 2. The Effect of Framing on Preferences for Equality

1. INTRODUCTION
Cost –effectiveness analysis (CEA) solves the problem of how to prioritize health programs so as
to maximize health. However, CEA may not always agree with our social preferences for
prioritizing health programs. For example, suppose for a cohort of persons, two health programs
deliver at the same cost, the same aggregate health gain. However, the first program gives the
health gain mostly to those poor in health and the second program gives it mostly to those rich
in health. Individuals may strictly prefer the first health program to the second, yet CEA would
consider these health programs equivalent. We call this preference behavior ‘inequality
aversion’. Inequality aversion may explain, in part, why there is sometimes negative reaction to
policies prescribed by CEA. For example, Viagra™ has been shown to be more cost-effective
than lung transplant, yet legislative and public reaction to its purported value as formulary drug
has been remonstrative (Stolk et al., 2003). This may be because Viagra™ confers a health
benefit to many otherwise healthy persons. More recently, the Department of Health and
Human Services panel on mammography recommended, based on six cost-effectiveness and
decision models, that women should no longer receive mammography at age 40 years, but
rather wait until age 50 years (Madelblatt et al., 2009). Public reaction to this recommendation
has been negative and strong with 76% of women saying they disagree or strongly disagree with
the recommendations (Szabo, 2009). This negative reaction may, in part, be because those
persons with breast cancer that are the worst-off are young women who die from the disease,
and these individuals benefit the most from early screening. Hence, this new recommendation
may have been perceived as one that forsakes the worse-off patients. Consideration of
15

inequality aversion in economic modeling may reduce the frequency and intensity of negative
public reaction to model results.

Most empirical research has concluded that persons evidence some inequality aversion (see
Dolan et al. 2005 for review). To account for this phenomenon, researchers have proposed
defining an additive social utility function over distributions of health (Atkinson, 1970; Dolan,
1998; Wagstaff, 1991). For each health program, a social utility function assigns to each
individual health beneficiary a utility that values that person’s particular allocation under the
program. The social utility function is additive because these individual utilities are added
together across all persons to determine the program’s health value. Formally, the value of
persons 1, …, n receiving a health allocation Q
1
, …, Q
n
is U(Q
1
) + … + U(Q
n
). By this method, the
value of a year of good health given to someone poor in health may exceed the value of a year
of good health given to someone rich in health (i.e., inequality aversion is permitted). Further,
additive social utility functions represent preferences prescribed by CEA as a special case: When
the social utility function is ‘equity neutral’ (neither inequality averse nor inequality seeking).
Wagstaff (1991) and Dolan (1998) have proposed parametric forms for additive social utility.
Doctor, Miyamoto & Bleichrodt (2009) demonstrated that health values given by the person
tradeoff (PTO) method imply (and are implied by) an additive social utility function. Other
researchers have proposed methods for eliciting additive social utility (Pinto-Prades, Abellan-
Perpinan, 2005). The goal in economic evaluation of health programs when social health
preferences are considered is to maximize social utility. Additive social utility functions are
16

desirable in part because they strongly separate persons in the analysis. This practice is
defensible as each person makes their own (independent) contribution to overall equity.

The validity of additive social utility models depends on a common sense preference condition.
Namely, persons unaffected by a policy choice should not impact a policy maker’s decision
about that choice. We call this “the sure thing” principle (c.f. Savage, 1954). If, regardless of
policy choice, it is a sure thing that a person (or group) gets a designated amount of health, then
that person (or group) exercises no influence on the policy maker’s choice of policy. For
example, if the formulary choice of including either cancer medication A or cancer medication B
has no effect on outcomes for patients with heart disease then patients with heart disease
should be ignored in making the decision between Medication A and Medication B. The sure
thing principle is a fundamental condition of CEA and additive social utility models.

Inequality Aversion and Framing

Our analysis of inequality aversion and framing is facilitated by the following decision problem:

Suppose 383 newborns suffer a terminal illness, fortunately there are
two medications that could save their lives. For some children given the
medication, they will suffer no ill effects (that is, they will return to
“good health”). While other children when taking the medication, will
suffer from either “poor health” for the rest of their lives or sudden
“death.” “Poor health” is defined as some problems with walking,
washing and dressing; difficulty performing work, study, housework and
leisure activities; and moderate pain and discomfort.
17

Problem 1 below shows the number expected to experience “Good
Health”, “Poor Health” and “Death” with each medication. Please
choose the medication you most prefer to save the newborns.

Problem 1: Good Health Poor Health Death
Medication A 0 23 360
Medication B 19 0 364
Which do you prefer?
Now consider Problem 2:
Problem 2: Good Health Poor Health Death
Medication C 360 23 0
Medication D 379 0 4
Which do you prefer?

18

Problems 1 and 2 we call a “standard frame”. Each presents directly the numbers of persons in
each health group. Pinto et al. (2005) gives examples of this frame for 3 health states and the
person tradeoff method similarly gives numbers of persons achieving health states. Under
additive social utility, we see that Problem 1 and 2 involve the same QALY tradeoff and thus
preference for A over B requires preference for C over D and vice versa. This becomes clear by
application of additive social utility, where we find that if,

23U(Poor) > 19U(Good),

then this implies in Problem 2 the same preference relation, because by adding 360U(Good) to
each side of the inequality, 23U(Poor) > 19U(Good), we get,

360U(Good) + 23U(Poor) > 379U(Good),

which by Equation 1 describes preference in Problem 2. Clearly, were we to begin with
23U(Poor) < 19U(Good) in Problem 1, the converse holds.

19

Therefore, a person choosing either A and D or B and C is inconsistent with additive social utility.
Now consider problems 3 and 4 with added instruction, “…. In the table below, the newborns
have been numbered from 1 to 383, and the outcomes (“Good Health,” “Poor Health,” and
“Death”) are reported for the 383 newborns with each medication.

Please choose the medication you most prefer to save the newborns”:

Problem 3: Newborn #: 1 – 4 5 – 23 24 – 383
Medication A: Poor Health Poor Health Good Health
Medication B: Death Good Health Good Health

Which do you prefer?

Problem 4: Newborn #: 1 – 4 5 – 23 24 – 383
Medication C: Poor Health Poor Health Death
Medication D: Death Good Health Death
Which do you prefer?

Problems 3 and 4 are an alternative frame of Problems 1 and 2. Unlike Problems 1 and 2, 3 and
4 group persons so that those receiving the same outcome regardless of decision choice are
identified; persons 24-383 receive a “sure-thing” irrespective of policy. In Problem 3 that sure
20

thing is “Good Health” and in Problem 4 it is “Death”. Problems 3 and 4 are “the sure thing
frame”. In each question, a person maximizing an additive social utility function eliminates
persons 24-383 from consideration, thus rendering the Problems 3 and 4 effectively the same;
because the tradeoff is the same for persons 1-4 and persons 5-23.

In this paper, we report an experiment which examines the rate of adherence to additive social
utility principles under the standard frame and the sure thing frame. The issue as to whether
numeric sensitivity is linear in numbers has received much attention in economics and
psychology. Human beings do not appear to have the capabilities to easily register response
changes that are linear in numeric changes in decision under risk (Kahneman & Tversky, 1979),
the perception of money (Shafir et al., 1997) and compensation to achieve fairness (Mellers &
Hartka, 1989). It is likely that the same phenomena also occurs in the perception of health.

Research suggests, however, that linearity may be improved when underlying qualitative
preference principles (such as the “Sure Thing” principle) are made transparent to the subjects.
For example, the linear perception of probability is observed more often when common
consequences are made clear in question format (Birnbaum, 2004; Keller, 1985; Moskowitz,
1974). The possibility exists then that the degree to which empirical preferences support the
use of the additive social utility framework depends on how questions are framed or formatted.
Such is the topic of this paper. We seek to study if the additive social utility models proposed in
the literature are more plausible empirically when the sure thing principle is better explicated in
the choices. If so, this would have implications for how social utilities ought to be elicited. In
21

addition, this may imply that social preferences are affected by how problems are framed. And,
policy makers could benefit from learning that their preferences may be influenced by how
information is presented to them.

2. Experiment 1

We ran two separate experiments to test for violations of the sure thing principle. The first of
these experiments is described below

2.1 Methods

Subjects

The subjects were 162 pharmacy students from the University of Southern California, School of
Pharmacy and Loma Linda School of Pharmacy in the United States; of which 44 students were
male and 118 were female. Subjects volunteered to participate in the experiment and those
who completed the survey received extra credit for their class.

22

Design and Procedure

Mode of Administration: Subjects completed a paper-based survey in class . All subjects
completed the survey at the same time.

Survey contents: The survey contained 4 questions (not counting filler questions). Each
question asked participants to select one of two possible treatments with each treatment
resulting in a different distribution of outcomes for the treated population. After treatment,
patients could have one of three outcomes: “Good Health”, “Poor Health”, or “Death.” We
defined “Good Health” as “health with no symptoms or problems” and “Poor Health” as “some
problems with walking, washing and dressing; difficulty performing work, study, housework and
leisure activities; and moderate pain and discomfort.” In each experiment, two questions had a
“standard frame”, indicative of commonly asked questions in the equity literature. In addition,
two questions had a “sure thing” frame, in which common outcomes between the two
treatments were made apparent. Frame order was randomized for each of the participants.

23

The first medication listed always had 19 fewer people in “Good Health”, 23 more people in
“Poor Health” and 4 fewer people in the “Death” state relative to the second medication listed.
The only aspect that varied between questions was the number of patients unaffected by
treatment choice. Two additional questions acted as fillers to minimize memory of responses
across frame.

The questions from the first experiment are reproduced in Figure 1.

Statistical Analysis

We examined the proportion of violations of the “sure-thing” principle under the “standard”
frame” and the “sure-thing” frame. A violation under the “standard frame” was defined as the
proportion of subjects who switched their preference of medication A (medication B) in
question 1 to medication D (medication C) in question 2. A violation under the “sure-thing
frame” was defined as the proportion of subjects who switched their preference of medication
A’ (medication B’) in question 3 to medication D’ (medication C’) in question 4.

First, we computed the proportions that switched preference (“sure-thing” principle violation) in
both frame conditions; then assessed the significance of the difference between the proportions
of the two frame conditions using McNemar’s test for equality of correlated proportions.
Analyses were performed by using STATA software version 10.0 (StataCorp, College Station, TX).
24

2.2 Results

The proportion of violations of additive social utility (indicated by switched preference) in the
“standard” frame was 0.44 (72/162); while in the “sure-thing” frame, the proportion was 0.28
(45/162). The McNemar’s test indicated that there was significant difference in proportions of
violations between the “standard” frame and the “sure-thing” frame (p <0.002). 29% (47/162)
of subjects had a standard frame only violation, 15% (25/162) had a sure-thing only violation
and 15% (25/162) had a violation in both frames. Hence of the 162 subjects only 1 out of 6.5
violated the “sure-thing” principle in both frames.

3. Experiment 2

One concern with Experiment 1 is that the format of the “sure-thing” frame is different than
that of the “standard” frame. In the standard frame the headings of the columns are health
states; in the sure-thing frame they are numbers referring to newborns. This change in format
could possibly confound our results. To address this concern we designed a second experiment.
In Experiment 2, the format of both frames are identical and all column headings are health
states. The only exception is an added column in the “sure thing” frame that obviates the
common elements of each treatment.
25

3.1 Methods

Subjects
The subjects were 183 pharmacy students from the University of Southern California, School of
Pharmacy in the United States; of which 61 students were male and 122 were female. Subjects
in this experiment were also volunteers and those who completed the survey received extra
credit for their class. No respondent who participated in experiment 1 also participated in
experiment 2.

Design and Procedure

Mode of Administration: Subjects were enrolled in one of five computing lab sessions with
between 30 and 40 subjects per session. A computer-based survey was administered using
Qualtrics survey software. All five administrations of the survey were completed within a three
day period.

Survey contents: The instructions and definitions of health states for the second survey were
identical to that of the first. Frame order was still randomized for each of the participants. 18
26

filler questions were used between frames. The filler questions in the second experiment were
for part of a separate, unrelated study being conducted by the current study’s authors.

The questions from both experiments are reproduced in Figure 1.

Statistical Analysis

The statistical analysis of Experiment 2 was identical to that of experiment 1.

3.2 Results

The proportion of violations of additive social utility (indicated by switched preference) in the
“standard” frame was 0.31 (56/183); while in the “sure-thing” frame, the proportion was 0.08
(15/183). The McNemar’s test indicated that there was significant difference in proportions of
violations between the “standard” frame and the “sure-thing” frame (p < 0.001). 27% (49/183)
of subjects had a standard frame only violation, 4% (8/183 ) had a sure-thing only violation and
4% (7/183) had a violation in both frames. Hence of the 183 subjects only 1 out of 25 violated
the “sure-thing” principle in both frames

27

Table 2-1. Violations of the Sure Thing Principle by Frame
Experiment 1
Frame Type n # of violations violation %
Standard 162 72 44%
Sure Thing 162 45 28%

Table 2-2. Violations of the Sure Thing Principle by Frame
Experiment 2
Frame Type n # of violations violation %
Standard 183 56 31%
Sure Thing 183 15 8%

4 Discussion

Prior studies on equity assume a numerical equity model and then test numerical parameters
under model assumptions (Bleichrodt et al., 2005; Dolan et al., 2005). The parameters index the
degree of deviation from traditional health economic models that try to maximize health in
society without any regards to the distribution of health. These studies have generally found
that these traditional models fail and that respondents do exhibit a preference for equity. In
contrast, our current work emphasizes the testing of a qualitative law that is implicit in additive
social utility models. As has been stated elsewhere, the testing of qualitative laws has the
distinct advantage of focusing statistical power on the critical differences between numerical
models (Krantz & Tversky, 1971).

28

We hypothesized that in prior studies the way questions were framed would distort
respondents’ preferences for equity. Our findings agreed with our hypothesis; different frames
of equity questions yielded different results with respect to postures toward inequality. The
frame commonly used in the literature generated more violations of the sure thing principle.
Our finding is consistent with other studies on equity and framing which have found differences
in inequality aversion that are frame dependent (Ubel et al., 2001; Schwappach, 2005). We note
that standard frames emphasize the number or proportion of persons receiving an outcome. In
order for respondents to satisfy the sure thing principle under such a frame, respondents must
faithfully register response changes that are linear in stimulus changes. Such linearity
requirements may be too difficult to adhere to because of the potential for nonlinearity in
numerical perception. Further, empirical separation of numerical perception and true posture
of aversion to inequality are hard to obtain under this standard frame. These frames can be
improved by clarifying common outcomes between treatment options.

Our results have an important normative implication. Health care resource allocation is a
prescriptive activity that ideally should not be affected by biases in people’s preferences. Our
data suggest that people behave according to the sure thing principle when common outcomes
between treatments are made clear but not when they are obfuscated. Hence, our data suggest
that an additive social evaluation function corresponds closely with how people feel about
equality.

29

Limitations and Avenues for Future Research

This study is limited in that it only applies to additive social choice models. Other models have
been proposed that do not require the sure thing principle as an underlying preference
condition. One example of such a model is the Rank-Dependent QALY model proposed by
Bleichrodt, Diecidue, and Quiggin (2004).

Although violations of the sure thing principle are minimized with the sure thing frames,
violations still occur even after making the sure thing apparent. Future studies may consider
resolving such inconsistencies by asking the respondents who violated the sure thing principle to
reconsider their inconsistent choices. The paper by Payne et al (1999) is a good exposition of
this approach.

Our results suggest that different frames focus attention on different aspects of the decision
problem. Whether or not a particular frame is “more correct” than another is a matter for
debate. We only conclude that frames matter in social choice and that frames may be chosen to
achieve greater consistency with preference assumptions of the social choice model being used.

30

Another limitation of this study is that we use a convenient sample of students instead of a
representative sample of the general population. However, we suspect that the framing effect
found in this study is a “cognitive bias” common to all persons. Moreover, it is common to use
convenience samples to test new concepts. Future studies may wish to further validate our
study in a more general sample.

Finally, future studies may wish to test different equity questions to demonstrate how violations
of the sure thing principle vary by problem type. We focus on one problem in the present study
to make the framing problem clearer to the reader.

Conclusion

In conclusion, our study shows that preferences for equality are volatile and the common way of
asking for preferences for equality tends to violate the sure thing principle. When an additive
social utility model is assumed, question frames that occasion preferences consistent with the
sure thing principle are desirable because they are more likely valid when this is the case. We
hope that these findings will serve as a caveat when considering the role of preferences for
equality in health policy.

31

Funding
This work was supported by a Baxter Doctoral Training Fellowship in Pharmaceutical Economics
and Policy.

Figure 2-1. Questions Asked in Experiment 1 and Experiment 2
Experiment 1:
Standard Frames (Q1&Q2) “Sure Thing” Frames (Q3&Q4)
Problem 3: Newborn #
Problem 1: Good Health Poor Health Death 1-4 5-23 24-383
Medication A 0 23 360 Medication A’: Poor Health Poor Health Good Health
Medication B 19 0 364 Medication B’: Death Good Health Good Health
Problem 2: Good Health Poor Health Death Problem 4: Newborn #
Medication C: 360 23 0 1-4 5-23 24-383
Medication D: 379 0 4 Medication C’: Poor Health Poor Health Death
Medication D’: Death Good Health Death
Experiment 2:
Standard Frames (Q1&Q2) “Sure Thing” Frames (Q3&Q4)
Problem 1: Good Health Poor Health Death Problem 3: Death Good Health Poor Health Death
Medication A 0 23 360 Medication A’: 360 0 23 0
Medication B 19 0 364 Medication B’: 360 19 0 4
Problem 2: Good Health Poor Health Death Problem 4: Good Health Good Health Poor Health Death
Medication C: 360 23 0 Medication C’: 360 0 23 0
Medication D: 379 0 4 Medication D’: 360 19 0 4
32
33
Chapter 2 References
Atkinson, A.B., 1970. On the measurement of inequality. Journal of Economic Theory 2: 244–263.
Birnbaum MH. 2004. Causes of Allais common consequence paradoxes: An experimental
dissection. Journal of Mathematical Psychology 48: 87-106.
Bleichrodt H. 1997. Health utility indices and equity considerations. Journal of Health Economics
16: 65-91.
Bleichrodt H, Doctor JN, Stolk E. 2005. A nonparametric elicitation of the equity- efficiency
tradeoff in cost-utility analysis. Journal of Health Economics 24: 655-678.
Broome J. 1988. Goodness, fairness and QALYs. In: Bell, M., Mendus, S. (Eds.), Philosophy and
Medical Welfare. Cambridge University Press, Cambridge, pp. 57–73.
Culyer AJ. 1989. The normative economics of health care finance and provision. Oxford Review
of Economic Policy 5: 34–58.
Doctor JN, Miyamoto JM, Bleichrodt H. 2009. When are person tradeoffs valid? Journal of Health
Economics 28: 1018-1027.
Dolan P. 1998. The measurement of individual utility and social welfare. Journal of Health
Economics 17: 39-52.
Dolan P, Shaw R, Tsuchiya A, Williams A. 2005. QALY Maximisation and people’s preferences: a
methodological review of the literature. Health Economics 14: 197-208.
Harris J. 1988. More and better justice. In: Bell, M., Mendus, S. (Eds.), Philosophy and Medical
Welfare.Cambridge University Press, Cambridge, pp. 75–96.
Kahneman D, Tversky A. 1979. Prospective theory: an analysis of decision under risk.
Econometrica 47(2): 263-291.
Keller LR. 1985. The effects of problem representation on the sure-thing principle and
substitution principles. Management Science 31: 738-751.
Krantz DH, Tversky A.1971. An exchange on functional and conjoint measurement. Psychological
Review 78(2): 457-458.
Lockwood M. 1988. Quality of life and resource allocation. In: Bell, M., Mendus, S. (Eds.),
Philosophy and Medical Welfare. Cambridge University Press, Cambridge, pp. 33–55.
Mandelblatt J. 2009. Effects of mammography screening under different screening schedules:
model estimates of potential benefits and harms. Annals of Internal Medicine 151: 738-747.
Mellers B, Hartka E. 1989. Test of a subtractive theory of “fair” allocations. Journal of
Personality and Social Psychology 56: 691-697.
Moskowitz H. 1974. Effects of problem presentation and feedback on rational behavior in Allais
and Morlat type problems. Decision Sciences 5: 225-242.
34
Payne JW, Bettman JR, Schkade DA Measuring constructed preferences: towards a building
code. Journal of Risk and Uncertainty 19(1-3): 243-270
Pinto-Prades JL, Abellan-Perpinan JM. 2005. Measuring the health of populations: the veil of
ignorance approach. Health Economics 14(1): 69-82.
Savage LJ. 1954. The Foundations of Statistics. Dover Publications, Inc. New York.
Schwappach DLB. 2005. Are preferences for equality a matter of perspective? Medical Decision
Making 25(4): 449-459.
Shafir E, Diamond P, Tversky A. 1997. Money illusion. The Quarterly Journal of Economics
112(2): 341-374.
StataCorp, College Station, TX, (http://www.stata.com).
Stolk EA. 2003. Are patients and the general public like-minded about the effect of erectile
dysfunction on quality of life. Urology 61: 810-815.
Szabo L. 2009. Women are insistent on mammograms, poll shows. USA Today. 23 Nov.
Ubel PA, Baron J. Asch DA. 2001. Preferences for equity as a framing effect. Medical Decision
Making 21: 180-189.
Wagstaff A. 1991. QALYs and the equity-efficiency trade-off. Journal of Health Economics 10:
21–41.
Wakker PP, Kobberling V, Schwieren C. 2007. Prospect-theory’s diminishing sensitivity

35
Chapter 3. The Equity-Efficiency Tradeoff and Cumulative Prospect Theory: Extending the
Rank-Dependent QALY Model to Reference Dependence

1. Introduction

A cost effectiveness analysis typically presents an incremental cost-effectiveness ratio (ICER),
which relates the incremental cost that society must bear to the benefit the intervention will
provide to the patient in terms of quality of life years (QALYs) gained. Cost-effectiveness
analysis is usually based on the assumption of equity neutrality which makes no distinctions as
to how the QALYs are distributed in the population. For example, a treatment that gives an
additional QALY to a person who is already in relatively good health is valued the same as a
treatment (with similar costs) that gives an additional QALY to a patient who is near death. This
assumption of equity neutrality may not reflect actual societal preferences. People may be
willing to sacrifice some efficiency for equity.

Equity Models in the Literature

Given that equity is a concern, how can we incorporate it into cost-effectiveness analysis?
Several different methods have been proposed in the literature including Bleichrodt’s
multiplicative social welfare function (1997), Williams’ ‘fair innings’ approach (1997), Dolan’s
iso-elastic social welfare function (1998) and Bleichrodt et al.’s rank-dependent QALY model
(2004). We will focus on the rank-dependent QALY model because it is more general in form
than the other equity models proposed in the literature, holding each of the others as a special
36
case. Further, the elicitation of its equity weights is straight forward, and the model can easily
be used in cost effectiveness analysis.

The Rank-Dependent QALY Model

The Rank-Dependent QALY model has two main components that determine society’s
preference over QALY-profiles. The first component, denoted by π
j
, models society’s equity
weights and the second component, denoted by U(q
i
), models a social utility function for
quality-adjusted life expectancy. Bleichrodt, Crainich, and Eeckhoudt (2008) refers to the
former as the “dual” model and the latter as the “utility” model. We will adapt this terminology
for the present paper. The formula for this can be seen in the following equation:

∑
=
n
i
i i
q U
1
) ( π [1]

Bleichrodt, Crainich, and Eeckhoudt distinguish between the equity concepts underlying the
utility model and the dual model: “The former reflects an attitude towards health (extra health
is more desirable when in poor health than when in close to perfect health), whereas the latter
expresses an attitude towards inequality (inequality is undesirable).” The study conducted by
Bleichrodt, Doctor, and Stolk (2005) reflects a combination of these two models as does the
present study. The Bleichrodt, Doctor, and Stolk (2005) study found the social utility function
for QALYs to be almost linear. In other words, they found that extra health for those poor in
health was valued the same as extra health for those rich in health. In addition, they found that
respondents have a strong aversion to inequality as measured by the “dual” model.
37

In their elicitation of the Rank-Dependent QALY model, Bleichrodt, Doctor, and Stolk (2004)
found that the elicited equity weights (per the “dual” model) were determined by both
preferences for equity and by a behavior they defined as ‘insensitivity to group size.’
Insensitivity to group size describes a psychological phenomenon where people tend to
overestimate small proportions and underestimate large proportions. For example, if treatment
A were to give 10 QALYs to 5% of the population and give 10 QALYs to 95% of the population,
people would overestimate the 5% proportion and underestimate the 95% proportion when
valuing the treatment option. This insensitivity to group size distorts a person’s true preference
for equity and thus results in biased estimates of equity weights. Bleichrodt, Doctor, and Stolk
corrected for insensitivity to group size by estimating the following parametric form for the
equity weighting function which was first proposed by Goldstein and Einhorn (1987):

,
) 1 (
) (
γ γ
γ
δ
δ
p p
p
p w
− +
= [3]

where γ determines the sensitivity to group size and δ measures preferences for equality. For γ
values less than 1, we find insensitivity to group size and δ values less than 1 indicate an
aversion to inequality. Because insensitivity to group size and equity weights are approximately
independent, insensitivity to group size can be correct for by replacing γ with 1 and using the
calculated δ to estimate the true equity weights.

38
Potential Problems with the rank-dependent QALY model

In practice, policy choices that draw a line between funded and unfunded treatments always
involve choosing to distribute gains and losses to members of society. The rank-dependent
QALY model assumes a decision maker does not distinguish gains and losses in choosing QALY
allocations. Considerable research in behavioral economics suggests that the carriers of value in
decisions are gains and losses, not the final outcomes (Kahneman & Tversky, 1979). This theory
of economic choice, called prospect theory, has revolutionized how economic behavior is
described. It is likely that the rank-dependent QALY model could be improved by incorporating
a decision maker’s attitude toward gains and losses. Our belief is that decision makers are more
concerned with how decisions made today will change the expected QALYs of various members
of their populace and that these changes will be coded as “gains” and “losses” as is the case in
prospect theory.

There are also concerns regarding the utility model elicited in the Bleichrodt, Doctor and Stolk
study. They found significant variance in respondents’ utility functions but on average they
were linear, a finding Bleichrodt himself found to be somewhat surprising (Bleichrodt, Crainich,
and Eeckhoudt, 2008). We will investigate the shape of the utility function further in the
present study.

2. The Rank Dependent QALY-impact model

The idea of the Rank Dependent QALY-impact model is to apply Quiggin’s rank-dependent
method separately for losses and gains and then sum the two resulting evaluations. A weighting
39
function w
+
is defined for the proportions associated with gains and a separate weighting
function w
-
is defined for proportions associated with losses. Suppose that x
1
≤
…
≤

x
k
≤ 0 ≤ x
k+1
≤x
n.
Then the value of the scenario (x
1
, p
1
;…; x
n
; p
n
) is given by the following formula:

∑

∑

Where the equity weights are defined by:

i=1

2

1 1

i=n

The scale q is the familiar one for quality-adjusted life expectancy. This scale is commonly
assumed to be linear in the health economic literature. For example, linearity means that the
social utility gained by moving a patient from 2 QALYs to 3 QALYs is worth the same as moving
another patient from 52 QALYs to 53 QALYs. We do not make this assumption in the present
paper. We allow for a non-linear social utility function for QALYs.

∑

∑

40
In particular, we assume the social utility function for QALYs is a power function and thus U(q
i
) =
q
i
r
.

∑

∑

A policy maker who is a QALY-maximizer will have an r equal to one. A policy maker who has a
diminishing marginal utility for QALYs will have an r less than one. A policy maker with an
increasing marginal utility for QALYs will have an r greater than one.

Further, we assume that the social utility function for gains of QALYs is different than the social
utility function for losses of QALYs. Thus we have two parameters for the power utility function,
r
+
and r
-
.

∑

∑

The importance of measuring a utility function for QALYs.

It is important to measure a policy makers utility function for QALYs prior to estimating his
equity weighting function. Failing to measure a utility function and merely assuming that his
utility function is linear can lead to misleading estimates of a policy maker’s preference for
equity. A preference for a more equal distribution of QALYs is often a product of two
conceptually different factors, a preference for equality and the marginal utility a QALY
provides. For example, a policy maker may prefer a policy that gives 6 QALYs to person A and 4
QALYs to person B over a policy with similar costs that gives 7 QALYs to person A and 3 QALYs to
41
person B for two reasons: 1) the utility a policy maker receives from moving person A from 3 to
4 QALYs is greater than the utility he loses by moving person B from 7 to 6 QALYs and 2) the
policy maker prefers to have a more equitable distribution of QALYs. A policy maker’s
preference for equity will be overstated if they have a decreasing marginal utility function and a
linear utility function is assumed.

The Equity Weighting Function (The “Dual” Model)

After their utility function for QALY profiles is determined, a policy maker’s equity weighting
function must be established. In our model we use a weighting function that has previously
been used by Birnbaum and McIntosh (1996), Gonzales and Wu (1999), Kilka and Weber (1998),
Lattimore, Baker, and White (1992), and Tversky and Fox (1995):

, 0 , ,
) 1 (
) ( >
− +
= δ γ
δ
δ
γ γ
γ
p p
p
p w [4]

which has a useful odds formulation:

, 0 , , )
1
(
) ( 1
) (
>
−
=
−
δ γ δ
γ
p
p
p w
p w
[5]

Where δ measures an individual’s posture towards equity and γ measures the shape of their
utility function across QALY profiles. This form encompasses equity weighting functions with
both concave and convex regions.
42
Gains vs. Losses

In this study we will be measuring separate utility functions and weighting functions for “gains”
and for “losses.” It is our hypothesis that that these functions will be statistically significantly
different. Such a finding would signify that preferences for equity in a new healthcare policy
depend upon whether a policy expands or curtails existing coverage.

3. Elicitation

3.1 Elicitation of the utility function

Table 3-1. Scenarios used in Elicitation of Utility Function
Basic Times 2 Times 3 Plus 10 Plus 20 Zero
1/10 2/20 3/30 11/20 21/30 0/32
2/10 4/20 6/30 12/20 22/30 0/36
3/10 6/20 9/30 13/20 23/30
4/10 8/20 12/30 14/20 24/30
1/12 2/24 3/36 11/22 21/32
2/12 4/24 6/36 12/22 22/32
3/12 6/24 9/36 13/22 23/32
4/12 8/24 12/36 14/22 24/32
Scenarios presented in the form z/x with .25 of population receiving x QALYs and .75 of
population receiving z QALYs

Let (x, .25, z) denote the rank-ordered QALY-profile that gives (takes away) x QALYs to .25 of
the population and z QALYs to .75 of the population. Respondents were asked to complete 42
gain scenarios and 42 loss scenarios detailed in table 1. In each scenario, respondents were
confronted with an inequitable health policy that gave (took away) x QALYs to 25% of the
population and z QALYs to 75% of the population and an equitable health policy that gave (took
away) .25*x +.75z QALYs to 100% of the population. Respondents chose between the
43
inequitable health policy and the equitable health policy. We then determined the number of
life years needed in the equitable health policy to make the subject indifferent between the
equitable health policy and the inequitable health policies. We call this indifference point the
constant allocation equivalent (CAE). For more detail on the method used to determine the
CAE, please refer to section 6 below. The CAE was recorded for each of the scenarios listed in
table 1 above. We then measured a gains power utility function and a losses power utility
function using this data. The function we specified was the following:

CAE
r
= w(.25)*x
r
+ [1-w(.25)]*z
r

This function was evaluated for each respondent using non linear least squares. The starting
values used were w(.25)=.25 and r=1. The elicited values for r for each respondent were then
used in the elicitation of the each respondent’s equity weighting function.

3.2 Elicitation of the equity weighting function

Table 3-2. Scenarios used in Elicitation of Weighting Function
Proportion
Outcomes .01 .05 .10 .25 .50 .75 .90 .95 .99
(0, 1) x x x
(0, 5) X x x
(0, 10) x x x x X
(0, 20) x X x x x
(0, 40) x x
Scenarios marked by an x were used in the elicitation of the weighting function.
Outcomes are presented in the form (0, x) with p% of the population receiving
(losing) x QALYs and (1-p)% of the population receiving 0 QALYs

44
To elicit the equity weighting function, respondents were asked 18 gain scenarios and 18 loss
scenarios detailed in table 2 listed above. In each scenario a CAE was determined using the
same method that was used to determine the utility function (see section 5.1). We then fit the
data to the following weighting function

, 0 , , )
) 1 (
(
) ( 1
) (
>
−
=
−
δ γ δ
γ
p
p
p w
p w

By first taking the log of both sides:

, 0 , , )
) 1 (
ln( ln
) ( 1
) (
ln >
−
+ =
−
δ γ γ δ
p
p
p w
p w

Where w(p) = (CAE/x)^r.

We solved for δ and γ using ordinary least squares.

45
4. Experiment

Subjects

The subjects were 113 pharmacy students from the University of Southern California, School of
Pharmacy in the United States; of which 29 students were male and 84 were female. Subjects
volunteered to participate in the experiment and those who completed the survey received
extra credit for their class.

Design and Procedure

Mode of Administration: Subjects were enrolled in one of four computing lab sessions with
between 20 and 37 subjects per session. A computer-based survey was administered using
Qualtrics survey software. All four administrations of the survey were completed within a two
week period.

Survey contents: The survey contained 120 scenarios. These questions were split into 3
segments. Participants were given 45 minutes to complete each segment. A 10 minute break
was given between segments. The first segment contained 36 scenarios and was used to
estimate the equity weighting function (the dual model). The computer displayed an
inequitable health policy (e.g., 25% of the cohort will receive an additional 15 QALYs, 75% of the
cohort will receive an additional 5 QALYs) and its average value (7.5 QALYs in this example). The
display also included an equitable health policy in which everyone received the average number
of QALYs (7.5 QALYs in this example). Subjects indicated a preference for one of the two
46
policies. A follow-up question was asked which displayed a descending series of up to 15
equitable health policies (gains or losses) linearly spaced between the extreme values of the
inequitable health policy. The equitable policies displayed depended upon the subject’s
previous answer. For example, if the subject chose the equitable health policy in the first part of
the example question, the equitable health policies displayed would be 7.5, 7, 6.5, …, 1, 0.5, 0.
The subject then indicated the point at which they would be indifferent between the equitable
health care policy and the inequitable health care policy. We call this indifference point the
constant allocation equivalent.

This segment of the experiment consisted of 18 positive and 18 negative scenarios. In each of
these scenarios the constant allocation equivalent was recorded. Example questions can be
found in the Appendix B.

We used methods similar to Miyamoto & Eraker (1989) to estimate utility curvature. The
second and third segments of the survey consisted of 42 scenarios for gains and 42 scenarios for
losses. In all scenarios, p was set to .25 (In gains scenarios, 25% of the treated cohort would
receive an additional x years of life and 75% of the cohort would receive an additional y years of
life with certainty.) For example, consider the 3/12 “gain” scenario. In this scenario 25% of the
treated cohort receives an additional 3 years of healthy life beyond their current life expectancy
and 75% of the cohort receives an additional 12 years of healthy life beyond their current life
expectancy. Similarly, we asked a “loss” scenario in which currently treated patients would lose
their treatment. 25% of the cohort would lose 3 years of life from their current life expectancy
and 75% would lose 12 years of life from their current life expectancy.

47
5. Results
Table 3-3. Demographics
Variable N %
Age
21-25 69 61%
26-30 36 32%
31-35 7 6%
36-40 1 1%
Sex
Male 29 26%
Female 84 74%
Race
Asian 71 63%
Hispanic 6 5%
White 25 22%
Other 7 6%
Multiracial 2 2%
Prefer not to respond 2 2%
Political Affiliation
Democrat 51 45%
Republican 14 12%
Independent 16 14%
Other 10 9%
Decline to State 22 19%
Prior participation in a choice-
based experiment?
Yes 21 19%
No 92 81%
Special training in decision
theory?
Yes 7 6%
No 106 94%

Tables 4 and 5 below report the median constant allocation equivalents for each of the 18 gain
scenarios and 18 loss scenarios. The rows list the possible outcomes of each scenario and are
listed in the form (0. x) where p% of the population receive x QALYs and (1-p)% of the
population receive 0 QALYs. The columns list the proportions of patients who receive x QALYs.
48
The constant allocation equivalent divided by x (CAE/x) in each loss scenario is greater than or
equal to the CAE/x in the corresponding gain scenarios.

Table 3-4. Median constant allocation equivalents (in years) for gain scenarios
Proportion
Outcomes .01 .05 .10 .25 .50 .75 .90 .95 .99
(0, +1) 0.25 0.42 0.58
(0, +5) 0.50 2.00 3.50
(0, +10) 0.58 2.50 3.00 6.00 7.50
(0, +20) 0.20 2.00 7.00 15.00 18.00
(0, +40) 0.40 37.00
Note: The two outcomes of each scenario are given in the left-hand side of each row; the
probability of the second (i.e., more extreme) outcome is given by the corresponding column. For
example, the value of .25 in the first row is the constant allocation equivalent of the scenario (+0
years, .75; +1 years, .25).

Table 3-5. Median constant allocation equivalents (in years) for loss scenarios
Proportion
Outcomes .01 .05 .10 .25 .50 .75 .90 .95 .99
(0, -1) 0.25 0.50 0.63
(0, -5) 0.50 2.50 3.50
(0, -10) 1.00 2.50 5.00 6.00 8.00
(0, -20) 1.00 2.50 10.00 15.00 18.00
(0, -40) 1.00 38.00
Note: The two outcomes of each scenario are given in the left-hand side of each row; the
probability of the second (i.e., more extreme) outcome is given by the corresponding column.
For example, the value of -.25 in the first row is the constant allocation equivalent of the scenario
(-0 years, .75; -1 years, .25).

Figure 1 below juxtaposes the median weighting function for gains next to the median weighting
function for losses. The weighting function for losses is close to the 45 degree line across all
proportions indicating equity neutrality. The weighting function for gains is close to the 45
degree line for low proportions and then deviates below the 45 degree line for medium to large
proportions. This indicates equity neutrality for low proportions and equity seeking preferences
for medium to large proportions.

49
Table 6 summarizes the results of the Wilcoxon Signed-Rank Test. δ, which measures posture
towards equity, is statistically significantly different between the loss and gain scenarios
(p<.0001). It is important to remember that this table assumes linear utility functions for both
losses and gains of QALYs.

0.000
0.100
0.200
0.300
0.400
0.500
0.600
0.700
0.800
0.900
1.000
0 0.2 0.4 0.6 0.8 1
W(p)
p
Figure 3-1. Median W(p) by p - assuming r=1
Gains
Losses
Linear (Linear)
50
Table 3-6. Median Gonzales and Wu Parameters for Gains and Losses
- Before r adjustment
Parameter Gains Losses
γ 0.73 0.69
δ 0.57 1.25
* δ is statistically significantly different between gain scenarios and loss
scenarios (p<.001) under the Wilcoxon Signed-Rank Test.
** δ is statistically significantly different between gain scenarios and equity
neutrality (p<.001) under the Wilcoxon Signed-Rank Test.
*** δ is statistically significantly different between loss scenarios and equity
neutrality (p<.001) under the Wilcoxon Signed-Rank Test.

The assumption that a social value of a QALY is constant regardless of how many QALYs a person
has (ie there is no diminishing marginal utility for QALYs) is frequently made in the health
economics literature. The results of our utility elicitation (table 7, diagram 2) indicate that this is
not a valid assumption to make and that subjects do indicate having a diminishing marginal
utility for QALYs. This is especially apparent in the loss scenarios. The utility lost from moving
from losing 0 QALYs to losing 1 QALY is much larger that the utility lost from moving from losing
39 QALYs to losing 40 QALYs. In our utility model, we assumed that the U(71 QALYs)-U(70
QALYs) = 1 unit of utility and U (0 QALYs) = 0. The choice of these values is arbitrary and will not
affect the relative rank of therapies in our model.

Table 3-7. Median Values for r
r
Gains 0.66
Losses 0.36

51

After adjusting for each respondent’s utility function for QALYs, the equity weighting function
for losses and gains are much closer than was the case in the unadjusted equity weighting
function (Figure 3). The Wilcoxon Signed-Rank Test indicates the gains and losses weighting
functions are no longer statistically significantly different after utility adjustment(Table 8). This
indicates that differences in preferences for equity between gains and loss scenarios are due
mainly different utility functions for gains and losses.

0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
11.00
12.00
13.00
14.00
15.00
16.00
0 20 40 60 80 100
U'(QALYs)
QALYs
Figure 3-2. Elicited Marginal Social Utility
Function for QALYs
U'(QALYs) - Gains
U'(QALYs) - Losses
52
Table 3-8. Median Gonzales and Wu Parameters for Gains and Losses
After r adjustment
Parameter Gains Losses
γ 0.63 0.67
δ 0.95 0.78
* δ is not statistically significantly different between gain scenarios and loss
scenarios under the Wilcoxon Signed-Rank Test.
** δ is not statistically significantly different between gain scenarios and
equity neutrality under the Wilcoxon Signed-Rank Test.
*** δ is not statistically significantly different between loss scenarios and
equity neutrality under the Wilcoxon Signed-Rank Test.

0.000
0.100
0.200
0.300
0.400
0.500
0.600
0.700
0.800
0.900
1.000
0 0.2 0.4 0.6 0.8 1
W(p)
p
Figure 3-3. Median W(p) by p - adjusting
for r
Gains
Losses
Linear (Linear)
53
6. Implementation in health policy

In the 2005 Rank Dependent QALY model, Bleichrodt Doctor and Stolk proposed a model of
equity that looked at preferences for equity in terms of lifetime QALYs. In their framework, a
policy maker would prefer to give a QALY to someone whose expected number of lifetime
QALYs is less than the population average relative to someone who is expected to live a full
healthy life. In the present paper we take a similar approach with one major difference. Our
framework assumes that policy makers’ preferences for equity vary based on whether they are
looking to expand or curtail existing health coverage.

To illustrate how our findings can be implemented in health policy we have computed equity-
adjusted cost effectiveness ratios for 12 treatments. We chose the same 12 treatments that
were considered in the Bleichrodt, Doctor, and Stolk (2005) paper to facilitate comparability
between the models. It is important to note that this is only an example of how our model
could be applied and is not meant to be a guide for policy making.

Application of the “Dual” Model – Determining Equity Weights

We used equation 4 and the elicited δ for “gains” and “losses” to compute the equity weights
for the proportions of people in each expected lifetime QALY group (listed in the second column
of table 9 below). We then divided the equity weights by the group size. Finally, we divided the
resulting ratios by the ratio for the reference group. In our case, we chose the 65-70 group to
be our reference group (our rationale for this can be found in the subsequent paragraph). This
procedure produces normalized equity weights for each proportion.
54
There are two assumptions we made when creating this application of our model. The first
assumption is that 65-70 expected lifetime QALYs is an appropriate reference group. This
assumption is based on Willaims’ Fair Innings approach (1997) which found 70 QALYs to be what
society considers as being the ‘normal’ amount a person can hope to enjoy, anything below
which a person may feel “cheated.” This assumption is not crucial to our results. Were we to do
away with it, the resulting equity weights would be similar to what is seen in table 9.

The second assumption is that the correct weights for us to use are the weights that have been
corrected for “insensitivity to group size.” We believe that an individual’s stated preference for
equity is a function of their true preference for equity and a phenomena called “insensitivity to
group size” which occurs when a respondent perceives small proportions as being larger than
they actually are and when they perceive large proportions as being smaller than they actually
are. By correcting for this phenomena (ie by setting γ=1 in equation 4) we believe we are more
accurately reflecting a respondents true preference for equity. It may be the case that some of
what we are correcting is actually true equity preference. However, we believe that the
corrected weights are a more accurate portrayal of equity posture.

55
Table 3-9. Distribution of QALYs and Equity Weights
Equity Weights
Lifetime QALYs Proportion Gains Losses
γ=1, δ=.95 γ=1, δ=.78
<1 0.006 1.039 1.218
1-15 0.003 1.039 1.216
15-30 0.007 1.038 1.212
30-40 0.011 1.037 1.206
40-50 0.032 1.035 1.192
50-55 0.043 1.031 1.168
55-60 0.064 1.025 1.135
60-65 0.111 1.016 1.084
65-70 0.204 1.000 1.000
70-75 0.265 0.977 0.892
75-80 0.214 0.954 0.798
80-82.5 0.033 0.942 0.755
>82.5 0.009 0.940 0.748

The first two columns in table 9 list various groups of the population based on their expected
lifetime QALYs and the proportion of people within each group. These figures are based on
mortality and quality of life estimates from the Netherlands and are reproduced from the study
conducted by Bleichrodt, Doctor and Stolk (2005). The third column lists the equity weights
associated with an expansion in healthcare coverage as measured by the current dual model.
The fifth column lists equity weights associated with a reduction in healthcare coverage as
measured by the current dual model.

Consider three new hypothetical treatments, treatments A, B, and C, that are being considered
by a health plan for addition to formulary. Treatment A would give 1 QALY to patients who fall
in the 15-30 category (ie they can expect to live between 15 and 30 quality adjusted life years in
their lifetime). Treatment B would give 1 QALY to patients who fall in the 65-70 category and
Treatment C would give 1 QALY to patients who fall in the >82.5 category. The elicited “gains”
56
weights for the 15-30 category, the 65-70 category, and the >82.5 category are 1.038, 1, and .94
respectively. This indicates that a QALY given to a person who can only expect to live between
15 and 30 years of age is worth 3.8% more than a QALY given to someone who can expect to
experience between 65 and 70 QALYs in their lifetime and 10.4% more than a QALY given to
someone who can expect to experience more than 82.5 years in their lifetime.
Now consider three existing hypothetical treatments, treatments D, E, and F, that are being
considered for removal from coverage due to budget cuts. Removing treatment A would take 1
QALY away from patients who fall in the 15-30 category. Removing treatment B would take 1
QALY away from patients who fall in the 65-70 category. Removing treatment C would take 1
QALY away from patients who fall in the >82.5 category. The elicited “losses” weights for the
15-30 category, the 65-70 category, and the >82.5 category are 1.216, 1, and .748 respectively.
This indicates that a QALY taken away from a person who can only expect to live between 15
and 30 years of age represents a 21.6% larger loss than a QALY taken away from someone who
can expect to experience between 65 and 70 QALYs in their lifetime and a 62.5% larger loss than
a QALY taken away from someone who can expect to experience more than 82.5 years in their
lifetime.

Application of the Utility Model

The marginal utility function displayed in figure 2 was used to estimate the value of an
additional QALY given the expected lifetime QALYs a person could expect in a given condition.
The social utility gained by giving one QALY to someone poor in lifetime QALYs is worth more
than giving one QALY to someone rich in lifetime QALYs. For example, giving someone with
Congenital Malformation (expected lifetime QALYs of 9.6) is worth twice as much as giving a
57
QALY to someone with Erectile Dysfunction (expected lifetime QALYs of 77). Moreover, losses
loom larger than gains. Taking a QALY away from someone with Congential Malformation
represents a 4 times greater utility loss (3.6 / .9) relative to taking a QALY away from someone
with Erectile Dysfunction.

Table 3-10. Equity-adjusted cost-utility ratios Gains Losses
Condition Treatment
Cost/
QALY Rank
Lifetime
QALYs
U'(QALYs)
Gains
U'(QALYs)
Losses
Equity
Weight
Cost/
U(QALY) Rank
Equity
Weight
Cost/
U(QALY) Rank
Congenital anorectal
malformation Surgery $2,482 1 9.4 2.0 3.6 1.039 $1,195 1 1.216 $567 1
Erectile dysfunction Sildenafil $5,656 2 77 1.0 0.9 0.954 $6,130 2 0.798 $7,535 2
Non-Hodgkin lymphoma Chemotherapy $7,771 3 73.3 1.0 1.0 0.977 $8,084 3 0.892 $8,974 4
Artherosclerosis Clopidogrel $11,629 4 54.9 1.1 1.2 1.031 $10,373 4 1.168 $8,524 3
Benign prostatic
obstruction Finasteride $12,788 5 80.7 1.0 0.9 0.942 $14,259 5 0.755 $18,554 7
Onychomycosis Terbinafine $16,843 6 83.7 0.9 0.9 0.940 $19,058 7 0.748 $25,243 9
Osteoporosis Oestrogen $18,151 7 83.2 0.9 0.9 0.940 $20,495 9 0.748 $27,099 10
High Cholesterol Statins $18,151 8 56.1 1.1 1.2 1.025 $16,402 6 1.135 $13,885 5
Metastatic Breast Cancer Chemotherapy $22,441 9 56.1 1.1 1.2 1.025 $20,279 8 1.135 $17,166 6
Heart Disease Heart Transplant $38,206 10 42.2 1.2 1.4 1.035 $31,004 10 1.192 $23,201 8
End-stage renal disease Kidney Transplant $44,607 11 57.8 1.1 1.1 1.025 $40,726 11 1.135 $34,779 11
Pulmonary Hypertension Lung Transplant $79,412 12 41.6 1.2 1.4 1.035 $64,125 12 1.192 $47,786 12

The first five columns of Table 10 above lists 12 conditions and treatments along with unadjusted cost-effectiveness ratios, a rank which ranks
the treatments by their cost-effectiveness ratio from lowest to highest, and the number of lifetime QALYs a person in each condition can expect
to experience in their lifetime. Each of these columns are reproduced from Bleichrodt, Doctor, and Stolk (2005). The 6
th
and 7
th
columns list the
value of the derivative of the utility function (see table 7 and diagram 2) evaluated at the lifetime QALYs of each condition. This equates to the
marginal utility of a QALY gained (lost) given each condition’s expected lifetime QALYs. The 8
th
and 11
th
columns list the equity weight
58
59

associated with the lifetime QALYs of a given condition (based on Table 9) for the “gains” model
and the “losses” model respectively. The 9
th
and 12
th
columns list the equity-adjusted cost-
effectiveness ratios for each of the models. The 10
th
and 13
th
columns list the cost-effectiveness
rank of each treatment after adjusting for the equity weights.

Table 3-11. Ranking comparison between studies Equity-adjusted Ranks
Condition Treatment
Bleichrodt,
Doctor,
Stolk
(2005)
Current
Study:
Gains
Current
Study:
Losses
Congenital anorectal malformation Surgery 1 1 1
Erectile dysfunction Sildenafil 2 2 2
Non-Hodgkin lymphoma Chemotherapy 4 3 4
Artherosclerosis Clopidogrel 3 4 3
Benign prostatic obstruction Finasteride 7 5 7
Onychomycosis Terbinafine 9 7 9
Osteoporosis Oestrogen 10 9 10
High Cholesterol Statins 5 6 5
Metastatic Breast Cancer Chemotherapy 6 8 6
Heart Disease Heart Transplant 8 10 8
End-stage renal disease Kidney Transplant 11 11 11
Pulmonary Hypertension Lung Transplant 12 12 12

Table 11 compares the treatment rankings from the current study to the rankings in the
Bleichrodt, Doctor, and Stolk (2005) study. Coincidentally, the losses model produces the exact
same rankings as the Bleichrodt, Doctor, and Stolk paper. The gains model has less movement
in rankings relative to the other two models.

60

7. Discussion
In this study we have considered an equity concept similar to that of the Williams’ Fair innings
approach (1997) and the Rank Dependent QALY model (2004, 2005). This equity concept
considers the current distribution of expected total lifetime QALYs in society and postulates that
people may prefer to give a QALY to someone who is poor in health (in terms of expected
lifetime QALYs) relative to someone who is rich in health. We theorized that that preferences
for equity of lifetime QALYs are dependent on a social utility function for QALYs and an equity
weighting function for QALYs (ie the “dual” model). We further theorized that preferences for
equity would depend upon whether a policy was expanding existing coverage or curtailing it and
thus we considered losses and gains separately.

Before correcting for utility curvature (i.e. if we assume a linear utility function for QALYs) we
found that the equity weighting function in the gains scenario were statistically significantly
different than preferences for equity in the losses scenario. In particular, we found that
respondents were more likely to be equity seeking when it came to an expansion of existing
coverage and respondents were more likely to be equity neutral when it came to a reduction of
existing coverage. The one deviation from this pattern came when the proportion of the better
off group was small. When this was the case, respondents tended to be equity averse for loss
scenarios and equity neutral for gains scenarios.

We estimated a utility function for gains and losses of QALYs using a power function. These
utility curves were concave indicating a diminishing marginal utility for QALYs. The marginal
utility curve for losses was steeper than that for gains.
61

After adjusting for utility curvature, the equity weighting functions were no longer statistically
significantly different. Respondents tended to be equity neutral when the better off group was
small and equity seeking when the better off group was moderate to large in size. However,
these effects were not statistically different from equity neutrality. Note that this is only true
for the equity function (ie the “dual” model). Our elicitation still indicates a strong preference
for equity and this preference is captured by the diminishing marginal utility function.

The Bleichrodt, Doctor, and Stolk (2005) study found the social utility function for QALYs to be
almost linear. In other words, they found that extra health for those poor in health was valued
the same as extra health for those rich in health. In addition, they found that respondents have
a strong preference for equity per se, as measured by the dual portion of the model. In the
present study, we have found the opposite to be true. Our elicited social utility function for
both gains and losses are highly concave, indicating that extra health is much more desirable,
from a social perspective, if given to those poor in health relative to those close to perfect
health. Also, if forced to make cuts, respondents would prefer to take health away from those
rich in health rather than those poor in health. After adjusting for the social utility function, we
found almost no desire for equity as measured by the dual portion of the model. Our results
suggest that preferences for equity can be sufficiently measured by a social utility function and
that the “dual” model adds little value.

62

8. Limitations
An inherent problem with this model is that it only considers equity in terms of lifetime QALYs.
Other models, such as the model proposed by Dolan (1995), considers equity of current health
status (moving someone at a .3 health state to a .4 health state may be seen as more desirable
than moving someone from a .9 health state to a 1 health state.) The proportional shortfall
procedure considers the ratio of QALYs lost over the number of QALYs remaining (Stolk 2004).
None of these models consider all aspects of equity. Future studies should focus on
incorporating each of these aspects into their models. Conjoint analyses could potentially be
used to help us understand which aspects of equity are more important to society.
Another limitation of the current study is that we used a convenience sample of students.
However, we also note that the Bleichrodt, Doctor, and Stolk (2005) study analyzed both a
student sample and a general population sample and found almost no difference between the
two. Moreover, it is common to use convenience samples to test new concepts. Future studies
may wish to further validate our study in a more general sample.

63

Chapter 3 References
Bleichrodt, H., Diecidue, E., Quiggin, J., 2004. Equity Weights in the Allocation of Health Care:
the Rank-Dependent QALY Model. Journal of Health Economics 23, 157–171.

Bleichrodt, H., Doctor, J., Stolk, E., 2005. A Nonparametric Elicitation of the Equity-Efficiency
Trade-off in Cost-Utility Analysis. Journal of Health Economics 24, 655–678.

Borger, C., et al. Health Spending Projections Through 2015: Changes on the Horizon. Health
Affairs Web Exclusive. W61: 22 February 2006.

Chateauneuf, A., Wakker, P., 1999. An Axiomatization of Cumulative Prospect Theory for
Decision Under Risk. Journal of Risk and Uncertainty 18:2, 137-145

Fennema, H., Wakker, P.,1997. Original and Cumulative Prospect Theory: A Discussion of
Empirical Differences. Journal of Behavioral Decision Making 10, 53-64

Kahneman, D., Tversky, A.,1979. Prospect Theory: An Analysis of Decision Under Risk.
Econometrica 47:2, 263-291

Tversky, A., Kahneman, D.,1992. Advances in Prospect Theory: Cumulative Representation of
Uncertainty. Journal of Risk and Uncertainty 5, 297-322

64

Bibliography

Atkinson, A.B., 1970. On the measurement of inequality. Journal of Economic Theory 2: 244–263.
Birnbaum MH. 2004. Causes of Allais common consequence paradoxes: An experimental
dissection. Journal of Mathematical Psychology 48: 87-106.
Bleichrodt H. 1997. Health utility indices and equity considerations. Journal of Health Economics
16: 65-91.

Bleichrodt H, Diecidue E, Quiggin J. 2004. Equity Weights in the Allocation of Health Care: the
Rank-Dependent QALY Model. Journal of Health Economics 23: 157–171.

Bleichrodt H, Doctor JN, Stolk E. 2005. A nonparametric elicitation of the equity-efficiency
tradeoff in cost-utility analysis. Journal of Health Economics 24: 655-678.

Bleichrodt H, Crainich D, Eeckhoudt L. 2008. Aversion to health inequalities and priority setting
in healthcare. Journal of Health Economics 27:1594-1604

Borger, C., et al. Health Spending Projections Through 2015: Changes on the Horizon. Health
Affairs Web Exclusive. W61: 22 February 2006.

Broome J. 1988. Goodness, fairness and QALYs. In: Bell, M., Mendus, S. (Eds.), Philosophy and
Medical Welfare. Cambridge University Press, Cambridge, pp. 57–73.

Chateauneuf, A., Wakker, P., 1999. An Axiomatization of Cumulative Prospect Theory for
Decision Under Risk. Journal of Risk and Uncertainty 18:2, 137-145

Cher, DJ, Miyamoto J, Lenert LA. 1997. Incorporating risk attitude into Markov-process decision
models: Importance for individual decision making. Medical Decision Making 17(3): 340-350.

Culyer AJ. 1989. The normative economics of health care finance and provision. Oxford Review
ofEconomic Policy 5: 34–58.

Doctor JN, Miyamoto JM, Bleichrodt H. 2009. When are person tradeoffs valid? Journal of Health
Economics 28: 1018-1027.
Dolan P. 1998. The measurement of individual utility and social welfare. Journal of Health
Economics 17:39-52.
Dolan P, Shaw R, Tsuchiya A, Williams A. 2005. QALY Maximisation and people’s preferences: a
methodological review of the literature. Health Economics 14: 197-208.
Dolan P. 1998. The measurement of individual utility and social welfare. Journal of Health
Economics 17:39-52.

65

Dolan P, Shaw R, Tsuchiya A, Williams A. 2005. QALY Maximisation and people’s preferences: a
methodological review of the literature. Health Economics 14: 197-208.

Edgeworth FY. 1881. Mathematical Physics: An essay on the Application of Mathematics to the
Moral Sciences. 16.

Fennema, H., Wakker, P.,1997. Original and Cumulative Prospect Theory: A Discussion of
Empirical Differences. Journal of Behavioral Decision Making 10, 53-64

Harris J. 1988. More and better justice. In: Bell, M., Mendus, S. (Eds.), Philosophy and Medical
Welfare. Cambridge University Press, Cambridge, pp. 75–96.
Kahneman D, Tversky A. 1979. Prospective theory: an analysis of decision under risk.
Econometrica 47(2): 263-291.
Keller LR. 1985. The effects of problem representation on the sure-thing principle and
substitution principles. Management Science 31: 738-751.
Krantz DH, Tversky A.1971. An exchange on functional and conjoint measurement.
Psychological Review 78(2): 457-458.
Lockwood M. 1988. Quality of life and resource allocation. In: Bell, M., Mendus, S. (Eds.),
Philosophy and Medical Welfare. Cambridge University Press, Cambridge, pp. 33–55.
Mandelblatt J. 2009. Effects of mammography screening under different screening schedules:
model estimates of potential benefits and harms. Annals of Internal Medicine 151: 738-747.
Mellers B, Hartka E. 1989. Test of a subtractive theory of “fair” allocations. Journal of
Personality and Social Psychology 56: 691-697.
Mill J. 1836. On the Definition of Political Economy, and on the Method of Investigation Proper
to It. London and Westminster Review.

Mill J. 1874. Essays on Some Unsettled Questions of Political Economy. 2nd ed. Longmans,
Green,Reader & Dyer. Essay 5.

Moskowitz H. 1974. Effects of problem presentation and feedback on rational behavior in Allais
and Morlat type problems. Decision Sciences 5: 225-242.

Payne JW, Bettman JR, Schkade DA Measuring constructed preferences: towards a building
code. Journal of Risk and Uncertainty 19(1-3): 243-270

Persky J. 1995. Retrospectives: The Ethology of Homo Economicus. The Journal of Economic
Perspectives 9(2): 221-231

Pinto-Prades JL, Abellan-Perpinan JM. 2005. Measuring the health of populations: The veil of
ignorance approach. Health Economics 14(1): 69-82
66

Savage LJ. 1954. The Foundations of Statistics. Dover Publications, Inc. New York.
Schwappach DLB. 2005. Are preferences for equality a matter of perspective? Medical Decision
Making 25(4): 449-459.
Sen AK. 1997. Rational fools: A critique of the behavioural foundations of economic theory.
Philosophy and Public Affairs 6:317-344.

Shafir E, Diamond P, Tversky A. 1997. Money illusion. The Quarterly Journal of Economics
112(2): 341-374.
StataCorp, College Station, TX, (http://www.stata.com).
Stolk EA. 2003. Are patients and the general public like-minded about the effect of erectile
dysfunction on quality of life. Urology 61: 810-815.

Stolk EA. 2004. Reconciliation of economic concerns and health policy: Illustration of an equity
adjustment procedure using proportional shortfall. Pharmacoeconomics 22(17): 1097-1107.

Szabo L. 2009. Women are insistent on mammograms, poll shows. USA Today. 23 Nov.

Tversky, A., Kahneman, D.,1992. Advances in Prospect Theory: Cumulative Representation of
Uncertainty. Journal of Risk and Uncertainty 5, 297-322

Ubel PA, Baron J. Asch DA. 2001. Preferences for equity as a framing effect. Medical Decision
Making 21: 180-189.

Wakker PP, Kobberling V, Schwieren C. 2007. Prospect-theory’s diminishing sensitivity

Wagstaff A. 1991. QALYs and the equity-efficiency trade-off. Journal of Health Economics 10:
21–41.

Williams A. 1997. Intergenerational equity: An exploration of the ‘Fair Innings’ argument.
Health Economics 6: 117-132.

67

Appendix A: The Sure Thing Principle and Additive Welfare Functions
1
For QALY allocations to n persons (Q
1
, … Q
n
), preferences over the product set of such
allocations that satisfy the sure-thing principle imply an additive welfare function W
1
(Q
1
) + … +
W
n
(Q
n
) (Fishburn & Wakker (1995) p.1138-1139). Requiring also that the identity of the QALY
recipient not affect policy preference (anonymity) then yields a welfare function that maximizes
QALYs (Bleichrodt, 1997, Theorem 1). Anonymity is widely regarded as a desirable property for
social choice and, hence, the desirability of additive social utility really hinges on the desirability
of the sure thing principle.

68

Appendix B: Sample Elicitation Questions

Abstract (if available)

Abstract This dissertation investigates methods to incorporate societal preferences for equity in health economic decision making. Cost–effectiveness analysis (CEA) solves the problem of how to prioritize health programs so as to maximize health. However, CEA may not always agree with our social preferences for prioritizing health programs. For example, suppose for a cohort of persons, two health programs deliver at the same cost, the same aggregate health gain. However, the first program gives the health gain mostly to those poor in health and the second program gives it mostly to those rich in health. Individuals may strictly prefer the first health program to the second, yet CEA would consider these health programs equivalent. We call this preference behavior ‘inequality aversion’. Inequality aversion may explain, in part, why there is sometimes negative reaction to policies prescribed by CEA.

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Asset Metadata

Creator Turpcu, Adam (author)

Core Title Essays on the equitable distribution of healthcare

School School of Pharmacy

Degree Doctor of Philosophy

Degree Program Pharmaceutical Economics

Publication Date 12/13/2010

Defense Date 06/30/2010

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag equity,framing,healthcare distribution,OAI-PMH Harvest,QALYs,rank-dependent models

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Doctor, Jason N. (committee chair), Siegmund, Kimberly D. (committee member), Sood, Neeraj (committee member)

Creator Email adamht@gene.com,aturpcu@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m3598

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Document Type Dissertation

Rights Turpcu, Adam

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

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Repository Location Los Angeles, California

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