Download Thesis - Amherst College

Towards a Theoretical Understanding of Diabetes Management
Jon Ettinger
Faculty Advisor: Professor Walter Nicholson
Submitted to the Department of Economics at Amherst College in
partial fulfillment of the requirements for the degree of Bachelor of Arts
with Distinction
April 27, 2007
1
Acknowledgements
First off, I would like to thank my advisor, Professor Walter Nicholson for his
support and guidance throughout the thesis process. In addition to his help on this
project, Professor Nicholson’s Law and Economics class really changed the way I think.
Thanks to Professor Rivkin for his instruction and help both this semester and the last,
and to Jeanne Reinle and her uplifting smile for making the third floor of Converse a
great place to work. Thank you also to all the great friends here at Amherst that have
been there along the way. Thanks to Lucy Sheehan for her timely edits and
encouragement, and of course, huge thanks to all the 2007 Converse Hall-Stars for
creating such a great community amongst the Econ majors this spring. Finally, I owe a
huge debt of gratitude to my parents. Their comments on this paper were invaluable, and
their support of my ongoing skirmish with diabetes has been unflappable. Although this
may be tautologicalI, without my mother and father, none of this would have been
possible.
I
After all, behavioral economics is just one big tautology anyway.
2
Table of Contents
I. Introduction………………………………………………………………
3
II. Literature Review……………………………………………………….
9
IIa. Compliance and Empowerment Models
IIb. Cost-effectiveness of Diabetes Management
IIc. Behavioral Economics and Modeling Diabetes Management
III. Theoretical Model of Diabetes Management…………….……………
24
IIIa. The Components of DMRL
IIIb. Discussion of Price Levels
IIIc. The HbA1c Production Function
IIId. Lifetime Utility as a Function of HbA1c Level
IV. Externalities and Informational Problems……………………………
40
V. Conclusion………………………………………………………………..
44
Appendix. Depression and Diabetes………………………….…………….
46
References……………………………………………………….…………...
48
3
I. Introduction
In 2002, the American Diabetes Association (ADA) estimated the economic cost
of diabetes to be $132 billion, adding the disclaimer that this figure likely underestimates
the true burden of the disease. Direct medical expenditures constituted $91.8 billion of
the total cost, up from an estimated $44 billion in 1997. Although the 2002 ADA study
represents the most recent comprehensive examination of the economic costs of diabetes
in the US, one can safely assume that this figure has increased significantly. Since 2002,
the diagnosed population of diabetics has increased by 20.7%, from 12.1 to 14.6 million.
An estimated 6.2 million diabetics remain undiagnosed.
Given these staggering statistics on the prevalence, growth trends, and economic
burden of diabetes, it is essential that policy makers, healthcare professionals, and
diabetic patients themselves find ways to reduce the impact of diabetes. Many studies
have examined the cost-effectiveness1 of various treatments and regimens in an effort to
reduce the total cost of diabetes. While there is great variation in the efficacy from one
program to another, it seems clear that there are diabetes intervention measures that are
very cost-effective, yet continue to be under-utilized by the diabetic population that they
are intended to help. To the consternation of healthcare professionals, many diabetics fail
to comply with treatment regimens that are intended to minimize the progression of the
disease and the occurrence of long-term complications associated with poor diabetes
management2. Healthcare economists contend that the implementation of better diabetes
management would lower the economic burden of diabetes.
1
For the remainder of this paper, cost-effectiveness and cost-effective analysis is understood to be
interchangeable with cost-utility analysis.
2
A CDC analysis of data from the 1997-1999 Behavioral Risk Factor Surveillance System estimates that
less than 40% of diabetics achieved guideline levels of medical care in 1999.
4
The notion that improved diabetes management, and the associated increase in
diabetes management expenditure, might lower the total cost of diabetes requires an
understanding of how the economic costs of diabetes are incurred. Diabetes is a general
term used to describe two distinct but similar diseases: type 1 diabetes, also known as
juvenile diabetes, and type 2 diabetes, or adult-onset diabetes3. Type 1 diabetes is an
auto-immune disease in which the immune system attacks and destroys the cells in the
pancreas that produce insulin. Type 2 diabetes, which accounts for 90-95% of all
diabetes cases, is a metabolic disorder characterized by insulin resistance, or the body’s
inability to use insulin efficiently. Both diseases eliminate the body’s ability to
effectively regulate glycemic levels in the blood, resulting in hyperglycemia or an
excessively high blood-sugar level. Chronic hyperglycemia causes gradual cellular
damage throughout the body, while acute hyperglycemia leads to diabetic ketoacidosis, a
potentially life threatening condition that causes further damage to bodily organs.
The Diabetic Control and Complications Trial (DCCT), conducted from 1983 to
1993, gave the medical community conclusive evidence of what they had long believed:
it is hyperglycemia caused by diabetes, rather than diabetes in and of itself, that leads to
the development of costly long-term complications and the associated increase in
morbidity and mortality amongst diabetics. Fortunately, through oral medications and
intensive blood-glucose management (IBGM)4, diabetics can manage their glycemic
3
There are two other types of diabetes, namely gestational diabetes and type 1.5 diabetes. Gestational
diabetes is usually a temporary condition that occurs during pregnancy, and is thus not relevant to a
discussion of the long-term cost-benefit calculus of managing chronic diabetes. Type 1.5 diabetes exhibits
characteristics of both type 1 and type 2 diabetes, but treatment for type 1.5 diabetes is not significantly
different from managing type 1 diabetes. Also, note that the terms juvenile diabetes and adult-onset
diabetes have fallen out of favor in the medical community to eliminate confusion owing to the fact that
adolescents can develop type 2 diabetes and adults occasionally develop type 1 diabetes.
4
IBGM is a process that involves self-monitoring of blood-glucose levels and using appropriate amounts of
insulin to compensate for carbohydrate intake and hyperglycemia.
5
levels and avoid hyperglycemia. Early treatment of developing complications can reduce
their impact, and close attention to diet and exercise helps blood-sugar levels stay within
a normal range. Regular appointments with healthcare professionals may help diabetics
formulate a plan for controlling their diabetes. In essence, through vigilant diabetes
management, diabetics can regulate their blood-sugar levels and mitigate the
development of costly long-term complications.
Thus, the severity and cost of diabetes related complications is a function of the
amount of resources devoted to diabetes management, and the effective use of those
resources. Formulating diabetes treatment strategies begins with this fundamental
relationship. Cost-effectiveness analyses of various diabetes management techniques
exploit this principle, comparing the cost to implement a specific intervention with the
costs saved in diabetes complications. Cost-effectiveness modeling has become quite
accurate and is a crucial tool for informing medical professionals and diabetics about how
best to allocate their diabetes management resources.
The most effective measure of diabetes control is the HbA1c level. HbA1c refers
to glycosylated hemoglobin, a measurement for the level of hemoglobin exposure to high
plasma levels of glucose. HbA1c levels approximate the average glycemic level over a
roughly three month period – higher average blood-glucose raises HbA1c – and can
therefore be used to measure the quality of overall diabetes care. Normal HbA1c levels
in non-diabetics range from 4.0%-5.9%, whereas the HbA1c average for diabetics is
roughly 8.0% with outliers well over 10%. Because HbA1c levels reflect the degree of
chronic hyperglycemia in an individual, they are a very strong predictor of the extent of
long-term diabetes complications.
6
Knowing how to best distribute diabetes management resources is only half of the
picture in preventing costly diabetes complications. The other half is selecting the level
of resources to devote to diabetes management. While efficient strategies of resource
allocation are largely determined by the medical community, the level of diabetes
management maintained by an individual diabetic is a personal consumption choice.
Despite the significant implications associated with choosing a level of diabetes
management consumption, no theoretical work has been done to approach this issue.
Conventional wisdom merely asserts that diabetics do not devote enough resources to
diabetes management, causing the total cost of diabetes to be higher than it could
otherwise be. However, from the perspective of rational choice theory, diabetics should
devote a personal utility-maximizing level of resources to their disease management,
contradicting the notion of underconsumption given no externalities and complete
information.
Measuring the amount of resources a diabetic commits to diabetes management is
made difficult by the fact that there are several types of resources that diabetics devote to
their disease management. I identify three broad categories of resources in order to
simplify this problem; blood-glucose management (BGM) resources, professional
healthcare (PHC) resources, and changes in lifestyle that diabetics adopt to control their
diabetes, which I call habits. Each of these categories can be further decomposed into
their various components. From this point on, I refer to the total quantity of resources as
the diabetes management resource level, or DMRL. The concept of resources as it is
used here can be equated with “costs” and includes both financial and non-financial costs
to the individual of diabetes management. Changing one’s habits to manage glycemic
7
levels, or dealing with the pain of an insulin injection are both examples of costs to the
individual diabetic. The value of these suffered costs is understood to be a component of
the DMRL an individual chooses. These non-financial costs are implicitly converted to
dollar amounts using willingness to pay (WTP) schemes so that the cost of DMRL is
given in consistent units.
There are several reasons to believe that rational diabetic agents choose utilitymaximizing DMRLs that do not simultaneously maximize social welfare. Diabetes
management creates certain externalities; the costs of diabetes are not endured
exclusively by diabetics. Costs are also borne by employers, family members and
friends, and health-insurance plans (which are generally structured in such a way that
creates moral hazard problems). Self-control problems brought on by inconsistent time
preferences as well as systematic sources of imperfect information may also contribute to
inefficiently low DMRLs.
The main question I investigate in this paper is how diabetics choose the level of
resources they devote to diabetes management from a rational choice, utility-maximizing
perspective. Secondarily, I look at possible explanations for why this level of resources
may not be optimal for social welfare maximization. The basis for my analysis is a
theoretical model I create to understand the consumption decision diabetics face when
they choose a level of diabetes management.
Section 2 provides a literature review and background to cost-effectiveness
research on diabetes management as well as behavioral economics concerns in creating a
diabetes management model. Section 3 presents a theoretical model of diabetes
management from an individual utility maximizing perspective. In Section 4, I discuss
8
the potential externalities of diabetes management, the systematic gaps in information
that hinder rational choice, and the policy implications they create. I conclude the paper
with a summary of my diabetes management theory and its potential importance in
understanding the true total economic burden of diabetes.
9
II. Literature Review
Most of the literature on diabetes management focuses on a compliance-based
model of diabetes care and on the effectiveness of specific medical practices in treating
diabetes. Little work has been done that accurately portrays the agency of informed
diabetics in determining their own utility maximizing strategies for treating diabetes.
This section will characterize the literature on patient agency and existing models on the
cost-effectiveness of diabetes management. It includes a review of the literature on
expected utility healthcare models, as well as the issues that are relevant to diabetes in
particular.
IIa. Compliance and Empowerment Models
Many medical studies investigate the issue of patient compliance with assigned
diabetic management regimens. They examine the risk factors associated with noncompliance and give suggestions to medical professionals about how to encourage
compliance in their patients.
Recent empirical evidence suggests that the compliance model of diabetes care
leads to poor diabetes management. The patient compliance model minimizes the
individual agency that diabetics have in their own self-management of diabetes. It places
the responsibility of creating a diabetes management regimen primarily on the physician.
However, maintaining steady, normal glycemic levels is a more complicated and
dynamic process than the compliance model assumes5. Not allowing diabetics the ability
5
Hill-Briggs (2003) characterizes the problem-solving skills necessary to effectively maintain normal
blood-sugar levels. Besides technical knowledge, she cites four components of problem-solving in disease
self-management: problem-solving skill, problem-solving orientation, disease-specific knowledge, and
10
to allocate their diabetes management resources or adjust their DMRL to suit their own
personal preferences causes a perceived lack of control that further undermines
compliance (Dunn, 2005).
Problems with the compliance model have led to a new model for diabetes
management, referred to as the “Empowerment Model” (Meetoo and Gopaul, 2005).
This new philosophy of diabetes treatment involves collaboration between physician and
patient. In this model, the healthcare professional provides the patient with information
about the consequences of poor diabetes management and how he or she can most
effectively manage the disease. A central concern of the Empowerment Model is
diabetes education. One of the main objectives of professional healthcare is to train the
patient to utilize effective diabetes management techniques and to teach the patient about
the long-term cost of complications resulting from poor glucose control. Proper
instruction of these two concepts lays the foundation from which diabetic patients can
make the rational decisions regarding their diabetes management that are essential to
patient empowerment. Equipped with a better understanding of diabetes and how best to
manage blood-sugar levels, the patient can then customize a management regimen that
maximizes his or her lifetime utility.
The new, patient-based approach to diabetes management necessitates a better
understanding of how informed patients choose their DMRL. Existing compliance
literature focuses on the healthcare professional, but the agency in diabetes management
has shifted to the consumer. Perhaps owing to the relatively recent shift in treatment
transfer of past experiences. Her study illustrates the importance patient agency in effective diabetes
management.
11
philosophy, no clear framework has been made to analyze the patient’s decision from a
lifetime utility maximizing perspective.
IIb. Cost-effectiveness of Diabetes Management
The ability to measure the cost-effectiveness of various diabetes management
practices is severely limited by the difficulty of isolating the effects of a specific
treatment and the long time-frame over which diabetes-related costs are incurred6.
Nevertheless, many studies have conducted cost-effective analyses (CEA) of various
diabetes interventions, the most relevant of which being intensive blood-glucose
management (IBGM). In a 2000 article, Klonoff and Schwartz conducted a metaanalysis of CEA studies spanning 17 different interventions for diabetes. Because of the
difficulty in evaluating the cost-effectiveness of these interventions, most of their results
were inconclusive. However, they found that improved glycemic control was a clearly
cost-effective intervention. The cost-effectiveness of glycemic control through IBGM
has been corroborated by many other studies (See Rubin et al., 1998; Steffens, 2000;
Sidorov et al., 2002). These studies measured improvements in glycemic control owing
to IBGM by looking at HbA1c test results and determining the average cost of diabetes
complications associated with various HbA1c levels. Blood-glucose control is by far the
most important aspect of diabetes management, and it is also the aspect over which a
diabetic has the most control. For this reason, I use the terms diabetes management and
Gold et al (1996) writes “Very few epidemiologic studies or clinical trials are able to measure disease
progression and intervention effects over a lifetime. Yet it is just such information—the natural history of
disease and the long-term impact of interventions on costs, quality of life, and health outcomes—that is
most germane to the formulation of health policy.”
6
12
DMRLs to refer to an individual’s attempts to regulate blood-sugar and avoid hypo and
hyperglycemia.
A 2006 paper by Beaulieu et al. gives the most recent and comprehensive CEA of
diabetes disease management. They examine the incentives for health plans to offer
comprehensive diabetes management programs according to new chronic care guidelines
that follow through with the Empowerment Model of disease management7. As health
plans bear most of the financial cost of diabetes care spending for individuals they insure,
net savings caused by greater diabetes disease management will be passed on to the
healthcare plan. Adverse selection problems and patient turnover8 may potentially negate
the cost savings to the health plan, and indeed Beaulieu estimates that HealthPartners
Minnesota roughly breaks even on their diabetes disease management program over a
ten-year period9. Meanwhile, they calculate the total societal benefit of the ten-year
program to be $64,000 per diabetic patient.
Beaulieu arrives at this figure by estimating the value of the three primary
benefits from improved diabetes management: improved quality of life, long term cost
savings from avoided complications, and workplace productivity gains. To valuate
improved quality of life, Beaulieu assumed the HealthPartners program brought HbA1c
down from 10% to 7.2%, and furthermore assumed that this yielded an increase of 0.87
7
Beaulieu et al. look at one health plan, the HealthPartners of Minnesota, to gather their data, and they
acknowledge that this limits the generalizability of their results. HealthPartners created a comprehensive
diabetes management program based on chronic care research by Wagner (2001).
8
Beaulieu points out that plans with high quality diabetes programs are likely to attract more infirm
patients than plans with lower quality programs. However, health plans typically do not receive higher
payments for sicker patients and thus receive no compensation for the extra costs sicker patients cause them
to occur. As most of the cost-saving benefits of good diabetes disease management are gained years into
the future, and as patients are likely to change healthcare providers over this time frame, investment in
diabetes management made by a healthcare provider may save future costs for a different healthcare
provider.
9
Using a discount rate of 7%, they find that the net cost to HealthPartners was a negligible $220 dollars
over the ten-year period.
13
quality adjusted life years (QALYs). Beaulieu valued a QALY at $100,000, and after
accounting for discount rates, calculated the net present value of the improved quality of
life to be $59,000. Healthcare savings from avoided complications were estimated to be
another $5,000, and workplace productivity gains were left out of the estimation due to
lack of data. One can easily argue with several of Beaulieu’s assumptions, especially the
relatively high valuation of a QALY. Still, his conclusion that disease management can
lead to significant societal benefits is quite robust.
The large benefits of the diabetes management program studied by Beaulieu
evidence the poor disease management Habits of many diabetics. Even if one adjusts
Beaulieu’s assumptions and accounts for additional costs (such as time costs) that the
study leaves out, it is hard to avoid the conclusion that some underconsumption of
diabetes management is occurring. Assuming that patients rationally choose the level of
resources they commit to diabetes, underconsumption may be indicative of large market
failures for diabetes care and in medical care market at large. Patients have imperfect
information about the benefits of diabetes management and how to efficiently allocate
their DMRL. As Beaulieu points out, health plans have insufficient incentives to provide
programs that resolve the patient informational problems. Because the market for
healthcare does not function like competitive markets with certainty (Arrow, 1963),
additional frictions may impede the ability of patients to consume their desired quantity
of professional care or switch to a healthcare provider that has sufficient diabetes
information to help patients allocate their DMRLs efficiently10.
10
Arrow wrote about the barriers to competitivity that uncertainty in the market for healthcare introduce.
Asymmetric information between physician and patient, the value of “trust” in the physician-patient
relationship, and the largely non-profit seeking incentives for physicians may undermine efficient market
functioning. Patients that trust their doctors may not seek alternative physicians that would be better
14
Although the model I develop is based on the agency of a patient to optimize his
DMRL under the assumption that healthcare professionals are a known quantity as they
fit into a patient’s overall allocation of diabetes management, there are problems with this
assertion as it plays out in actuality. Healthcare professionals are paid by schemes that
assume the non-contractibility of health outcomes (Dranove and White, 1987). Physician
effort is thus called into question, as physicians may have incentives to take on more
patients and give each a lesser degree of care. In the case of diabetes, where effective
management requires frequent collaboration between patient and doctor, this can be
doubly problematic. As a simplifying assumption to assess how patients choose their
DMRLs, I ignore the incentive problems inherent to healthcare professionals delivering
medical care. Instead, I treat professional care in the same way that I treat commodity
goods that are part of a diabetes management budget; I assume that there is no extra
uncertainty in the quality of professional care than there is in the integrity of insulin.
Any examination of the cost-effectiveness of diabetes management must include a
discussion on the valuation of future health, the primary benefit accrued from diabetes
management. The standard way to measure the long-term benefits of a medical
intervention in healthcare economics is through the use of quality-adjusted life years
(QALYs)11. An entire literature surrounds the benefits and drawbacks of using QALYs
to estimate the value of life quality and life duration that results from medical
interventions12. Most QALY analyses evaluate the cost-effectiveness of a specific
intervention in terms of cost (in dollars) per QALY gained. Because diabetes
equipped to help with diabetes management. Doctors that are poorly informed about diabetes management
may exploit this trust and not inform the patient of better alternative healthcare professionals.
11
A quality-adjusted life year is a year multiplied by a fractional value according to the state of health in
which the year lived. Worse health-states are given a lower adjusted value.
12
For an overview of concerns regarding the use of QALYs, see Prieto and Sacristán (2003).
15
management is characterized by constant monitoring and minor interventions rather than
a single medical procedure, calculating the cost of QALYs is more complicated. Given
the differences from one case of diabetes to another, the difficulty in defining diabetes
interventions, and the problematic nature of estimating cost per QALY in general, it is
not surprising that CEA studies on diabetes have come up with vastly different valuations
of the cost per QALY gained through disease management. As an example, Meltzer
(2002) studied the cost-effectiveness of intensive therapy in Type 1 diabetes and found
that the inclusion of future costs in the CEA model reduced the cost-effectiveness ratio
from $22,576 to $9,626 per QALY. In other words, accounting methodology alone
(specifically accounting for future utility from consumption) changed the ratio by roughly
60%. Nevertheless, both cost-effectiveness ratios fit well within accepted guidelines for
cost-effective medical interventions13. QALY analysis is fundamental to determining the
order in which to pursue diabetes interventions based on their relative cost-utility ratios.
However, as noted above, the purpose of the model in this paper is not to determine
which interventions and treatment regimens diabetics pursue, but rather to understand the
DMRL they choose under the assumption that they can allocate their diabetes
management resources efficiently.
Empirical data on the cost-effectiveness of diabetes interventions have led to the
development of complicated models that simulate the progression of diabetes given
disease and intervention parameters (Eastman et al., 1993; Eddy and Schlessinger, 2003).
As opposed to Beaulieu’s QALY valuation of $100,000, most discussions value achieving one additional
QALY at around $50,000 (Meltzer, 1997). This number is, of course, highly subjective and dependent on
income for the cohort achieving the QALYs. Valuation of QALYs are related to a willingness-to-pay
(WTP) approach to health states and extended life. Although it is certainly a cynical way of approaching
the issue, a QALY in the US is worth considerably more than a QALY in sub-Saharan Africa. While the
“efficiency threshold” of QALYs is considered to be $50,000 in the US, roughly only 20% of new
interventions with QALY costs of less than $50,000 are undertaken (Prieto and Sacristán, 2003).
13
16
The accuracy of these models14 has allowed the healthcare industry to refine diabetes
treatment regimens and achieve more efficient allocation of diabetes management
resources. Of course, knowledge within the medical community about efficient
allocation of a given DMRL does not always translate to a knowledgeable diabetic
patient. Still, given the ease of acquiring information on diabetes on the internet15, a
diabetic population that understands how to efficiently allocate diabetes management
resources is a plausible (though imperfect) assumption from which to model diabetic
management behavior.
It must be noted that existing attempts to model the cost-effectiveness of diabetes
management leave out a set of costs and benefits that are essential to understanding the
DMRL consumption decision. A large portion of the benefits from diabetes management
are future utility gains and added longevity, as measured by QALYs16. However,
consumption of diabetes management also creates utility in the present and near-future by
producing a more normoglycemic state in the consumer. Little empirical research has
been done on the utility of various glycemic states17, and one can only guess at the extent
14
The Archimedes model, developed by Eddy and Schlessinger as a tool for KAISER PERMANENTE,
was validated by comparing its simulations to the results of various diabetes intervention trials that were
not used to create the model. The model was found to have a correlation coefficient of r = .97.
15
Zrebiec (2005) studied the effect that internet communities had on coping with diabetes. According to
his internet-based surveys, 80% of respondents cited the internet as a major source of diabetes information.
16
In his 1997 paper, “Accounting for Future Costs in Medical Cost-Effectiveness Analysis,” David Meltzer
creates a more nuanced CEA theoretical model to account for changes in future lifetime earnings, costs,
and consumption attributable to a medical intervention. Using a lifetime expected utility model, he breaks
down QALYs into both its quality of life (QOL) and longevity components. His general finding is that
QALY analysis in its traditional form overstates the value of life-extending treatments while understating
the value of QOL improvements. I refer back to his lifetime expected utility model in the creation of my
own model for diabetes management.
17
The utility gains from maintaining a normoglycemic state could be approximated empirically through
WTP studies or satisfaction surveys. However, given that the utility function U(gl), where gl is the
glycemic level, varies significantly from person to person and that this utility is hard to quantify, U(gl) is
much more useful at a theoretical level. The lack of research on the U(gl) function probably owes to these
empirical difficulties. In theory, the U(gl) function might also be determined by establishing the value of
other parameters that determine the level of diabetes management resource consumption and inferring its
characteristics.
17
to which utility gains from normoglycemia influence diabetes management Habits18. The
fact that glycemic state-dependent utility gains, as opposed to QALY gains, are not
subject to the time-discount factor supports their significance. Likewise, oft-ignored
costs are also borne in the present as a function of the DMRL; these include the time
costs and psychosocial costs of diabetes management (Dharmalingam, 2002). Efforts at
modeling diabetes management behavior must take these costs and benefits into account.
IIc. Behavioral Economics and Modeling Diabetes Management
Given the unique characteristics of the healthcare industry and the enormous
portion of the economy devoted to medical care, one might think that there would be a
rich literature devoted to the behavioral economics of medical decision making.
Certainly, some work has been done to create a general framework for the application of
expected-utility theory, rational choice theory, and more ambitiously, prospect theory to
healthcare behavior. Michael Grossman (1972) in particular develops a theoretical model
for individuals’ demand for health, and by proxy, healthcare. However, the application
of behavioral economics to the health sector has been quite limited in breadth and scope
(Frank, 2004). Many of the existing studies focus on the supply side – the behavior of
healthcare professionals – rather than examining how the demand side – patients seeking
healthcare – behaves. Theoretical research that deals with patient behavior focuses
almost exclusively on addictive behavior, stemming from Becker and Murphy’s paper,
“A Theory of Rational Addiction” (1988).
18
From personal experience, I would postulate that this is the primary incentive to consume diabetes
management. There is a consensus amongst diabetics that mood (read: utility) is very dependent on
glycemic level. There is also an established relationship between depression and glycemic control,
although the causality of this relationship is unclear (Van Tilburg et al., 2001).
18
Strangely enough, however, models of rational addiction can help inform the
creation of a model for diabetes management behavior. Addictions can be characterized
by past consumption of a good affecting future consumption of the good (Becker and
Murphy, 1988). In a world of perfect information, of course, rational consumers would
anticipate the change in their utility functions attributable to consuming an addictive good
for the first, second, or nth time. Consumption of addictive goods can also affect the time
preferences of the consumer, leading to a reduction in lifetime expected utility (Becker
and Mulligan, 1997). Given perfect information, rational agents would only consume an
addictive good if they received gains in lifetime expected utility, understanding the
propensity of an addictive good to change their future utility in potentially negative ways.
People, however, do not have perfect information regarding the addictiveness of certain
goods, the loss of future utility owing to their consumption, or even their own
susceptibility to certain kinds of addiction. Individuals are often mistaken about the
stability of their preferences (another example of imperfect information). Thus, it is not
surprising that so many cases of non-lifetime utility maximizing addiction occur.
Additionally, expected-utility rational behavior may seem irrational in retrospect if the
actual (as opposed to expected) outcome of the behavior was negative19.
Under the assumption of perfect information, rational theories of addiction can
help one understand consumption of diabetes management in two different ways. The
first similarity between addiction and diabetes management is the dependency of their
We might, for example, imagine the case of a heroin addict who “rationally” dies from drug-overdose,
despite his positive lifetime-expected utility. If the chance of death from overdose was rationally assessed
at say 0.01%, expected utility from drug use (given a specified utility function, discount rate, and set of risk
preferences) might overwhelm the expected cost of potentially negative consequences (i.e. death). Of
course, it may be just as (read: far more) reasonable to assume that heroin addicts suffered from imperfect
information both when they started the habit and when they decided to increase the dosage.
19
19
respective consumption-utility function on a previous stock of consumption. As
previously mentioned, future consumption of an addictive good depends on past
consumption20 (Becker and Murphy, 1988). Although diabetes management is not
traditionally thought of as an addictive good, it exhibits this same tendency21. In attempts
to explain their hesitancy to increase DMRLs, diabetics commonly cite factors such as
aversion to needles and blood tests, time costs, and frustration about the constant
vigilance of exercise, diet, and medication necessary to maintain steady glucose levels.
These are costs of diabetes management that are often ignored in CEA, but are
fundamental to the DMRL consumption decision. By nature, the magnitude of these
costs is a function of the consumption stock of diabetes management. As the
consumption stock grows, diabetics naturally habituate to needles and blood tests, lower
their time costs through management proficiency, and become better attuned to the
interaction between blood-sugar levels and exercise, diet, and medication. Because the
costs of diabetes management decrease as the consumption stock increases, future
consumption of diabetes management should increase with the consumption stock as
well.
Addictive goods are commonly thought of as “overconsumed”; addicts consume
such goods until the marginal costs of their consumption are greater than the marginal
20
In a sense, addictive goods are complementary with themselves. Becker and Murphy describe this
phenomenon as adjacent complementarity. One can also imagine cases in which the consumption stock of
good A could have an effect on future consumption of good B. This is probably an implicit argument in the
notion that marijuana, for example, is a “gateway drug.”
21
An esoteric counterargument to the positive correlation between one’s consumption stock in diabetes
management and future consumption in diabetes literature would be the notion of “diabetes burnout.”
Within Becker’s framework, diabetes burnout would be the idea that some diabetics have a threshold for
their stock of previous diabetes management consumption. This threshold is based on a variety of
psychosocial factors, and once it has been surpassed, the individual diabetic “gives up” on diabetes
management to an extent. However, diabetes burnout normally occurs in diabetics with poor glycemic
control, implying that perhaps their stock of previous diabetes management consumption is abnormally
low.
20
benefits. By definition, this is not the case for rational agents acting under perfect
information. Still, the perception of overconsumption is maintained because observers
may fail to acknowledge that the net present value (NPV) of future costs incurred is
discounted by time preferences. As most addictive goods can be characterized as
generating immediate utility followed by deferred costs, discount rates are crucial to
understanding the consumption decision and why overconsumption might indeed be
rational consumption.
Similarly, diabetes management as a good is generally thought of as
“underconsumed;” diabetics would be better off if they consumed a higher DMRL. If
one follows the analogy to addiction, this is not surprising. While diabetes management
consumption does create some immediate utility, it is best characterized as a tradeoff
between present costs and future benefits. For this reason, diabetes management (and
medical care in general) is often seen as an investment in future health. Thus, as the costs
of diabetes management are borne immediately while the NPV of diabetes management
benefits is discounted, rational consumption might seem to be underconsumption. Not all
people discount future utility at the same rate. It follows that individuals with greater
time preferences (i.e. higher discount rates) will tend to become more addicted and
exhibit poorer diabetes management22.
A common criticism of the rational model of addiction (and by extension, a
similar model for diabetes management) is the discrepancy between the stated and
revealed preferences of consumers of an addictive good. In a paper on obesity and selfcontrol, Cutler (2003) gives the example of overweight individuals who state their
preference for weight-loss, yet are unable to begin or maintain a diet. This discrepancy is
22
This theoretical result is supported empirically in a study by Ng, Darko, and Hillson (2004).
21
usually explained in behavioral economics by time-inconsistent discount rates, or
hyperbolic discounting23. An individual whose consumption is constrained by the pure
time discount rate δt (normally the short-term interest rate), but who discounts all future
utility at βδt, may want to start a diet tomorrow but not today. An individual who wants
to start a diet tomorrow implicitly states that the cost (over time) of extra food
consumption tomorrow is greater than the utility gained. However, unlike the utility and
disutility from consumption tomorrow, consumption in the present is not discounted by
the hyperbolic factor β. Thus, diets cost less to start in the future than in the present and
there is no discrepancy from wanting to start a diet (in the future) but not being able to (in
the present). By the same logic, hyperbolic discounting might cause a difference between
stated preferences for diabetes management and actual diabetes management Habits.
Hyperbolic discounting is an especially useful theoretical construct when dealing
with issues of “self-control” in behavioral economics. Prelec and Loewenstein (1991)
attribute self-control problems to the immediacy and certainty of consumption that results
in instant gratification. Small changes in the certainty and immediacy of an outcome lead
to much greater discounting than the basic expected utility and discounted utility models
would imply. The short-term gains in utility that diabetics receive from diabetes
management, however, are neither immediate nor certain. Blood-sugar management
techniques24 cause gradual changes in glycemic levels that may not be realized for
several hours, and there is a great deal of variance in the magnitude of the changes they
Peck and Laux (2004) give a simplified explanation of hyperbolic discount rates. Given a discount rate δ
and a hyperbolic discount factor β, a hyperbolic discounter will value W (t=0) at βδW when time t=1. At
t=2, the present value of W will be βδ2W, discounting t=2 only by the time-discount rate δ, and not by an
additional β. It is assumed that 0 < β < 1, and an exponential discounter is the special case where β = 1.
The use of a constant β is a simplification of β(t), the hyperbolic discount factor as a function of time.
24
Primarily oral agents, insulin injections, or exercise
23
22
cause (See, for example, Ferrari, et al.,1991 or Moberg, et al., 1995). Accordingly, the
quasi-immediate utility gains from glycemic control resulting from diabetes management
must be discounted to account for the delay and uncertainty of gratification.
In a 1997 paper titled “Golden Eggs and Hyperbolic Discounting, David Laibson
argues that this motive to “start a diet tomorrow,” caused by dynamically inconsistent
time preferences, implies that consumers in the present have an incentive to constrain
their future consumption25. Laibson finds that constraining future spending by holding
illiquid financial assets (limiting one’s set of choices) over liquid assets can increase
welfare for the present self, given dynamically inconsistent time preferences. These
implications carry over to diabetes; constraints on future diabetes management can cause
welfare gains in diabetics with hyperbolic time preferences. The large amount of costeffective diabetes interventions that are not undertaken, as well as diabetics’ stated
preferences for higher future DMRLs suggests that hyperbolic discounting does occur for
diabetes management.
While there is no way to hold onto high future DMRLs as one might hold illiquid
assets, one could imagine mechanisms that would act as constraints on future DMRL
choice. Committing to a healthcare plan that charges a higher premium but also
incentivizes high levels of diabetes management by rewarding diabetics for low HbA1c
levels26 could change future preferences so that future selves would maintain a higher
25
Camerer and Loewenstein (2003) characterize the paradox of consumption choices for hyperbolic
discounters: “Somebody with time-inconsistent hyperbolic discounting will wish prospectively that in the
future he will take far-sighted actions; but when the future arrives he will behave against his earlier wishes,
pursuing immediate gratification rather than long-run well-being.”
26
Car-insurance companies have a similar reward system, lowering insurance rates for students with high
GPAs. Of course, there is a major difference between these two reward mechanisms. In the case of car
insurance, GPA serves as a signaling device for lower-risk drivers; there is a correlation between higher
GPAs and costs to insurance companies, but one can hardly argue that there is a causal relationship
23
DMRL. Informal mechanisms also play a considerable role in constraining future
diabetes behavior. Familial encouragement or diabetic support groups can both serve to
socialize the value of maintaining a high DMRL and “punish” deviations from
maintenance routines.
between the former and the later. Rewarding low HbA1c levels, on the other hand, may incentivize
diabetics to choose a DMRL that reduces the total cost to the health insurance plan.
24
III. Theoretical Model of Diabetes Management
There are four major issues I confront in creating a theoretical model of diabetes
management. First, the independent variable that I use to characterize the level of
resources a diabetic devotes to diabetes management, DMRL, is a global construct
developed to simplify and aggregate many different independent decisions into a single
consumption choice. Second, the intertemporal nature of the benefits gained from
diabetes management creates time-preference problems. Behavioral economic theory has
not reached a consensus on how to discount these future utility gains27. Third, many of
the costs and benefits of diabetes management are not monetary, but must be included
and combined with monetary costs and benefits to create a comprehensive model of
diabetes management as a utility-maximization problem. Like many behavioral
economics models, the inability to accurately quantify parameters and utility in general
makes the model more useful as a theoretical framework for understanding individuals’
diabetes management choices rather than an empirical tool. The final complexity is that
diabetes management is not a commodity to be consumed at one point in time, but a form
of constant economic activity.
Healthcare inputs are an essential part of the broad production function that
individuals use to produce “health” (Grossman, 1972). Along with general healthcare
inputs, diabetics must invest in the healthcare inputs particular to their disease. For the
model of diabetes disease management, I look specifically at three diabetes healthcare
inputs that are part of a diabetes management production function. The total cost of these
27
For a discussion on discounting future utility derived from medical interventions, see Cohen, 2003. For a
more amusing discussion of problems involving discounting and behavioral economic models in general,
see Rubenstein, 2006.
25
three inputs is the DMRL, and each quantity input serves as part of the production
function for achieved diabetes management, as measured by HbA1c.
DMRL is best thought of as a stream of consumption, as the consumption of
diabetes management resources takes place continuously. A rational diabetic agent seeks
to consume an optimal stream of DMRL over his or her lifetime. Consequently, the
problem of solving for this optimal stream requires dynamic optimization in a dynamic
model of the costs and benefits of DMRLs. However, the mathematics of dynamic
optimization is beyond the scope of this paper. Instead, I present a simplified model and
theoretical framework for understanding the decision to consume a particular DMRL by
looking at DMRLs over one-year periods. The first portion of this model looks at the
components of DMRL, and then isolates the quantities of healthcare inputs that are part
of the production function for HbA1c. It is assumed that sophisticated diabetics can
minimize their total resource cost to achieve a given HbA1c level of glycemic control.
This is similar to a Hicksian demand function; consumers find the cheapest bundle of
healthcare inputs for a particular HbA1c. The last part of the model analyzes the benefits
of diabetes management by looking at lifetime utility as a function of HbA1c, or
U(HbA1c).
26
IIIa. The Components of DMRL
In my discussion, I defined the DMRL to be the total cost of all the resources
devoted by an individual to diabetes management over the course of the following year.
The components of annual DMRL are the costs of blood-glucose management (BGM),
professional healthcare (PHC), and the cost of behavioral changes that are intended to
assist in glycemic control. Each of these components requires some decomposition and
explanation to understand.
The cost of BGM to an individual is the sum of the total out-of-pocket cost of
BGM medical supplies and the costs of displeasure brought on by blood-glucose
management. Such “displeasure costs” include pain, fear, time-costs, and stress.
(1a) CostBGM = (annual cost of BGM medical supplies)*(1-i) + κBGM
In this equation, i represents the percent of medical costs covered by insurance while
κBGM represents the non-financial costs of BGM.
The cost of PHC borne by an individual can be expressed in a similar fashion:
(2) CostPHC = (annual cost of professional healthcare)*(1-i) + κPHC
As mentioned, κBGM and κPHC can be monetized using WTP schemes in order to express
costs as a single unit.
The annual cost of behavioral changes, CostHABITS is harder to arrive at, given that
this cost has no major financial components28. Quantifying CostHABITS involves putting a
price on the total lost utility from behavioral changes intended to assist in diabetes
management. The “anti-diabetes” habits that a diabetic would drop relate largely to diet,
28
There are financial components CostHABITS such as the cost of exercise equipment, or the increased cost
of food in a diet more suitable for diabetes. Because these costs are relatively minor, I do not identify them
specifically. Rather, they are understood to be implicitly included in the total cost of habits.
27
exercise, smoking and drugs, although more obscure activities can be included as well29.
I define this set of anti-diabetes behaviors as (h0 ……. hk) where hi indicates a specific
anti-diabetes behavior. Each behavior is normalized so that ceasing behavior hi will have
the same effect on the HbA1c as ceasing behavior hj. The set (h0 ……. hk) is organized
in such a way that the costs in terms of lost utility from forgoing behavior hi are less than
the costs of forgoing behavior h(i+1). Thus, behavior h0 is the cheapest to give up and
individuals will continue to give up behaviors until the cost of giving up a specific
behavior hi is greater than the benefits from gains to diabetes management30.
As a concrete example, behavior h0 might be binging on Pepsi, a behavior that is
very detrimental to blood-glucose control but may bring only marginally positive utility
gains if the individual were in a counterfactual non-diabetic state. Here, losses to utility
are small, while gains to blood-glucose control31 are very large. Meanwhile, behavior hk
might be scuba diving, an activity that produces minor, unpredictable swings in bloodglucose levels, but which brings a great amount of utility to the individual. In this case,
the gains to diabetes management are overwhelmed by the cost of forgoing scuba diving,
so the individual will continue to dive. CostHABITS is then the total cost in lost utility of
all anti-diabetes behaviors that an individual abstains from over the course of a year. Φ
converts a given utility value into a cost by implicitly using WTP methodology.
29
Scuba diving (a situation in which blood-sugar is more variable and where there are no means to monitor
or treat glycemic levels) is an example of an activity that might have some effect on diabetes management.
That being said, there are few if any absolutes regarding behavior that diabetics must avoid. Rather, such
behaviors contain potential added costs because of the disease.
30
Note that a behavior such as drinking soda is not confined to a single hi. hi represents a single unit of
habit that is equal to every other unit of habit in terms of its contribution to diabetes management. It may
take many units of h to describe soda drinking, and because soda consumption is subject to decreasing
marginal utility, the units h that describe soda drinking may not be adjacent in the set of behavior (h0 … hk).
31
Gains in blood-glucose control translate into utility gains through a production function for HbA1c and
the utility function U(HbA1c) that I will elaborate on later.
28
(3) CostHABITS = φ
j
U (h )
i 0
i
(4) DMRL = CostBGM + CostPHC + CostHABITS
As mentioned, the non-financial components of the DMRL are assumed to be expressible
in dollar terms through WTP or other methods.
The three cost equations implicitly contain both a quantity and a price level for
BGM, PHC, and HABITS respectively. One may rewrite the cost equations as follows:
CostBGM = PBGMQBGM; CostPHC = PPHCQPHC; and CostHABITS = PHABITSQHABITS, where P is
the price level and Q is the quantity. It is important to isolate the quantity component of
DMRL because it is the quantity component, and not the total cost, that is relevant to the
HbA1c production function. The units of quantity are somewhat arbitrary by nature as
the units are lost the HbA1c production function. Still, for purposes of clarification and
for possible empirical applications, I define units for QPHC, QHABITS, and QBGM. Each
price level then depends on how the units are defined.
Professional healthcare is easiest to measure in terms of hours. Thus, one unit of
QPHC is equal to one hour of professional healthcare, while PPHC, the price of one unit of
QPHC is the out-of-pocket cost of one hour of professional healthcare (total cost * (1-i))
plus the non-financial costs κPHC32 associated with one hour of professional care33.
The unit for QHABITS relies on the previous definition of a normalized unit of antidiabetes habit, hi. PHABITS is then the dollar valuation of the utility lost due to abstention
from activity hi over a one year period. (h0……hj) is the set of anti-diabetes activities
that a diabetic abstains from out of the total set of anti-diabetes activities (h0……hk). By
32
Mostly time costs, but perhaps factors such as dislike of doctors, fear of healthcare costs as well.
Non-financial costs are assumed to be combinable with financial costs by using WTP schemes or other
valuation methodology.
33
29
definition, u(hi) < u(h(i+1)) for all values of i, 0 < i < k. This implies that PHABITS
increases for each unit of QHABITS; the marginal utility lost for each unit of QHABITS grows
as costlier behaviors are given up.
Defining QBGM is difficult because unlike QPHC, QBGM is not made up of a single
type of good (such as hours of healthcare). Rather, QBGM or the blood-glucose
management component of DMRL is best understood as the basket of goods related to
BGM consumed over the course of a year. The basket of BGM medical supplies includes
blood-glucose test strips for glycemic self-monitoring, oral medications, insulin and
needles for insulin-dependent diabetics, as well as any devices used in BGM, such as
glucometers, insulin pumps, or continuous glucose-monitors. Each element of the BGM
basket, 0 through k, is consumed at a given quantity over the course of a year, (q0 …….
qk), and has an associated price level (p0…… pk) that includes both financial costs and
non-financial costs, κBGM. Consequently, CostBGM can be expressed as:
i k
(1b) CostBGM =
q p
i 0
i
i
An individual is assumed to choose the quantity of each element in his or her BGM
basket of goods efficiently, so as to get the greatest amount of HbA1c reduction for a
given level of CostBGM. QBGM is normalized so that a unit of QBGM derived from element
i is the same as a unit of QBGM from element j. In order to account for the different
i k
returns to (q0 ……. qk), QBGM can be expressed as QBGM =
K q
i 0
i i
where Ki is a scalar
that represents the returns to the ith element of the BGM basket for a particular
30
individual34. Assuming a rational diabetic is aware of the price level for each element,
(p0……. pk), and the returns to each element in his or her BGM basket, (K0 …… Kk),
QBGM is maximized for a given CostBGM. PBGM is then the value of CostBGM ÷ QBGM.
IIIb. Discussion of Price Levels
Analyzing the price levels PBGM, PPHC, and PHABITS can lead to insights about the
optimal allocation of diabetes management resources, QBGM, QPHC, and QHABITS to
minimize total cost for a fixed HbA1c level.
Given the dependency of PBGM and PPHC on insurance rates, one might expect that
the presence of health-insurance that covers medical costs would cause an increase in the
quantity of BGM and PHC (QBGM and QPHC) demanded over the course of a year. Higher
QBGM and QPHC will then lead to better HbA1c levels. The correlation between healthinsurance and improved HbA1c levels has been shown empirically (Bowker, 2004).
A lot of research has been devoted to the κBGM component of PBGM, often referred
to in the literature as the psychosocial barriers to blood-glucose management (See
Dharmalingam, 2002, and Peyrot et al., 2005, among others). These barriers are
normally viewed as independent of PBGM, as irrational obstacles to overcome rather than
inherent components in the cost of blood-glucose management. The view of
psychosocial costs as irrational may have to do with the tendency of these costs to
diminish over time. It appears as if we “learn” our old fears of blood-glucose
management were irrational.
34
For example, the return to good i for Type 1 diabetics, where i is oral medication intended for Type 2
diabetics, will be 0. Meanwhile, the return to insulin and syringes will be 0 for non-insulin dependent Type
2 diabetics.
31
As mentioned earlier, the psychological principal of habituation35 may shed some
light on κBGM. In “A Theory of Rational Addiction” (1988), Becker and Murphy develop
the idea that future consumption of a given good may depend on its stock of past
consumption. The magnitude of κBGM depends on factors such as needle aversion, fear of
blood, and the stress and time-costs of BGM. Each of these psychosocial factors
becomes less pronounced as diabetics adjust to the routine of the disease; few veteran
diabetics, for example, still fear giving themselves insulin injections. We may thus
characterize κBGM as a function of c, the consumption stock of QBGM accrued over the
duration of the disease. Naturally, there are decreasing marginal returns to c as
habituation effects are limited and occur most sharply at initial diagnosis. As κBGM
decreases due to habituation, QBGM will increase; this may partly account for gradual
lowering of HbA1c levels after diagnosis.
Habituation also lowers PHABITS over time. As one adjusts to the behavioral
changes that diabetes management demands, the value of the utility function U(hi) where
hi is a given anti-diabetes behavior is likely to decrease. The example of soda
consumption as an anti-diabetes behavior can clearly illustrate the changing utility
function. When first diagnosed with diabetes, an individual may consider the switch
from regular to diet soda as a drastic but necessary lifestyle change; the net utility from
switching from regular to diet soda was positive but near 0. As the individual adjusts or
habituates to diet soda however, the utility, ignoring effects on diabetes management, that
would be gained from drinking regular over diet becomes smaller and smaller.
35
I definite habituation here to mean a decrease in responsiveness to a given stimuli.
32
IIIc. The HbA1c Production Function
The objective of diabetes management is to maintain blood-sugar levels that are
as close to normal as possible. The difference between a diabetic’s blood-sugar level and
the normoglycemic range36 reflects, inter alia, the amount of resources devoted to
diabetes management over a short period of time. Because blood-sugar levels are highly
variable and only reflect diabetes management over the past few hours, they do not serve
as a meaningful indicator of diabetes management in general. In contrast, an individual’s
HbA1c level reflects average blood-sugar levels over a roughly 3 month period, and is
thus the best measurement of the available achieved level of diabetes management.
Higher DMRLs are consumed in order to lower HbA1c levels, thereby avoiding
diminished future health from associated high HbA1c levels (or chronic hyperglycemia)
and gaining short-term utility from maintaining more normal blood-sugar levels37.
The efficacy of diabetes management, and the source of utility gains from
diabetes management, can be interpreted as the difference between a diabetic’s HbA1c
levels with and without good diabetes management. Now that the DMRL has been
decomposed into a set of quantities, QBGM, QPHC, and QHABITS as well as their
corresponding prices PBGM, PPHC, and PHABITS, we can look at how these variables affect
HbA1c. I use a production function to characterize this interaction, where QBGM, QPHC,
and QHABITS, and ε serve as inputs that determine the output, HbA1c. ε represents the
endogenous characteristics particular to each individual, such as intrinsic problem-
36
A normal blood-sugar level, or normoglycemia, is considered to be in the range of 80 to 120 mg/dL.
Diabetes presents an additional problem called hypoglycemia, or excessively low blood sugar.
Hypoglycemia causes disutility at low levels and can be potentially fatal at extreme levels. Hypoglycemia
is not incorporated into this model.
37
33
solving skill (See Hill-Briggs, 2003) and health characteristics that also play a role in
determining HbA1c levels38.
Formula 1 gives the basic production function for HbA1c.
(5) HbA1c = F(QBGM, QPHC, QHABITS, ε)39
Given this production function, and the price levels PBGM, PPHC, and PHABITS, a
rational diabetic with perfect information will minimize his resource consumption, or
DMRL, for any achievable HbA1c level40. This minimization problem takes the form
min(QBGMPBGM + QPHCPPHC + QHABITSPHABITS) subject to the constraint
HbA1c = F(QBGM, QPHC, QHABITS, ε)
where HbA1c is a fixed HbA1c level41. Price levels are also taken as fixed, with the
exception of PHABITS which is a function of QHABITS for the aforementioned reasons. The
optimal levels of QBGM, QPHC, and QHABITS can be solved using the Lagrange Method.
Meanwhile, the solution to min(QBGMPBGM + QPHCPPHC + QHABITSPHABITS) represents the
minimum DMRL needed to achieve a specific HbA1c level. Any HbA1c level will
therefore have an associated minimum DMRL, or minimum total cost of resources
needed to achieve the given HbA1c level. The choice of an optimal HbA1c level based
on the associated minimum DMRL is the subject of the third section of the theoretical
model. From the optimization equations, we can also determine the marginal rates of
38
In a 2002 study, Rohlfing et al. looked at variation in the baseline HbA1c levels of diabetics that occur
independent of diabetes management and blood-glucose levels. The biological mechanisms that cause this
variation are unknown.
39
To avoid
40
Achievable HbA1c levels are assumed to be any HbA1c level equal to or greater than a normoglycemic
HbA1c level.
41
Solving for this minimum involves the Lagrange method of optimization. Because no meaningful
conclusions result from solving this minimization problem (mainly because the HbA1c function is not
specified), I leave out the math.
34
substitution between the blood-glucose management, professional healthcare, and
behavioral changes.
While the exact HbA1c production function is difficult to determine and will
vary significantly from individual to individual (and even for the same individual over
time), we can generalize about the characteristics that all HbA1c production functions
will have. For one, the healthcare inputs QBGM, QPHC, and QHABITS will have decreasing
marginal returns to HbA1c. The theoretical upper bound of the HbA1c production
function is a normoglycemic HbA1c level. An individual diabetic approaches the
normoglycemic HbA1c level asymptotically as QBGM, QPHC, and QHABITS approach
infinity. Meanwhile, increases in QBGM, QPHC, and QHABITS will have a much larger effect
in cases of poorly managed diabetes, when the HbA1c levels are very high. The marginal
returns to QBGM, QPHC, and QHABITS will be highest at DMRL = 0, when the value of
HbA1c will be at its unmanaged level. This intuitive result, in more rigorous terms, takes
the form F′(Q) > 0 while F′′(Q) < 0 for each input42.
Further generalizations can be made about the interactions between the three
quantity variables in the HbA1c production function. Higher QPHC values will result in
larger returns to QBGM as professional healthcare consultation teaches diabetics
techniques to make their blood-glucose management more efficient. Higher HbA1c
values will create greater returns to QPHC as poor HbA1c levels increase the necessity of
42
One could argue that the marginal productivity of BGM becomes negative past a certain value of QBGM.
Too much self-monitoring and overcorrection of blood-sugar levels with insulin or oral medication can lead
to what is colloquially known as the “blood-sugar roller coaster.” One can picture the blood-sugar roller
coaster by imagining a driver who constantly overcorrects on the steering wheel. While Q BGM is high,
glycemic control is not.
35
professional healthcare and early intervention for diabetes-related complications43.
Larger values of QHABITS are necessary to reach a given HbA1c level for individuals who
have many behaviors that conflict with blood-glucose control.
The optimal quantities QBGM, QPHC, and QHABITS also depend on income of the
individual because of its effect on the relative prices PBGM, PPHC, and PHABITS. For most
individuals, the price PBGM will depend more heavily on financial expenditure and than
on the associated costs κBGM44. PPHC is largely financial as well, but has a major time-cost
component to it. On the other hand, PHABITS is almost entirely non-financial in nature.
The value of PHABITS is determined through a WTP scheme. Willingness to pay for a
given utility gain increases dramatically with income (Bala, 1999). This implies that the
extent of the correlation between income and quantity demanded depends on the relative
prominence of WTP components in the price of the good. Similarly, prices for goods that
do not depend on WTP will not increase with income, making the income effect for that
good larger. From this analysis, we can make conclusions about how income may affect
the ratio between goods QBGM, QPHC, and QHABITS assuming an optimal allocation within
the production function. A higher level of income causes the greatest percent increase in
PHABITS, followed by PPHC, and finally by PBGM. Accordingly, ceteris paribus, we might
expect individuals with high income levels to have higher relative levels of QBGM to both
QPHC and QHABITS, and a higher level of QPHC relative to QHABITS.
43
This relationship is caused by the fact that complications resulting from consistent chronic
hyperglycemia are more likely for lower DMRL values. The most important form of early intervention
deals with diabetic retinopathy which can lead to vision damage and eventually blindness. Early treatment
through laser surgery can reverse the effects of diabetic retinopathy and prevent more extreme vision
complications from occurring.
44
Unless the psychosocial costs of blood-glucose management for a particular individual are exceedingly
high.
36
Another crucial consideration in the HbA1c production function is the type of
diabetes an individual has. Insulin dependent diabetics and Type 1 diabetics in particular
have much greater fluctuations in blood-sugar levels than Type 2 diabetics without
insulin dependence. Dependence on insulin and the incidence of greater glycemic
fluctuations place a premium on QBGM. Accordingly, the HbA1c production function will
weigh QBGM much more heavily in such individuals (See Evans, 1999, and Bowker,
2004). Likewise, the HbA1c production function for Type 2 diabetics places a much
larger premium on QHABITS. This is due to the fact that cases of Type 2 diabetes are
largely controllable through diet and exercise in a way that cases of Type 1 diabetes are
not. QPHC is more important for individuals who have difficulty adjusting their own
diabetes management regimens. Professional healthcare and consultation may help such
individuals learn management techniques, increasing the returns to QBGM and QHABITS.
Diabetics who frequently self-monitor and have a natural grasp of the interaction between
medication, diet, exercise, and blood-glucose levels may have lower returns to QPHC. The
exact nature of the HbA1c production function will thus vary significantly from one
person to another depending on their disease and health characteristics.
IIId. Lifetime Utility as a Function of HbA1c Level
For rational agents trying to maximize their lifetime utility, health is a means and
not an end. Diabetics consume diabetes management to regulate their HbA1c level, a
primary input in the health production function for diabetics. They do so because
producing health creates utility. The DMRL of a diabetic represents the costs he or she
incurs in order to regulate the level of HbA1c. In order to understand the level of HbA1c
37
a diabetic seeks to achieve, however, we must break down the utility gains that result
from lower HbA1c levels. This requires the creation of a U(HbA1c) function. Diabetics
will try to maximize the following function:
(6) U( HbA1c ) – DMRL
HbA1c
Recall from IIb. that a fixed HbA1c level denoted as HbA1c has an associated
minimum DMRL level, denoted DMRL
HbA1c
. Equation (6) reflects the net utility for a
given HbA1c , and diabetics select a HbA1c , here an independent variable, to
maximize their net utility.
Equation (6) lays out the broad framework for the overall utility maximization
problem that diabetics face when choosing the level of resources to devote to diabetes
management. However, we can come to a more concrete understanding of this
maximization decision by describing the U(HbA1c) function.
Diabetics gain utility from HbA1c control in both the short-term and long-term.
The short-term utility gain is due to the more normal glycemic levels associated with
lower HbA1c levels, while long-term utility gains are due to decreases in expected
morbidity and delayed mortality. Rational diabetics choose a DMRL to maximize the net
present value of their lifetime utility. Thus, time-preferences for future utility are built
into the U(HbA1c) function.
A more accurate representation of the short-term utility from diabetes
management would be a function of glycemic levels, U(gl), rather than HbA1c. Similar
to the U(HbA1c) function, U(gl) is higher for more normoglycemic levels and lower
when blood-glucose deviates from the normal range. As mentioned, blood-glucose levels
38
fluctuate greatly within the timeframe of a day, while HbA1c levels are much more
steady and tractable. Blood-glucose levels are largely controllable through the
consumption of diabetes management resources over the previous few hours, but there is
still a large, inexplicably random component to them. Additionally, consuming diabetes
management is not a form of instant gratification like many other forms of consumption,
because the effect of diabetes management on glycemic levels, and thus U(gl), is delayed
considerably. As short-term utility U(gl) is a function of glycemic level which depends
on both diabetes management and random factors, the consumption of diabetes
management is something of a Markov decision process.
Using Prelec and Loewenstein’s 1991 model45, the delay and uncertainty of utility
gains from consuming diabetes management might cause a considerable devaluation of
the net present value of utility U(gl) gained in the near future. This effect is lost in the
function U(HbA1c), as short-term utility as a function of HbA1c does not account for the
uncertainty and time-delay between diabetes management resource consumption and
utility gains from the expected more normoglycemic state. Embedded in the Prelec and
Lowenstein concept of utility devaluation is the notion of hyperbolic discounting.
Adding in a hyperbolic factor will decrease the utility output from the functions U(gl) and
U(HbA1c)46.
45
Loewenstein also introduces the concept of anticipal utility, or utility that is gained in the present based
on the anticipation of future utility. With regards to diabetes, the anticipation of future utility from better
future health states would increase the utility experienced in the short term from consumption of diabetes
management resources.
46
As mentioned, the NPV of utility from diabetes management resource consumption is the sum of quasiimmediate utility from normoglycemia and future utility from improved health states. Normoglycemia
utility is quasi-immediate because there is a time gap of somewhere between 15 minutes and several hours
before diabetes management resource consumption affects glycemic levels. Without a hyperbolic discount
factor, the steady time-discount rate would be insignificant; the NPV of utility from diabetes management
resource consumption would be equal to the utility from resource consumption if the time gap did not exist.
Thus, introducing the hyperbolic factor significantly diminishes the NPV of U(gl).
39
The long-term component of the U(HbA1c) function is the net present value of
utility from improved future health states and longer life and the NPV of the financial
cost of diabetes complications that are avoided as a result of disease management. While
there are several different ways to discount future utility (Cohen, 2003), the simplest is to
apply a constant discount factor δt where δ is the risk-free rate of interest and t is time
measured in years. In relating HbA1c levels to future health, one must isolate the portion
of health that is specific to diabetes management. This is normally thought of as avoiding
diabetes complications. The ability to avoid complications depends not only on HbA1c
levels, but lifestyle and random factors as well. Consequently, deciding the optimal
HbA1c level based on gains to future health can also be seen as a Markov decision
process. Rather than determining the future diabetes component of health, HbA1c levels
alter the probably distribution of the chance that various diabetes health states occur over
the spectrum of future points in time. Each possible diabetes health state has a
corresponding quality of life adjustment factor, like those used to calculate QALYs. A
theoretically accurate valuation of these probabilistic outcomes at each time t, discounted
by a factor of δt might involve prospect theory (Kahneman and Tversky, 1979). A
simpler and more empirically useful evaluation could use QALY methodology and a
constant time discount rate.
Thus, the U(HbA1c) function can be broken down into short-term utility, longterm utility, and long-term costs. Further modeling could go into more detail of the
U(HbA1c) function.
40
IV. Externalities and Informational Problems
The framework I have set up examines the level of resources a rationally acting
diabetic devotes to diabetes management given perfect information. By definition, this
individual maximizes his or her personal welfare by consuming an optimal DMRL and
distributing these resources in such a way that minimizes HbA1c for a given resource
level. However, the presence of positive externalities to diabetes management means that
the optimal DMRL for an individual is lower than the socially optimal DMRL. These
externalities exist because the costs of diabetes, financial and otherwise, are not borne
exclusively by the individuals who have the disease.
In a 2002 study, Ramsey et al. analyzed the economic burden of diabetes borne by
employers. There are two major sources of costs that diabetes imposes on employers:
direct medical care costs and productivity loss. Many employers offer health-insurance
to their employees. The insurance premiums that employers pay to health-insurance
companies are dependent on the previous year’s total medical cost and reasonable
assumptions about next year’s costs. Diabetics invariably cost the medical system more
than non-diabetics47 and this cost is largely passed on to the employer. Insofar as
diabetes management is cost-effective in a strictly financial sense, a higher DMRL will
reduce the total medical cost of an employed diabetic that gets passed on to the healthinsurance plan and then to the company. Diabetics, however, do not receive the gains
from this reduction in total cost of medical expenditure.
47
A common methodology for estimating the cost of diabetes is the establishment of the ratio, R, of
healthcare costs for diabetics compared to healthcare costs for non-diabetics. The International Diabetes
Foundation cites the value of R at 2.6 for the United States, based on work by Rubin and Altman (1994). R
has likely increased in recent years.
41
Diabetics also have lower work productivity than their non-diabetic counterparts,
owing to medically related absences and potentially compromised on the job
performance. Medically related absences and lower productivity from diabetes are
almost inevitably the result of low levels of diabetes management. Because these costs
are borne by the employer, employed diabetics have insufficient incentives to manage
their disease. The Ramsey study found that the average annual extra cost to employers
(in 1998 dollars) for hiring a diabetic worker was $4,410. In theory, the market for labor
could take into account the extra costs that diabetic employees bring with them and pay
diabetic employees a lower wage in accordance with their diminished marginal revenue
product of labor. Employers could also fire diabetic workers who are relatively
unproductive and replace them with more able workers. However, strong barriers are in
place that prevent wage or hiring discrimination according to medical conditions.
Additionally, frictions in the labor market inhibit firing of diabetic workers who take
excessive medical leave of absence because of poorly controlled diabetes.
Part of the cost of diabetes complications and early mortality is the psychosocial
cost borne by family and friends of the diabetic individual. The poor health-state of a
loved one can be a source of anxiety and unhappiness. Early mortality from diabetes can
impose a great financial burden on the family of the deceased. Caring for a diabetic with
severe complications, such as kidney failure requiring blood dialysis, is another form of
cost resulting from poor diabetes management that is external to an individual’s
maximization function.
The effect of medical insurance on the difference between individual utility
maximizing DMRLs and social welfare maximizing DMRLs is unclear. When medical
42
insurance defrays part of the cost of medical expenditure, individuals may behave in
ways that are clearly not social welfare maximizing as explained by moral hazard. An
insured individual may engage in overly risky behavior, and when in need, may
overconsume medical intervention because he or she gains all of the benefits of the
intervention while only paying some of the costs. Medical insurance for diabetics,
however, is assumed to cover a portion of both CostBGM and CostPHC, while also insuring
against the medical cost of future complications. These two effects operate in opposite
directions. If only CostBGM and CostPHC (i.e. expenditure on diabetes management) were
insured, diabetics would overconsume diabetes management resources. Likewise, if
insurance only covered medical complications from diabetes, diabetics would tend to
underconsume management resources.
The structure of insurance coverage can therefore play an important role in
internalizing potential positive externalities to diabetes management. If insurance plans
(or government subsidies48) more heavily covered the financial burden of diabetes
management, diabetics would consume more diabetes management resources.
Externalities alone seem insufficient to explain “underconsumption” of diabetes
management resources. One could argue that perhaps the notion of underconsumption is
a myth; diabetics maintain optimal DMRLs and the perception of underconsumption
occurs because the true utility-maximization functions that diabetics use to select a
48
On the topic of subsidies, a recent New York Times Magazine article by Michael Pollan highlights a
different and seemingly unrelated government subsidy that seems to have important implications for the
incidence and cost of Type 2 Diabetes in the United States: agricultural subsidies. Through agricultural
subsidies, the US government creates an artificially low price for corn, which can be readily processed into
high-fructose corn syrup. This translates into artificially low prices for cheap, processed goods that are rich
in high-fructose corn syrup calories (sodas and Twinkies serve as prime examples). What’s more, these
highly processed, low nutrient food items offer a much higher calorie per dollar ratio than more nutritious
foods with a lower glycemic index. Because of this artificially high calorie/dollar ratio, poorer consumers
are drawn to these goods. In turn, high consumption rates of these processed foods have been linked to the
development of Type 2 Diabetes.
43
DMRL are not understood. Intuitively, this explanation seems unlikely. While there are
both hard-to-quantify benefits and costs in a diabetic’s DMRL utility maximization
function, I would argue that the benefits to diabetes management significantly outweigh
the costs. Additionally, the high cost-effectiveness ratio of diabetes management in terms
of $cost per QALY underscores the likelihood that underconsumption is indeed
occurring.
The alternative explanation of underconsumption is that diabetics suffer from a
great deal of imperfect information about their true lifetime utility as a function of the
resources they devote to diabetes management. Diabetics may underestimate the
potential damage from hyperglycemia and misguidedly think they are immune to the
devastating complications of diabetes. Similarly, diabetics may give up on their disease,
falsely accepting the notion that blood-sugar levels and HbA1c are outside of their locus
of control. Less educated diabetics may simply not know that alternative blood-glucose
management regimens exist. Imperfect information about the HbA1c production
function also prevents diabetics from optimizing the allocation of resources they do
devote to diabetes management.
Ironically, media attention given to potential cures for diabetes may further
undermine diabetes management. The phrase “a cure within five years” has been
something of a mantra within the diabetic community for roughly the last fifty years. The
optimistic notion that a cure will soon arrive (an example of imperfect information)
weakens the incentive to devote resources to diabetes management. If diabetics assume
that a cure in the near future is more likely than it actually is, the NPV of future gains to
health and avoided cost of complications will be discounted too heavily.
44
V. Conclusion
According to the Center for Disease Control, diabetes is the 5th leading cause of
death in the United States. Mortality rates alone, however, do not begin to describe the
toll that diabetes exacts on individuals and society as a whole. Based on statistics from
the 2002 American Diabetes Association estimate of the economic burden of diabetes,
the total cost of the disease may already exceed $200 billion. As the US population
continues to become more sedentary, and as obesity rates skyrocket, the incidence of
diabetes will only go up. This makes diabetes a timely subject for economic research
The chronic nature of diabetes demands that each individual diabetic takes the
lead role in managing his or her disease. Fortunately, the substantial morbidity and
mortality risks associated with diabetes can be largely avoided if blood-sugar levels are
controlled. Controlling blood-sugar levels is a costly process, and the level of control
that an individual diabetic obtains reflects the amount of resources that he or she is
willing to devote to diabetes management.
In this paper, I investigate the various factors that influence how an individual
decides to manage diabetes. If we assume that diabetics are rational agents, then the level
of resources devoted to diabetes management (the DMRL) can be understood as part of
an optimization problem in which diabetics maximize their lifetime utility. The DMRL
consists of a series of inputs that produce a level of diabetes control, best measured by
HbA1c. The net present value of lifetime utility can then viewed as a function of HbA1c
levels, because HbA1c reflects blood-sugar levels and can predict the likelihood of future
diabetes related complications.
45
The theoretical model I lay out is best viewed as a framework for understanding
the level of resources devoted to diabetes management. Within this broad framework,
there is much room for further behavioral economic modeling to better comprehend the
myriad decisions that diabetics make on a constant basis to manage their disease. My
model makes rough predictions that are largely substantiated by empirical research.
More detailed and specific modeling could point the way to empirical studies of how
diabetics actually behave.
Diabetes management is normally viewed as underconsumed; individual and
social welfare might be increased if more resources are devoted to managing diabetes.
The model I create starts with assumptions of rationality and perfect information.
Externalities create room for social welfare increases, but by definition, individual
DMRLs are understood to be optimal choices. However, the reality of diabetes
management is riddled with imperfect information. Based on evidence from empirical
studies of the cost-effectiveness of diabetes management, it is hard to argue that most
individuals choose an optimal DMRL. Imperfect information is the de facto explanation
for this inconsistency.
Of course, the ultimate solution to diabetes management can be summed up by the
elegant equation, DMRL = 0. “A cure within five years” has been repeated so often over
the years that, by the law of large numbers, one day it must come true. While the world
waits for a definitive cure, diabetics must find ways to optimize their diabetes
management. Hopefully, a theoretical model of how diabetics devote resources to
diabetes management will further our understanding of optimal management.
46
Appendix. Depression and Diabetes
One major “psychosocial cost” in diabetes management literature which I omit
from the discussion of price levels is depression among diabetics. A 2006 study by Mary
de Groot et al. found that roughly 25% of individuals with diabetes also suffer from
symptoms of depression. Meanwhile, depression is cited as the foremost psychosocial
barrier to blood-glucose control (Lin et al., 2004). There are two ways to interpret the
relationship between depression and poor blood-glucose control (as exhibited in high
HbA1c levels). One explanation is that depression changes the price levels, PBGM, PPHC,
and PHABITS, of diabetes management. As a result, individuals consume lower QBGM,
QPHC, and QHABITS, and experience higher HbA1c levels. However, there seems to be
little causal mechanism to significantly change the price levels.
The second possible interpretation of the link between depression and poor bloodglucose control is that the utility gains from diabetes management, or U(HbA1c), are for
lack of a better word, depressed. Depression may be seen as a state which reduces
present utility levels and creates a feeling of hopelessness about the future, which may be
understood as a higher discount rate of the NPV of future utility. U(HbA1c)Depressed <
U(HbA1c)Not Depressed. Utility gains from diabetes management as measured by HbA1c
are smaller for individuals with depression. If PBGM, PPHC, and PHABITS are largely
unchanged in a depressed state, however, the cost of diabetes management remains the
same. This implies that the optimal level of diabetes management and the corresponding
optimal HbA1c level are lower for depressed diabetics. Depressed diabetics who exhibit
poor blood-glucose control are simply responding to the parameter of depression within
this diabetes management utility maximization framework.
47
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