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

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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.

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Table of Contents

I. Introduction……………………………………………………………… 3

II. Literature Review………………………………………………………. 9

IIa. Compliance and Empowerment ModelsIIb. Cost-effectiveness of Diabetes Management

IIc. Behavioral Economics and Modeling Diabetes Management

III. Theoretical Model of Diabetes Management…………….…………… 24

IIIa. The Components of DMRLIIIb. Discussion of Price LevelsIIIc. The HbA1c Production FunctionIIId. Lifetime Utility as a Function of HbA1c Level

IV. Externalities and Informational Problems…………………………… 40

V. Conclusion……………………………………………………………….. 44

Appendix. Depression and Diabetes………………………….……………. 46

References……………………………………………………….…………... 48

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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.

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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.

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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.

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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

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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 utility-

maximizing 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

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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.

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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 non-

compliance 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 transfer of past experiences. Her study illustrates the importance patient agency in effective diabetes management.

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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

philosophy, no clear framework has been made to analyze the patient’s decision from a

lifetime utility maximizing perspective.

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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 meta-

analysis 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

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 6 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.”

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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 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

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.

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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.

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 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 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.

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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

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

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).

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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).

The accuracy of these models14 has allowed the healthcare industry to refine diabetes

treatment regimens and achieve more efficient allocation of diabetes management

13 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).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.

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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

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

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.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).

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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).

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

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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

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

19 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.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.”

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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

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

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.

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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 self-

control, 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

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

22 This theoretical result is supported empirically in a study by Ng, Darko, and Hillson (2004).23 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.

21

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 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

24 Primarily oral agents, insulin injections, or exercise

22

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 cost-

effective 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

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.

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 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.

23

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

24

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

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

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

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).

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.

26

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, 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

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.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.

27

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 blood-

glucose 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.

(3) CostHABITS = φ

(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

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

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 anti-

diabetes 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

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

32 Mostly time costs, but perhaps factors such as dislike of doctors, fear of healthcare costs as well.33 Non-financial costs are assumed to be combinable with financial costs by using WTP schemes or other valuation methodology.

29

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:

(1b) CostBGM =

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

returns to (q0 ……. qk), QBGM can be expressed as QBGM = where Ki is a scalar

that represents the returns to the ith element of the BGM basket for a particular

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

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.

30

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 health-

insurance 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.

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

35 I definite habituation here to mean a decrease in responsiveness to a given stimuli.

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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.

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

36 A normal blood-sugar level, or normoglycemia, is considered to be in the range of 80 to 120 mg/dL.

32

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-

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

37 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.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

33

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

= F(QBGM, QPHC, QHABITS, ε)

where 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 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

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

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 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

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 QBGM is high, glycemic control is not.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.

35

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.

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

36

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

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() – DMRL

Recall from IIb. that a fixed HbA1c level denoted as has an associated minimum DMRL

level, denoted DMRL. Equation (6) reflects the net utility for a given , and diabetics

select a , 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.

37

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

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 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.

38

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.

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

46 As mentioned, the NPV of utility from diabetes management resource consumption is the sum of quasi-immediate 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).

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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, long-

term utility, and long-term costs. Further modeling could go into more detail of the

U(HbA1c) function.

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

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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 health-

insurance plan and then to the company. Diabetics, however, do not receive the gains

from this reduction in total cost of medical expenditure.

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 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.

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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

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

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(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

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

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.

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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.

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

44

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.

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

45

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.

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 blood-

glucose control is that the utility gains from diabetes management, or U(HbA1c), are for

46

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.

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