THE UTILITY FUNCTION OF ANTIHYPERTENSIVE THERAPY

THE! UTILITY FUNCTION OF ANTIHYPERTENSIVE THERAPY * Lewis B. Sheiner and Kenneth L. Melmon

Division of Clinical Pharmacology Departments of Medicine, Clinical Pathology and Laboratory Medicine, and Pharmacology; and the

Cardiovascular Research Institute University of California

San Francisco, California 94143

It is axiomatic when one is speaking about decisions, whether they be in business, medicine, or any other field, that optimal behavior consists in acting so as to maximize profits. Profit is further defined as the excess of gains over losses (FIGURE 1 ) . In medicine, we almost always attempt to arrive at optimal decisions by intuitive means, rather than as the result of a formal analysis of gains and losses. There are good reasons for this, which we will discuss shortly, but it is our contention that the framework of a formal analysis can provide insight into the nature of the problems in decisions that we face. In the process, it can aid us, if not in making the decisions themselves, then at least in planning a strategy for decision-making, and a strategy for seeking knowledge.

This thesis is particularly well illustrated in the area of hypertension. It will be our purpose to discuss briefly the elements of the formal theory of decision- making, to illustrate some of its strengths and weaknesses, and to apply it as a framework to the decision problems confronted when we deal with patients with hypertension. We hope to point out that this approach reveals some particular gaps in our knowledge, and some blindspots in our decision making.

Turning first to the theoretical aspects of decision theory, we define the utility of an action as the profit associated with it. That is, utility equals gain minus loss. Thus, an optimal decision involves maximizing utility.’

Next, we must refine the notion of a gain or a loss. In the medical arena, these are usually referred to as benefit and risk. The latter term, however, is inappropriate because it mixes the notion of an untoward event with the probability of that event; two aspects that must be kept separate. We therefore prefer the two terms, benefit and harm, In fact, the confusion of “risk” with “harm” indicates the first major advantage of a theoretical analysis: whereas the generic idea of benefit and harm is not unfamiliar to anyone, it is not so apparent to all that each of these concepts contains a factual portion and a value judgment portion (FIGURE 2). Consider death from a drug: the factual part of this harm concerns the probability that death results from the use of the drug. I t can be expressed by a number: x deaths per y doses, or x deaths per average course of treatment, or some other number. The important point is that it is a quantity that can, at least in theory, be measured and known. The other part of the harm of death from a drug concerns a value judgment about just how serious and undesirable death itself is. To someone about to ingest an overdose

*This research was supported in part by National Institutes of Health Grants

112 GM-16496, GM-00001, and GM-01791.

0077-8923/78/0304-0112 $01.75/0 @ 1978 New York Academy of Sciences

Sheiner & Melmon: Antihypertensive Therapy 113

U = Gains - Losses

U = B e n e f i t - R i s k

R i s k = harm o f untoward event x p r o b a b i l i t y o f event

Risk = expected medical harm

U t i l i t y = Benef i t - Harm

FIGURE 1. The general definition of utility (U).

of drug with suicidal intent, death from the drug is not a harm, it is a benefit! The exact same process of analysis applies to the concept of benefit; the factual portion concerns the probability of some named benefit, and the value part concerns the worth of that benefit.

Decision theory states that benefits and harms must somehow be reconciled so as to arrive at a “net” effect of their probabilities and values. A natural idea for this reconciliation is to deal with “expected harms” and “expected benefits.” These are average harms and benefits. They are computed as follows: if the probability of winning a lottery worth $10,000 with one ticket is one chance in 10,000, then the expected gain from each ticket is $1.00; that is, one can expect (over the long run) to win this amount per ticket bought, and this sets a rea- sonable price on the ticket itself. Thus, an “expected benefit” is simply the probability of the benefit times its value. Similarly, an “expected harm” is the probability of the harm times its value or cost. The problem of balancing benefits and harms by using this sort of calculus then becomes straightforward: the expected benefit minus the expected harm is computed (the expected payoff from the lottery ticket minus the cost of the ticket) : If it is positive, the benefit outweighs the harm, and vice-versa if it is negative.

In a medical context, benefits are usually indirect; that is, they consist in the capacity of the medical treatment to prevent or ameliorate some other harms from a disease or condition. As far as we know, medical interventions as yet do not extend health beyond “normality.” As a beginning, then, to a formal theory of utility in a medical context, we see that we need three distinct types of information: an enumeration of the harms of a condition and the harms associated with therapy, a set of probabilities for these harms, and a set of values to associate with these harms. The expected benefit of a given therapy will

U t i l i t y = Benefit - Harm

The components of Benefit and Harm are:

For each e f f e c t : Probabil i ty o f e f f e c t x cost o r value o f e f f e c t

Ef fect Probabi 1 1 t y Value or cost

\ For each death:

Factual; Science Judgmental ; Others. including

the patient

FIGURE 2. The medical adaptation of utility.

114 Annals New York Academy of Sciences

consist in the change in the probabilities of the harms of the condition that the therapy engenders, weighted by the values of these harms. The expected harm of the therapy will consist in the probabilities of the possible new harms caused by the treatment itself, weighted by the values of these harms. The utility of the therapy is the difference between these quantities.

Because many alternative therapies may be available for a given condition, and because the probabilities of benefits and harms may vary continuously with the intensity of therapy, the intensity of disease, and other factors pecu- liar to the individual patient, one usually speaks of a utility function; that is, a continuously variable function of continuously variable decisions. In this context, an optimal decision consists of adjusting that set of variables that the physician controls to the particular values that serve to maximize the utility function.

Before turning to the advantages of regarding medical decision-making from the decision-theoretic point of view, it is appropriate to examine the problems inherent in trying to apply the approach at all.

The first major problem concerns the notion of expected harm or benefit itself. In the payoff per lottery ticket example, it is sure that any given ticket pays either $10,000 or pays nothing. It is true that in the long run, if payoff is averaged over many tickets, it will come out to the dollar per ticket figure, but unless one is in the lottery (or insurance) business, this is not very interesting. When it comes to medical harms, one may be able to compute the expected harm of death, for example, to be 1 in 1,000 for the use of a particular drug; but no one loses one-thousandth of his life; one in a thousand persons loses his whole life. It is only when the probability of a harm or a benefit is quite high that the expected harm or benefit expresses anything like what any individual can actually expect.

A second major problem concerns the units in which to measure harms and benefits. They must be conformable because they are subtracted from each other in the utility function, Should the units be dollars? If so, what is the value of a human life? of a headache? of a stomach-ache? There have been serious attempts to assign dollar values to these things and up to a certain point it is possible. The cost to society of a given medical condition in terms of the cost of medical care, the loss of time at work, etc. can be measured; but what about the intangibles? Pain? Depression? Loneliness? The task seems hope- lessly difficult.

Finally, a technical problem; we rarely know enough about any medical condition, or treatment, to be able to come up with an exhaustive enumeration of harms and benefits, or with accurate estimates of their probabilities.

It is thus clear that there can be no hope of a definitive calculus of benefit and harm. What, then, are the general advantages of the theoretical framework?

Its major advantages stem from the crucial distinction it makes between factual items and value judgments. It thus provides us with a clear indication of where our scientific efforts must be directed: it is the business of medical science to provide the enumeration of events associated with diseases and treat- ments, and the probabilities associated with these events, both with and without treatment. Furthermore, the framework makes it clear that value judgments must be made. Should these be the concern solely of the physician? Values or costs of events are subjective, and will always be so. When the issue is not the probability of a harm, but is its relative value, we must clearly recognize that

Sheiner & Melmon : Antihypertensive Therapy 115

the patient may have something to say about this. It is surely our task to aid him in his evaluation, but is it our task to substitute our preferences for his?

Finally, the framework itself serves as a check on our own decision proc- esses; if we use it, that is, if we attempt to be explicit about the factors affecting our decisions, we may note where our knowledge is deficient, where our argu- ments primarily involve values versus facts, and where we are inconsistent or irrational. It is impossible to discuss these features in a general context. It is, however, possible and instructive to discuss them in a specific one. Let us, now, examine hypertension, and its treatment, from the point of view of decision theory and see what we can learn.

UTILITY FUNCTION AND HYPERTENSION

As was discussed above, to know the utility function of any therapy implies that the harms of disease can be explicitly listed; that their probabilities and the values or costs of each can be known in each of the various circumstances of the disease. One would need to know the alterations in the probabilities of disease-related events caused by therapy and how these changes are altered in different circumstances. The utility function could then be calculated. Examin- ing the areas where we are unable to complete this information may aid us in deciding which gaps to close.

WHAT Is KNOWN ABOUT THE ENUMERATION, PROBABILITIES, AND COSTS OF THE HARMS CAUSED BY HYPERTENSION?

Most doctors and some patients have become aware that death and some well-defined morbid events can be caused by hypertension. We know that most of these events have a probability that directly relates to the degree of elevation of blood pressure. We also know that certain other aspects of the individual patients allow us to individualize the probability of harm, e.g., the older the patient the greater the probability of most harms; the longer the duration of disease the greater the probability of harm; blacks are at higher risk than are whites; and men are at higher risk than women. Actuarial data com- piled by life insurance companies * and information from the cooperative studies of the Veteran’s Administration 3-5 and Public Health Service have begun to allow us to form a far better impression of the probabilities of harm to a fairly broad subset of patients with hypertension. They do not allow us, however, to evaluate the costs of those harms to society or the individual patient (FIGURE 3). We have more trouble assessing the probabilities of harms due to hypertension per se when these harms are commonly caused by other conditions. For example, precisely how much does a given degree of hypertension increase the probability of myocardial infarction? As a corollary, if the change in the probability of a disease-related event associated with treatment is obscured by a high “background noise,” then even if the costs of that event are high it may become unrealistically expensive to define the value of therapy. Thus, the cost of evaluating whether an antihypertensive medication can reduce the probability of myocardial infarction may exceed the value of the minor reduction (if any) that might be produced by the medication.

Associating values with the various harms that can be produced by hyper-


Placebo therapy

01astolIc blood p m s s ~ r e 1 1 5 - 1 2 9 n L

cvent P m b b i 1 Itylyerr cost or value

k i t h 2/10 1

s t r i a t e hemorrhage In

> 1 r e t l " l 1 quadrant

Cerebral or subdrachnold

M m r i h a w

Dissecting aort lc aneurysm

Uncsntrol l r b l e congertire

heart failure

Elevation of Bull > 501

( 0 1 > 59 W I l W cc)

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3/10 ?

CeiebrOvaICular throrborls

Tranrient I rchenlr attacks

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FIGURE 3. Schematic representation of the type of listing of events, their probabilities, and their costs or values that immediately allows us to categorize data, define what we really know and what we still need to learn. This listing considers the harm of disease only. (Derived from the Veteran's Administration. Cooperative Study. 1967. JAMA 202: ,1028-1034.)

tension is not easy (FIGURE 3). True dollar values have been placed on the loss of life, sight, o r limb by insurance companies o r courts of law, which are variously sensitive to society's and the individual's independently derived figures about these factors. Costs often are derived by the patient and they are very important but are not always systematically considered by the physician. The physician's estimate of costs are more often based on his impressions of the people he has seen with these events and how he "would feel" about having them himself than they are on the views of insurance companies or courts or even those of the particular current patient. The degree to which a harm is important to a patient will vary depending on his life circumstances; the value of that harm to an actuarial company may not. We have to begin to recognize overtly that the value or cost of harm caused by a disease (or therapy) is not the same to the doctor, his patient, or to society. Although we may never be very precise about such values, we should realize that the patient's judgment, as well as our own, should systematically enter into any interpretation of the costs associated with his disease and therapy. It is the job of science alone to enumerate events and assess their probabilities; it is the patient and society, and perhaps least of all the medical scientists, who must determine values.

As we have heard from Dr. Syme,' investigators are now beginning to gfapple with the concept of value judgments in the context of hypertension and its treatment. The work of Syme et al. implies that value judgments are malle- able and that some techniques to modulate them are better than others.' It is


to be hoped that additional educational procedures can be devised to modify the judgments on value made by physicians and allow them to incorporate in their value system the values of their patients.

WHAT Is KNOWN ABOUT THE BENEFITS AND HARMS OF THERAPY?

Although our knowledge of the harms of disease, their probability of occurring, and their costs leaves much to be desired, even less is understood about benefits, their probabilities, and values, or about the harms of therapy itself. The monumental work by the cooperative studies of the Veteran's Administra- tion 3-5 and the Public Health Service have given us a startling and impressive new knowledge about therapy. But if arriving at a utility function is our goal, we have a very long way to go.

We know that despite our lack of knowledge of the etiology and pathogenesis of essential hypertension, drugs that have been available for decades can (on an empirical basis) lower blood pressure and do dramatically and positively d e c t the prognosis of a subset of hypertensive patients (e.g., FIGURE 4). We know that adverse responses that are costly to the individual, or society, and that occur with high probability have been found without a carefully planned surveillance system. It is likely that, as time passes, we will continue to detect high probability or dramatic biologic events (if any) that can be attributed to chronic therapy. We can also surmise that if the pathogenic mechanisms of

P m b b l l l W h e l r cost or value -

!ioiom g@&! ThLI(S 3 81194 1.61186

11194 O I l 8 6

,21194 01186

7 1

.2/194 01186

11194 01186

.2/194 011w

,21194 01186

FIGURE 4. Benefit of therapy =J, in harm of disease. Schematic representation listing the benefits of therapy. Note that only very small subsets of the population at risk are considered. Note the vast areas of clinically relevant information that are totally unknown. (Derived from the Veteran's Administration Cooperative Study. 1970. JAMA 213: 1143-1 152.)


hypertension can be defined in terms of altered physiology or biochemistry, drugs that might be more efficacious and safer than the ones we now have will be developed. No one needs a utility function to remind himself of the sure profits that will accrue to the manufacturer of these new drugs.

We know that most of one subset of hypertensives can have their blood pressure lowered by one type of therapy. The effect of the drugs on blood pressure seems inversely related to the degree of starting blood pressure. Even in some people with moderate increases in blood pressure, there is improvement of prognosis of certain events caused by hypertensi~n.s-~

Let us review these data in terms of the concept of a utility function and see where our deficiencies lie. Some of the holes in our knowledge related to the Veteran’s Administration Study are discussed by the authors of these studies and have been extended today by Dr. Frolich.8 We should now understand that those results may not apply to the majority of patients with hypertension. Furthermore, we do not have all the pertinent data on those who have been studied. For example, did patients who were removed from therapy have a greater or lesser risk of harm from the disease than they would have had if they had never been treated? Did patients who were on therapy but had only a minor change in blood pressure derive benefit? Most important, however, is the question of what would have happened to hypertensive patients who were not studied by the Veteran’s Administration if they had been given and had taken drugs.

Included in the Veteran’s Administration studies were males whose blood pressure was persistently elevated for 4 days after they were in the hospital and who had been known as hypertensives for about 4 to 5 years. All were in the older age groups (>40), many had other established diseases, and all were followed on therapy for a maximum of about 5 years. Those who were alco- holics, or vagrants, or who had surgically remediable diseases or cerebrovascular accidents were not studied. Neither were those who would not consistently take the offered antihypertensives (this group amounted to fully 50% of those who otherwise would have been eligible for the study). All who were treated were given one group of drugs. Yet the use of reserpine has diminished greatly since its patent expired; hydralazine is often shunned by M.D.’s for a variety of reasons; and many other drugs have become more popular than those studied.

Finally, an assumption has arisen (not promulgated by the investigators) that the only therapeutic endpoint or event that counted was a decrease in blood pressure. Has the connotation of a drug’s “name” prematurely narrowed our focus on its effects?

From the point of view of a utility function, we can immediately see deficiencies not only in terms of our lack of knowledge about the effects of therapy on patients whose demographic characteristics excluded them from study, but because only one regimen was tested and, perhaps every bit as important, only one therapeutic endpoint was sought (FIGURE 5 ) . Let us dwell on the latter for a moment as an illustration of another advantage of thinking in terms of utility.

The usual assumption appears to be that a lowering of blood pressure (by any means) to “normal” levels constitutes a fixed benefit. In this case, the benefit of therapy can be regarded as a constant. Thus:

Utility = Constant - The sum of expected costs

Hence, maximizing utility simplifies to minimizing costs for a “normaliza-


tion” of blood pressure. If the assumption is true, then attention can be directed solely to determining the relative total expected costs of alternative regimens (engendering the same blood pressure change) to the individual, the physician, and society. Bearing the concept of utility in mind, however, helps us to focus on other issues. For example, what fixed change in blood pressure should be sought for an individual? Is “normalization” the objective for everyone? More importantly, is lowering the blood pressure the whole answer? Do drug effects other than a decrease in blood pressure contribute to the ultimate outcome of

BENEFIT OF THERAPY = t IN WRM OF DISEASE

FIGURE 5 . Schematic representation cataloging the information that must be considered to comprehensively consider therapy in most people at risk from hypertension. Left out of the almost infinite numbers of subsets are subdivisions by duration of disease, age, associated disease, coexistent drugs, etc. Consideration of this large subset may allow us to prospectively choose which areas we want to study and how to design comprehensive studies.

therapy in hypertension? What contribution does modulation of the velocity of blood flow or its turbulence play in the changes in prognosis?g What are the direct or ancillary benefits in selected patients of drugs that modulate the stickiness of platelets or the viscosity of blood or the turnover of collagen or the content and composition of lipids in blood? These questions could be approached with the same format used in the Veteran’s Administration Co- operative Studies. That format could also be used to compare the relative costs and benefits of various combinations of drugs considered “antihypertensive” or of “antihypertensive” drugs combined with others mentioned above. Without such studies, we cannot assume that all antihypertensives are equally effective


simply because they lower blood pressure equivalently, that other drugs cannot contribute to outcome, or even that we have focused on the most critical short- term effect of therapy.

Even if we were to know the answer to most of the questions asked above, how would we use the data to optimize therapy? We still would know very little about the characteristics of single patients that alter probabilities of benefit or harm. We still would not understand the contributions of drug disposition, the stage of disease, or the character and malleability of compliance as deter- minants of response to a drug regimen. We still would not have devised a means to detect unanticipated but biologically meaningful costs and benefits of a given

Dlastollc b l w d pnslum ~ W - l l ( l l l 9 I I n ham O f dliease - h i m o f tharapy

(bcneflt - ham) t 115-129

i n n t

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?

Avc~agc fo l lw-up 1.1 years. Adopted fm

veteran's A b l n l s t ~ a t l o n Coopra t lVc Study

ClrCulatlon 45.991-1003. 1972.

FIGURE 6. Illustration of a utility function for one subset of patients with hypertension. Note even with this small subset of patients, that costs or values are not easy to come by and that events, incidences, and values of harms are barely record- able even in this group with short-term follow-up.lo (Adopted from the Veteran's Administration Cooperative Study. 1972. Circulation 4 5 991-1003.)

therapeutic course. Perhaps most important, we would still have omitted an analysis of the absolute (with optimal therapy) or relative (with comparative regimen) costs or values of modulation of morbid events (FIGURE 6).

We now have only preliminary descriptions of events caused by the rap^,^-^ relatively little information on probabilities of those events occurring in hypertensive patient^,^-^ only notions as to the costs to individuals, doctors, or society, and bare hints as to how or whether to attempt to change those values.

For instance, consider the impact of our beginning to understand one unwanted effect of some antihypertensive drugs-impotence. Because we can explain the likely mechanism by which sympatholytic drugs could cause im-


potence, we have usually attributed impotence to the drugs when patients com- plained of the symptom. Knowing that impotence occurs about as frequently (25 to 28% of the t ime)fi-6 in some subsets of hypertensives whether or not they are receiving antihypertensive drugs should mandate sharpening of our predrug history-taking or at least slow our reflex of “blaming” the drug when symptoms appear and unnecessarily and perhaps unjustly discontinuing the drug that can create benefit. If we really knew the probabilities with or without their costs of a variety of adverse events of differing combinations of drugs, we could anticipate individual settings in which some could be avoided. As a result, compliance rates might change. Our contention is that such data might affect doctors and patients such that each could clarify his position regarding therapy. Motivation for drug use and compliance would perhaps change and techniques for facilitating acceptance of medically beneficial suggestions could be devised and tested.

The medical community cannot and will not attempt to study all the factors that allow us to define precisely the utility of most therapeutic strategies or even of a single dosage regimen. However, keeping the concept of utility in mind will perhaps force us to and allow us to consider what gaps in knowledge we still have and to assign priorities to future application of limited talent and funds. Without consideration of utility we may be tempted to explore the first good idea or to inadvertently bypass minor modifications of a research plan that could result in major pragmatic gains.

CONCLUSION

Despite the indisputably helpful data that has shown that hypertension is usually a treatable disease, and our intuitive belief that the cost of treatment in terms of drug-caused morbidity is acceptable, we have almost no data that will allow us to establish a utility function for treatment in even the best char- acterized subset of the hypertensive population. A totally precise utility function in the economic sense does not seem feasible. However, medical application of the concept of utility has its attractions. Attempting to approach a utility function might allow us to dissect systematically the components of a medical problem, to define operationally the events or effects in which we are most interested and to approach systematically the most critical unknowns first. For example, data related to the type, probability, and cost of the harm of mild hypertension to well-defined subsegments of the population would convince us of the absolute need to treat. The data could also be used to allow our patient to make an informed choice as to whether he should exchange drug-induced symptoms for a currently asymptomatic disease. If the answers remain unknown, how many physicians will not (perhaps logically) choose to treat a young, vigorous, mentally alert woman of child-bearing age? Keeping the concept of utility in mind may allow us to realize that all of the research in therapy does not lie exclusively in the purview of the pharmacologist (more drugs), the biologist ( a better understanding of pathogenesis), or the epidemi- ologist (factors that influence development or severity of disease). Rather, we may also begin to encourage research into what attitudes of the doctor and patient should be separately studied, and what factors influence the value judgments of each and their relative importance in therapy. We will also begin to be able to assimilate the special circumstances of various patients. For instance,


how do we “discount” the costs of drug effects, or disease in people who already have disabling cerebrovascular accidents?

Some may argue that keeping the utility function in mind creates unneces- sary complications, and diffuses our efforts. We, however, argue that the concept rather is capable of intensifying the vigor of research and narrowing the focus of its objectives by not allowing over-interpretation of limited results. At this stage of our understanding of mild hypertension, we contend that keeping the concept of a utility function in mind will encourage critically important investigation.

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Medical Books. New York.

AGENTS. 1967. JAMA 202: 116.

AGENTS. 1970. JAMA 21% 1143.

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N.Y. Acad. Sci. New York. This volume.

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3. VETERANS ADMINISTRATION COOPERATIVE STUDY GROUP ON ANTHIHYPERTENSIVE

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5 . VETERANS ADMINISTRATION COOPERATIVE STUDY GROUP ON ANTIHYPERTENSIVE

6. SMITH, W. M. 1977. I n Mild Hypertension: To Treat or Not to Treat. Ann.

7. SYME, L. 1977. I n Mild Hypertension: To Treat or Not to Treat. Ann. N.Y.

8. FROHLICH, E. D. 1977. In Mild Hypertension: To Treat or Not to Treat.

9. SPENCE, J. D., J. PESOUT & K. L. MELMON. 1977. Effects of antihypertensive

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THE UTILITY FUNCTION OF ANTIHYPERTENSIVE THERAPY