Treatment selection for cancer patients: Application of statistical decision theory to the treatment of advanced ovarian cancer

J Chron Dis Vol. 38, No. 2. pp. 171-186, 1985 Printed in Great Britain. All rights reserved

Copyright

0021-9681~85 $3.00 f0.00 cm 1985 Pergamon Press Ltd

TREATMENT SELECTION FOR CANCER PATIENTS: APPLICATTON OF STATISTICAL DECISION THEORY TO THE TREATMENT OF ADVANCED OVARIAN CANCER R. JOHN SIMES Division of Biostatistics and Epidemiology, Dana-Farber Cancer Institute, 44 Binney Street, Boston, MA 02115, U.S.A. (Received in revised form 6 June 1984)

Ahstraet-Optimal treatment selection for patients with chronic disease, especially advanced cancer, requires careful consideration in weighing risks and benefits of each therapy. The application of statistical decision theory to such problems provides an explicit and systematic means of combining information on risks and benefits with individual patient preferences on quality-of-life issues. This paper evaluates the strengths and weaknesses of this methodology by using, as an example, treatment selection in advanced ovarian cancer. Possible treatment options and the major consequences of each are first outtined on a decision tree. The probability of various outcomes is estimated from the literature and methods for assessing the relative value or utility of each outcome are illustrated by interviews with 9 volunteers. Based on decision analysis, the recommended treatment for advanced ovarian cancer is found to be highly dependent on survival estimates but far less dependent on other probability estimates or the method of obtaining utilities. Individual preferences are also found to influence the treatment choice. The analysis illustrates that an important strength in using decision theory is its ability to identify key factors in the decision through sensitivity analysis. This may help both the physician selecting treatment and the investigator planning clinical trials which compare these therapies. In addition, this method can help in planning a trial’s sample size by determining what survival difference between therapeutic strategies is worth detecting. Some problems identified with this methodology include the need for several simplifying assumptions and the difficulties in assessing individual preferences. On balance, we believe decision theory in this setting can play a useful role in complementing the physician’s clinical judgement.

INTRODUCTION THIS PAPERexamines

the potential applications and limitations of using decision analysis for the physician faced with the decision of how to treat patients with chronic disease. The ideas presented focus principally on patients with advanced cancer but they can be applied to any area of medicine where the risks and benefits of each strategy need to be carefully considered before undertaking treatment. In dealing with cancer patients, the physician must choose between alternative treatment options, each of which may carry considerable risk. For patients with advanced disease at some cancer sites, the available therapies usually offer only a marginal survival advantage over no treatment. Consequently, in this setting, therapy is often prescribed just as a palliative measure, to relieve symptoms in the s~ptomatic patient or delay their onset in the asymptomatic. However, the treatments carry side effects, and sometimes these effects may be worse than the symptoms one is trying to alleviate or prevent. In making a decision, the physician must weigh the value of the outcomes according to their chance of occurring for each feasible treatment option. The uncertainty associated This work was supported

by an NH&MRC (Australia) Applied Health Sciences Fellowship I71

172

R.

JOHN SIMES

with the possible outcomes can make the decision process a difficult one, and normally this process is carried out only in an implicit sense. A variety of factors would usually be considered in weighing the advantages and disadvantages of each treatment: for example, overall survival, the severity and duration of side effects, the degree of physical and social mobility, the amount of time spent in hospital, treatment costs, and so on. These factors are then “combined” in some qualitative fashion, using clinical judgment or intuitive sense to arrive at a decision of the optimal treatment. Often the physician may be unaware of his own intuitive thought processes in making such a decision. Usually the therapies which are more promising in terms of response or survival are also more toxic, so that the final decision in selecting treatment requires some value judgment in balancing quality of life against quantity of life, or one state of ill health (e.g. painful disease) against another (e.g. side effects). The application of statistical decision theory provides a method for comparing such factors. It enables the physician to organize his thinking and examine the options in a systematic way. The method makes use of the probability (or likelihood) of each outcome and its utility (or value) for that particular patient [l]. This enables individual patient preferences for the possible outcomes to be explicitly incorporated into the decision making process. Decision theory has recently received much attention in the medical literature as a way of dealing with a variety of clinical problems [2-151. However, the enthusiasm of some decision analysts is not widely shared by practising physicians, and the adoption of decision analytic methods in clinical practice is still in its infancy. Most successful applications of decision analysis in clinical medicine pertain to relatively simple decisions, especially where much of the information is already contained in numerical form. The situation in selecting cancer therapies is often far more complex and the issues ill-defined. A legitimate concern is that by formalizing the problem, decision analysis may overlook important subtleties and perhaps distort the problem more than it serves to clarify it. This paper attempts to critically evaluate both the strengths and weaknesses of decision analysis for the physician, particularly with regard to treatment selection problems in advanced cancer. To provide a focus for discussion, a specific example is considered in detail: choosing a therapy for a 60-year old woman with advanced ovarian cancer. The decision discussed is whether to treat initially with an alkylating agent or more intensively with some form of combination chemotherapy. In order to apply decision theory to this problem, many simplifying assumptions are required, and these are explained. A decision tree displaying possible alternate decisions and outcomes is then constructed, and methods for estimating the probability and value for each outcome are described. The example considered demonstrates that the methodology of decision theory applied to treatment decisions has several practical limitations. However, it also has important implications for the planning of treatment protocols, for the development of methods of evaluating therapies and for the design of clinical trials.

METHODS

The clinical problem posed A 60-year old woman has recently been diagnosed as having advanced ovarian carcinoma. At laparotomy, debulking surgery failed to remove most of the tumor and the patient still has considerable pain controlled only by oral narcotic analgesics. An apparently simple decision needs to be made: whether to treat with a relatively nontoxic oral treatment, an alkylating agent; to treat more intensively with some form of combination chemotherapy; or to provide no specific anticancer therapy and just treat with analgesics. If the alkylating agent fails, the more intensive therapy (without the alkylating agent) may still be offered as a second-line treatment. To simplify the analysis, we will assume palliative radiotherapy or further surgery are not options in this patient.

Decision Analysis in Ovarian Cancer

r

173

treatnlent

i----r Res onse

Alkylating

No further

agent

(tr-eatlllent

Response FIG. 1.Decision tree

for advanced ovarian cancer. Decision nodes (0) refer to treatment options, Chance nodes (0) refer to possible outcomes.

The decision tree The treatment options are displayed in a decision tree in Fig. 1. At each decision node (O), one course of action must be selected; at each chance node (O), a variety of outcomes may occur, each with some probability or degree of uncertainty. The range of outcomes and their probabilities will vary according to the treatment selected and whether the patient responds to that treatment. Combination chemotherapy is considered more effective in controlling the disease but also more toxic than the alkylating agent. To consider all possible outcomes is not feasible, so, as a simplification, we have assumed that there are three major concerns to the patient: overall survival, painful symptoms and side effects of therapy. Other factors, such as the cost or inconvenience of treatment, time spent in hospital, etc. have been assumed to have a minor impact on the decision or to be similar for each alternative. As a further simplification, the outcomes of interest have been categorized into a number of states of health, viz.; (i) symptom-free, (ii) pain, (iii) mild side effects, (iv) moderate-to-severe side effects, (v) combinations of pain plus side effects. A full description of these states is contained in Appendix 1. For each state of health, a range of survivals is possible from 0 to 4 or more years. This range of survivals is depicted graphically by a chance node with a curved arrow (03). The full decision tree is shown in Fig. 2. It has been assumed that for each therapy an objective tumor response is equivalent to a symptomatic response with the relief of pain. For example, a response to alkylating agent is assumed to render the patient free of pain with the possibility of mild or no side effects. The patient failing to respond to alkylating agent may still possibly obtain relief of pain by responding to second-line treatment. If combination chemotherapy is selected, a response to treatment is considered more likely with the possibility of either mild side effects or moderate-to-severe side effects occurring while on therapy. After 12 months, it is assumed that the patient is maintained just on alkylating agent with either no or mild side effects. For patients failing to respond to treatment, side effects are assumed to cease after three months with cessation of therapy. Estimating probabilities The probability estimates for each outcome are based on the literature reviewed in Tables l-3 and are shown in Table 4. To keep the example reasonably simple, we classified complete and partial responders in one group and did not adjust the probability estimates for an individual on the basis of important prognostic factors. The implications of this are considered in the discussion. From Table 1, a response rate of about 45% can be expected with an oral alkylating agent, whereas a higher response rate, in the range of 5&75x, might be expected if

R. JOHN SIMES

Mild S/E

Mild S/E

Alkylating agent

Mild S/E Response

Mild S/E

<: 12 mos.

No or mild S/E

>

12 mos.

:

(: ;;I;

-,-d-s;zES,E

3 nos. 3 mos.

<3

mos.

> 3 mos. I Mild S/E fi

r

Mild S/E

-‘$( No or mild S/E

Response Nod-Sev S/E Mild S/E

\.

No

Response

Hod-W VE

Noor mild S/E

c

12 mos.

>

12 m05.

<

12 mos.

>

12 mos.

Pain + Mild S/E <

3 mos.

,

3 mos.

Pain + Mod-sev S/E

3 mos. 3 mos.

FIG. 2. Decision tree for advanced ovarian cancer. Decision nodes (0) refer to treatment options. Chance nodes (0) refer to possible outcomes. At chance nodes with a curved arrow (a>), there is a range of survivals possible for the described state of health. In some cases, the described state of health state changes at 3 months (3 mos.) or 12 months (12 mos.) as described in the text. Abbreviations: S/E = side effects, mod-sev = moderate to severe.

combination chemotherapy were used initially. The danger of using uncontrolled studies to provide these estimates is that biases may be introduced: for example, the selection of only the more favorable patients for the more intensive therapy. A comparison of treatments in randomized trials provides a more realistic guide to response rates such as from the data in Table 2. The response rates to alkylating agent vary across studies, presumably due to different patient groups but there is a similar increase in the response rate for the combination over alkylating agent in each study. One method for pooling these data is to estimate the odds ratio for two proportions using the mantel-~aenszei statistic [42]. This method can also be used to give a confidence interval for the odds ratio using test based limits [433. Based on this approach and the data in Table 2, if the response rate to alkylating agent were 45x, we would estimate the response rate to combination chemotherapy to be 64% with a 95% confidence interval of 56-71x. Each of these estimates will be considered in the analysis. The response rate to a second-line treatment is probably overestimated by the selected uncontrolled studies in Table 1.

Decision Analysis in Ovarian Cancer

175

TABLE I. RESPONSE RATES FOR ALKYLATING AGENTS, COMBINATLON CHEMOTHERAPY AND SECOND-LINE TREATMENT IN ADVANCED OVARLAiv CANCER No. of patients

Referencest

Treatment* Alkylatmg agent (oral) Melphalan Chlorambucil Cyclophosphamide

No. of responders4

Response rate (94)

16-20 16 16

796 280 126 1202

334 140 62 536

42 50 49 45

combination chemotherapy Cycle, Hexa, Adna. Plat Cycle, Hexa, MTX, FU Cycio, Adria, Plat Chlor, Adria, Flat Chlor. Pkdt Adria, Plat Cycle. Adria Melph, Adria

20-21 23 -25 26-29 30 30 22, 31 26 18

244 162 218 39 46 29 101 70

I88 87 167 21 26 23 46 44

77 54 77 54 52 19 46 63

Second-line treatments: Hexa. Adria, Plat Cycle, Ad&, Plat Cycle, Hexa, Adria, Pldt Adria, Plat Plat

20, 32-34 32 35 33 36-38

158 23 39 20 125

55 1 17 5 46

35 30 43 25 37

TOGIl

‘Abbreviations: Cycle = cycIophosphamide; Hexa = hexamethylmelamine; Adria = adridmycin; Plat = cisdiamminedichloroplatinum; MTX = methotrexate; FU = S-fluorouracil; Chlor = chlor~bucil; and Melph = meiphalan. tPatients from each reference have been pooled for this table. f?‘redtment for patients who had previously failed alkylating agent therapy. BDefinition of responses (complete plus partial) varied for different studies. It usually includes all patients with >50”,:, reduction in the product of two tumor dimensions for at least two months.

Therefore, three estimates for second-line treatment covering a more conservative range are considered in the analysis: 15, 25 and 35%. Obtaining estimates of survival is more difficult and controversial. There are some studies suggesting a survival advantage for patients receiving combination chemotherapy [ 18,22,39] while other studies [ 19,20,28,40,44,45] have not yet been able to demonstrate a significant survival advantage. Generally, the trend has been in favor of the combination. There are a number of ongoing clinical trials attempting to answer this question. TABLE2.

RAMOMIZED

CLINKAL ~~1Al.s COMPARING THERAPY

Studyt Melph vs Melph. Adria Melph YS Meipha, Hexa YS Cycle, Adria

AN

,N ADVANCED

ALKYLATING

OVARIAN

19

WITH

Median survival of all patients

Response rate:

Reference _.._ ___- ~. (r/u) 18 (29/72) (44170)

AGENT

COMBINATION

CHEMD-

CANCER*

Significant difference in survival8

% 40 63

Mos. II 17

Yes @ < 0.3)

38

No

(24/64) (50197) (35/72)

:

12 14 14

Melph YS Cycle, Hexa, Adria. Plai

20

(31170) (52183)

44 63

17 19

No

Melph vs Cycle, Hena, MTX, FU

22

(20137) (30/40)

54 75

17 29

Yes @ c 0.04)

(5i14) (4/13) (12,‘15)

36 31 80

Ii 20 19

Thiotepa + MTX YS Plat vs Plat, Adria Cycle “S Cycle, Plat

28 39

17 34

Yes @ = 0.01)

18 No (13)5 15 (11) *Trials compare an alkylating agent (not high dose intravenous) with a combination of drugs including at least adriamycin, c&platinum or hexamethylmelamine. tAbbreviations: see footnote Table 1. ZResponse rate expressed (i) in parentheses as I = number of complete plus partial responders/ n = number of evaiuable patients and (ii) as a percentage. §Statistically sjgni~cant difference in survival at the 0.05 level. (Two-tailed test). fResponse rate not reported. Number of patients in parentheses. Cycle + BCG vs Cycle, Plat k BCG

40

(2117 (21)

No

176

R. JOHN S&m

TABLE 3. SURVIVAL DATA FOR PATIENTSRECEIVINGNO TREATMENT OR ALKYLATINGAGENT THERAPY IN ADVANCED OVARIAN CANCER Median Treatment

Reference

~__.__ Nil Alkylating agent

41.16

Subgroup Nonresponders Responders Overall

survival 9 6-13 17-20 14

TABLE 4. PROBABILITIES OF RESPONSE. SIDEEFFECTSAND MEDLAN suRVwAL ESTIMATESFOR TREATMENT OF ADVANCED OVARIAN CANCER

Estimates* for

0.25 (0.1 S-0.35)

-.~ Combination chemotherapy .~ 0.64 (0.56-0.71)

0.0 0.3 (0.15-0.5) 0.7 (0.5-0.85)

0.0 0.3 (0.15-0.5) 0.7 (0.5-0.8s)

Alkylating agent

Probability of response

0.45

Probability of side-effects of treatmentt Nil 0.5 (0.3-0.7) Mild 0.5 (0.3-0.7) Moderate-severe 0.0 Median survivai (months)~ Nonresponders Responders I II III IV

9 18 18 18 18

Second-line treatment

9 18 15 12 12

9 18 24 30 36

*Numbers refer to initial estimates used in the analysis and those in parentheses to a range of estimates used in sensitivity analysis. ?See Appendix I for a full description of mild and moderate-severe side effects. fFour sets of estimates for median survival of responders are considered in the analysis. They offer I-marginat, II-small, III-moderate and IV-large survival advantage for combination chemotherapy over alkylating agent used as initial treatment. Survival is measured from time of initial treatment in each case. For example, in the first set of estimates, patients failing alkylating agent and responding to second-line treatment are assumed to have a median survival of 18 months.

In view of this uncertainty, four sets of estimates of median survival are considered for the patient responding to treatment. In the first set (I), responders have a median survival of 18 months regardless of treatment. In the other three sets of estimates (II, III, IV), responders to combination chemotherapy have a longer median survival compared with alkylating agent, and responders to second-line treatment a shorter one. For patients failing to respond to any treatment or having no treatment, median survival is assumed to be 9 months. Based on the initial estimates of response rates in Table 4, the four sets of median survival estimates all offer a survival advantage to combination chemotherapy over alkylating agent as initial therapy (I: marginal; II: small; III: moderate; IV: large). This advantage, in terms of median survival for all patients (responders and nonresponders) receiving combination chemotherapy vs initial alkylating agent, is I: 14 vs 13 months; II: 16 vs 13 months; III: 19 vs 12 months and IV: 21 vs 12 months*. Table 4 also contains estimates of the probability of side effects from treatment as the patient might perceive them: that is, in terms of nausea, vomiting, fatigue, etc. rather than side effects more objectively reported in the literature, such as altered blood counts. These estimates therefore are based mainly on personal experience and so a range of values is also considered in the analysis.

The utility or relative worth of each outcome can be estimated by assessing the patient’s preferences for a variety of outcomes [46]. To this end, 9 healthy volunteers were interviewed to ascertain their attitudes toward survival in later years in various states of health. A description of the 60-year-old woman with ovarian cancer and a scenario of each health state, as described in Appendix 1, were given to the volunteers: four, who were oncologists, were asked to express attitudes on behalf of their hypothetical patient; five, who were nonmedical women, were asked to imagine they were “in the shoes” of this *This assumes

survival

follows

an exponential

distribution

for each subgroup.

Decision Analysis in Ovarian Cancer

0

x2

4

Yeors of survival

0

x

2

4

117

cl

2

Years of survival

4

Years of surwval

(symptom-free) 50 50

4Yr CE x yr None

A

2 Yr

x Yr

with symptoms

symptom -free

A

P loo-p

4Yr symptom 4yr with symptoms

-free None

A

FIG. 3(a). Utility assessment

for symptom-free survival: Certainty equivalence method. The individual is asked to make a choice between a period of certain survival and a 50:50 gamble between 4 years survival and none. The period of survival considered equivalent to the gamble is called the certainty equivalent (CE = x years). This is assigned the same utility, 50, as the expected utility of the gamble. A risk neutral person (dashed line) considers 2 years for certain equivalent to the gamble, whereas a risk averse person (solid line) would choose a certainty equivalent of less than 2 years. FIG. 3(b). Utility assessment for survival with symptoms: Time tradeoff method. The individual is asked to consider for a certain period of survival with symptoms what period of shorter survival free of symptoms would be equivalent. Both outcomes are then assigned the same utility. In this example, an individual expected to live 2 years with symptoms would be willing to tradeoff 1 year’s survival to live symptom-free. Both are assigned a utility of about 40. Similar questions can be used to estimate other points on the curve. FIG. 3(c). Utility assessment for survival with symptoms: Gamble method. The individual is asked to make a choice between 4 years survival with symptoms and a gamble on 4 years survival free of symptoms or early death. The chance of symptom-free survival in the gamble @) is varied until the two choices are considered equivalent. In this example, the individual considers 4 years survival with symptoms equivalent to 75:25 gamble on 4 years survival without symptoms or early death.

While the preferences of volunteers may not be representative of the preferences of a patient actually confronted with such a decision, they will serve to illustrate some of the methods and principles involved. Also they represent preferences without the complication of an immediately stressful situation. The answers to the presentation of hypothetical outcomes were used to form a number of utility scores. In this paper we arbitrarily assigned a utility score of 0 and 100 to symptom-free survival of 0 and 4 years, respectively. Utility scores for other outcomes were estimated in relation to this scale, where higher utilities imply greater preference. (The choice of utility scale does not affect the conclusions of the analysis.) Figures 3a, b and c illustrate utility curves obtained under a variety of methods. In assessing attitudes toward survival, volunteers were asked to express preferences among a number of hypothetical options using a “standard gamble” or certainty equivalence method [5,8,46-501. (See Fig. 3a.) This involves considering a choice between a period of certain survival and a gamble on longer survival or early death. By considering a series of choices, each individual could specify the period of certain survival equivalent to the gamble, referred to as the certainty equivalent. If the period of certain survival is shorter than the expected survival of the gamble, the individual is said to be risk-averse and is willing to accept the shorter survival to avoid the risk of the gamble. Such a person would have a concave utility curve (viewed from below) like the one in Fig. 3a, placing greater value on the earlier years of life. The first gamble considered involved a 50:50 chance of 4 years survival or death within 2 weeks (assumed 0 years) and has an expected utility of 50 [or (100 + 0) + 21 since this is the value the gamble would return on the average. The period of survival considered equivalent to the gamble (certainty equivalent) is assigned the same utility, 50, as the

patient.

178

R. JOHN Smm

gamble. In practice, similar questions were used to determine the certainty equivalents at other utilities, and a smooth utility curve was fitted to the points (see Appendix 2). In assessing attitudes toward quality-of-life in various states of health, two methods were used to estimate utilities: a time trade-off method and a gamble method [5,46-501. The two methods were used to give some idea of the internal consistency of the estimates. The time trade-off method is illustrated in Fig. 3b. For a certain period of survival with symptoms, each individual was asked how many months or years she would give up to be able to live s~ptom-free. This shorter period of symptom-free survival and the longer period of survival with symptoms were each assigned the same utility. Similar questions were used to estimate the utility for survival with symptoms for 6 months, 1,2, and 4 years. The method was repeated to obtain a separate utility curve for each state of health: pain, mild side effects and so on. The gamble method used is illustrated in Fig. 3c. Volunteers were asked to make a choice between a certain period of survival with symptoms and a gamble between symptom-free survival for that same period or early death. The probability of having symptom-free survival was varied in the gamble until the two choices were considered equivalent. Note that, unlike the certainty equivalent method, here the period of certain survival with symptoms was fixed and the probability of the gamble allowed to vary. Again, similar questions were used to estimate the utility of survival with symptoms for 6 months, 1, 2, and 4 years and utility curves were constructed for each health state (see Appendix 2). The analysis In prescribing what treatment strategy is optimal for each individual patient, decision theory dictates choosing the strategy with the largest expected utility, that is, the strategy which on average is expected to yield the largest value for the patient. This is found by weighting the utility of each outcome according to its chance of occurring and summing all the weighted outcomes. The details for this example are explained in Appendix 2. Decision analysis was used to determine the optimal strategy for each individual based on the probability estimates in Table 4 and each person’s utilities. Since the probabilities of the outcomes are estimates, they were varied to determine how sensitive the decision is likely to be for each factor. RESULTS

Utility data “Typical” utility curves representative of values of the group as a whole are shown in Fig. 4. By drawing a vertical line on the graph, one may consider life in each health state expressed as the relative value (percentage) of symptom-free survival for the same period.* This is the form in which the individual’s preferences have been expressed, in Table 5. For example, oncologists on average valued life with pain at 75% that of symptom-free survival for the same period. As a group, the oncologists placed less emphasis on quality-of-life than the nonmedi~al female volunteers. This was particularly so when considering side effects of treatment. For these health states, the five women each expressed a smaller utility than any of the four oncologists. Most individuals considered life with pain controlled on oral narcotic analgesics preferable to moderate-severe side effects, although pain was not usually preferred to mild side effects. All individuals were risk-averse to some degree, placing more value on earlier years of life compared with the later. The degree of risk aversion was similar for both groups. Some discrepancy was found between the time trade-off and gamble methods for estimating utilities for the various states of health. Percentage scores of the form in Table 5 differed on average by 12 when comparing the two methods. The importance of such *The utility model (Appendix 2).

used assumes

that

this relative

value doesn’t

change

with the period

of survival

chosen

Decision Analysis in Ovarian Cancer “Typical”

utfiity

179

curves

25

0

1

2

Years

3

4

of survival

FIG. 4. Typical utility curves for volunteers expressing attitudes toward survival in various states

of health, as described in Appendix 1. Abbreviations: S/E = side effects, mod-sev = moderate-tosevere.

discrepancies though, is to what extent they affect the actual decision. This is considered further in the sensitivity analysis section.

Analysis of the decision tree for a typical individual is illustrated in Fig. 5, using the first set of estimates of median survival (a marginal survival advantage for combination chemotherapy). The expected utility for each outcome involved integration of the utility curves for that health status with the relevant survival probabilities. At each decision node (a), the action with the larger expected utility has been chosen. In this analysis, the alkylating agent would be advised as initial treatmeilt, and if no response occurred, second-line treatment would be recommended. Either treatment strategy (alkylating agent or combination chemotherapy) is preferred over no anticancer treatment. Sensitivity analysis By varying some of the numerical estimates (probabilities and utilities) and some of the basic assumptions of the decision framework, it is possible to gauge the reliability of the recommended decision. In addition, one may identify those factors to which the decision is particularly sensitive. A decision analysis was first carried out for each of the 9 volunteers using the four sets of median survival estimates in Table 4 and both methods for assessing utilities. The results. summarized in Table 6, show that combination chemotherapy is usualiy favored as initial treatment. However, the treatment choice is seen to be particularly sensitive to TABLE5. UTILITYDATA*FOR s WOMENVOLUNTEERS AND4 ONCOLOGLSTS Health status-! Symptom-free Pain Mild side effects Moderate-severe side effects Pain + mod-severe side effects

Mean (range) Women Oncologists

n-value$

56 (:: 77) 67 (59, 77) 31(19, 49)

100 75(62, 87) 84(79, 90) 63(52, 75)

CO.10 < 0.02 CO.02

22(14, 33)

49(xX, 66)


*Utility for each health status expressed as a percentage of symptomfree survival for the same period. ISee Appendix I for a full description. :Two-sided Mann-Whitney Test comparing utilities of women vs oncologists for each health status.

180

R.

Of 23

No specific

JOHN Sms

23

treatment

Response

5,

0.45

Response

FIG. 5. Treatment selection in advanced ovarian cancer. A decision analysis using the “typical” utility values from Fig. 3 and based on the first set of survival estimates(I) in Table 4. The expected utility at the end of each branch involved integration of utility curves with the relevant probabilities. The expected utility at each chance node is shown in the tear-shaped cell. The final expected value of each treatment strategy is shown in the oval cell. The estimated response rates used are shown on each branch of the tree.

the choice of survival estimates used. If the first set of survival estimates were used, offering only a marginal survival advantage to combination chemotherapy, the analysis favored alkylating agent as initial treatment in every case. However, by using the second set of estimates (overall median survival 16 vs 13 months), most analyses now favored the combination as initial treatment. For the third set of estimates, combination chemotherapy was recommended in all but one case and for the fourth set, for all cases. The treatment choice was much less sensitive to the method by which utilities were estimated. Although some discrepancy was noted between the utilities using the time trade-off and gamble methods, this seldom resulted in conflicting recommended strategies (in only one analysis in Table 6). The sensitivity of the analysis to other factors such as response rates and toxicity of treatment was also examined, and the results of this analysis are shown in Tables 7 and 8. Over the range of values chosen, the analysis is relatively insensitive to changes in response rate or degree of toxicity especially when compared with the influence of survival. The analysis shown is based on utilities using the time trade-off method. The same results were obtained for 97% (594/612) of the decision analyses using the gamble method indicating that the decision was also relatively insensitive to the method of estimating utilities. TABLE6. DECISIONANALYSIS (NUMBERS

FAVORING

Utilities estimates by

FOR

ADVANCED

ALKYLATING

I

OVARIAN

CANCER’

AGENTIt

Survival estimatesf III IV II

0 9 3 1 0 9 2 1 019 9/9 2/g I19 *Analysis based on the initial estimates in Table 4. PNumber of volunteers having utility functions which favor alkylating agent as initial treatment. Combined results in the bottom row express this as fraction of the 9 volunteers whose utilities estimated by either method do not give conflicting results. fThe four sets of median survival estimates are detailed in Table 4. They correspond to a marginal (I), small (II), moderate (III) and large (IV) survival advantage for combination chemotherapy, over alkylating agent as initial therapy.

Time trade-off method Gamble method Both

Decision

Analysis

in Ovarian

Cancer

181

TABLE 7. A SENSITWITY ANALYSIS VARIATION OF TOXICITY AND SURVIVAL ESTIMATES (NUMBERS FAVORlNG ALKYLATING AGENTt)

Surviva& estimates

Mild side effects from alkylating agent

Toxicity estimatesi Moderate-severe side effects from combination chemotherapy or secondline treatment 0.50 0.70 0.85

I

0.30 0.50 0.70

9 9 9

9 9 9

9 9 9

11

0.30 0.50 0.70

3 2 1

3 3 2

3 3 2

III

0.30 0.50 0.70

1 1 0

1 1 1

I

0.30 0.50 0.70

0 0 0

1 0 0

IV

1 1

I 0 0

*Response rates for this table are held constant at the initial values in Table 4. tNumber of volunteers whose utility functions, estimated by time trade-off method, favor alkylating agent as initial therapy. (Very similar results were obtained when analyses were based on utilities estimated by gamble method with only 3% of analyses giving conflicting results). IToxicity estimates refer to (i) for alkylating agent, the probability of mild side effects, other patients assumed to have none and (ii) for combination chemotherapy or second-line treatment, the probability of moderate-severe side effects, other patients assumed to have mild side effects. $As in Table 6. TABLE 8. A SENSLTlVLTY ANALYSIS: VARIATION OF RESPONSE RATES AND SURVWAL ESTIMATES (NUMBERS FAVORlNG ALKYLATLNG AGENT+)

Survivalt: estimates

Response rate to second-line treatment

Response rate to combination chemotherapy 0.64 0.71 0.56

I

0.15 0.25 0.35

9 9 9

9 9 9

II

0.15 0.25 0.35

3 3 5

2 3 3

III

0.15 0.25 0.35

1 1 1

1 1 1

IV

0.15 0.25 0.35

1 1 1

0 0 0

0 0 0

‘Toxicity estimates and response rate to alkylating agent are held constant at the initial values in Table 4. tAs in Table 7. ~AS in Table 6. DISCUSSION

This clinical example from advanced ovarian cancer demonstrates how complex the issues in making a clinical decision can be. We need to consider the many risks and benefits of each treatment strategy and also the relative importance of each factor from the patient’s perspective. Decision theory provides a formal procedure for synthesizing these factors. It by no means replaces good clinical judgment but it can provide invaluable new insights into a difficult clinical problem [5]. In this paper, we have described each stage of the analysis, and in so doing, have illustrated both the strengths and weaknesses of this approach. Some of the weaknesses of our analysis include the need to make several simplifying assumptions, the failure to adjust probability estimates for a particular patient on the basis of prognostic factors, and the difficulty in expressing an individual’s preferences for life-and-death events in terms of a number. Nevertheless, at least the formal and explicit nature of decision analysis makes each of these deficiencies apparent and allows us to more critically evaluate the impact of each one of the actual decisions. Let us consider some of these weaknesses in more detail. The present analysis failed to account for additional morbidity that could result from relapse on any treatment. To the

182

R. JOHNSIMES

extent that patients on alkylating agent relapse earlier than those on combination chemotherapy, the present results are biased in favor of the alkylating agent. In estimating the probability of each outcome, no attempt was made to adjust the estimates according to important prognostic factors such as bulk of disease, histological grade and ambulatory status. Quantitative adjustment on the basis of these factors could, in principle, be made with a sufficiently large data base. When the medical literature lacks such quantitative information, it may only be possible to make subjective estimates. This is one reason we considered a range of probability estimates in the analysis to determine how sensitive the decision was to our initial choice. Perhaps the major source of concern regarding the application of decision theory relates to the methods of assessing patient preferences to various outcomes and the need to express such ill-defined states as pain and fear of dying in terms of a number. An individual’s response to a hypothetical gamble may differ from his or her response to the same situation in reality. The decomposition of a highly complex problem into simpler ones has sometimes been considered an advantage of utility assessment; however, the human mind may cope better with the real complex problem at hand than with the abstract and hypothetical components [3]. Furthermore, one’s preference may be altered simply by framing the same problem in a different way, for example, in terms of lives saved rather than lives lost [51, 521. The patient’s values may be quite unstable over time and vary with changing circumstances. These arguments may seem both compelling and disturbing. Nevertheless, they principally reflect on the difficulty in eliciting patient preferences by whatever means we choose: formal or informal. The formal approach at least allows us to check the internal consistency of our utility estimates and judge the impact of any discrepancies on the recommended decision. To the extent that the different methods of eliciting preferences resulted in the same conclusions in the analysis, the more confident we can be about those conclusions. In fact, the present analysis showed that although there was some conflict in recommended decisions, the two methods of eliciting preferences generally gave concordant results for each individual. This provides some reassurance about the utility assessment. In contrast to the method of utility assessment, the decision was seen to be far more sensitive to the survival estimates used. Only a small change in the survival estimates was necessary to alter the recommended decision from alkylating agent to the combination for the majority of volunteers. Other probability estimates such as response rate and side effects from treatment were seen to have relatively little impact on this decision. Although the survival estimates were central to this analysis, the preferences of each volunteer also influenced the choice of treatment. As a rough guide, individuals who placed little value on life with moderate-severe side effects and were risk-averse (placing more value on the early months of survival) were more likely to benefit from the alkylating agent as initial treatment. The need to tailor the treatment to the individual patient was also emphasized in a study on treatment selection for laryngeal carcinoma [50]. In that case, the choice between surgery and radiotherapy depended on whether the patient placed more value on a longer expected survival with surgery or on retaining relatively normal speech with radiotherapy. When considering patient preferences in the decision, it is also important to recognize the value of the physician’s own experience of the possible outcomes. As already noted in Table 5, the oncologists as a group placed less emphasis on side effects of therapy and painful symptoms than survival compared with the nonmedical volunteers. These differences may be due to a more “realistic” apprasial of some of the outcomes by the oncologists who are more familiar with what each involves and who have more knowledge of what supportive therapy is available to control unpleasant symptoms. Or it may reflect a different set of values for the two groups. Whatever the reason in practice, it is probably important that both the patient’s values and the physician’s experience are incorporated in the decision-making process. Despite some of the limitations of the present analysis, the method does have some

Decision

Analysis

in Ovarian

Cancer

183

important advantages. For example, decision theory can help reduce the difficulties in assessing the medical literature, at least in the context of a clinical decision. There are several difficulties in obtaining reliable probability estimates from the literature, including: the underreporting of key statistical details necessary to interpret each study [53]; potential biases from patient selection in uncontrolled, and even randomized, clinical trials [54]; and a bias in favor of “significant” results among clinical trials which are selected for publication. These problems face any physician who tries to assess the medical literature when making a clinical decision. Decision theory does not make the task of estimating these probabilities any easier, but it does enable him, by sensitivity analysis, to assess the impact of the imprecision of each estimate on the clinical decision. Another benefit of applying decision theory in this setting relates to the planning and interpretation of clinical trials designed to evaluate new therapies from the patient’s perspective. Not only can decision theory be used to synthesize the information from clinical trials and assist in their interpretation (as already discussed), but it also can be used to guide us as to what information the trials should be collecting relevant to clinical management. For example, the present study illustrated the difficulty in obtaining objective information related to quality-of-life and suggests the need to incorporate quality-of-life indexes into clinical trials. This is true whenever the trade-off between quality and quantity of life can be shown to influence the decision. Decision analysis may also help by determining how large a difference for some outcome, such as survival, we should consider clinically important. This analysis of advanced ovarian cancer suggested that even a difference between 13 and 16 months median survival would be worth detecting. This can help in planning sample sizes for a clinical trial comparing these two strategies. Another strength of decision theory applied to clinical problems is its explicit nature. By formally structuring the clinical problem and stating the estimates used, the recommendations based on decision analysis can be more critically evaluated and its assumptions open to the scrutiny of others. This makes the method a useful educational tool where medical students and others can perceive a rational basis upon which decisions are made. Such an approach can improve communication among physicians and should help in the formulation of treatment protocols. This may be particularly useful in a field such as oncology where surgeons, radiotherapists, and medical oncologists may each have different views on the appropriate management of a clinical problem. In conclusion, the application of decision theory to treatment selection problems has both disadvantages and advantages: when considered specifically, as in the case of advanced ovarian cancer, and, more generally, for any clinical decision involving trade-offs in quantity and quality of survival. On balance, we believe decision analysis is a useful adjunct to less formal decision making processes and should be thought of as complementing rather than competing with good clinical judgment. Acknowledgements-The author is grateful to Drs Colin Begg, Kevin Cain, Harvey Fineberg, Milton Weinstein and Marvin Zelen who made several constructive suggestions on an earlier draft of this paper,

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Vogl SE, Kaplan B, Pagan0 M: Diamminedichloroplatinum-based combination chemotherapy is superior to melphalan for advanced ovarian cancer when age is greater than 50 and tumor diameter greater than 2 cm. Proc Am Sot Clin Oncol 1: 119, 1982 (Abstr) 21. Greco FA, Julian CC, Richardson RL, Burnett L, Hande KR, Oldham RK: Advanced ovarian cancer: Brief intensive combination chemotherapy and second-look operation. Obstet Gynecol 58: 199-205, 1981 22. Bruckner HW, Cohen CJ, Goldberg JD, et al: Cisplatin Regimens and Improved Prognosis of Patients with Poorly Differentiated Ovarian Cancer. Am J Obstet Gynecol 145: 653-658, 1983 23. Neijt JP, ten Bokkel Huinink WW, Burg MELvd et al: Combination Chemotherapy with Hexa-CAF and CHAP-5 in Advanced Ovarian Carcinoma: A Randomized Study of the Netherlands Joint Study Group for Ovarian Cancer. Proc Am Sot CIin Oncol 2: 148, 1983 (Abstr) 24. Young RC, Chabner BA, Hubbard SP et al: Advanced ovarian adenocarcinoma: A prospective clinical trial of melphalan (L-PAM) versus combination chemotherapy. N Engl J Med 299: 1261-1266, 1978 25. Carmo-Pereira J, Costa FO, Henriques E, Ricardo JA: Advanced ovarian carcinoma: A prospective and randomized clinical trial of cyclophosphamide versus combination cytotoxic chemotherapy (Hexa-CAF). 20.

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Budd CT, Livingston RB, Webster K, Reimer R, Martimbeau P, Hewlett JS: Treatment of advanced ovarian cancer with cis-nlatin. adriamvcin, and cvtoxan. Proc Am Sot Clin Oncol 1: 117, 1982 (Abstr) 27. Omura GA, Ehrlich CE, Blessing JAY A ‘randomized trial of cyclophosphamide plus adriamycin with or without cis-platinum in ovarian carcinoma. Proc Am Sot Clin Oncol 1: 104, 1982 (Abstr) 28. Williams CJ, Mead B, Arnold A, Green J, Buchanan R, Whitehouse M: Chemotherapy of advanced ovarian carcinoma: initial experience using a platinum-based combination. Cancer 49: 1778-1783, 1982 29. Stehman FB, Ehrlich CE, Einhom SD, Williams SD, Roth LM, Blessing JA: Long Term Follow-up and Survival in Stage III-IV Epithelial Ovarian Cancer Treated with cis-Dichlorodiamine Platinum, Adriamycin and Cyclophosphamide (PAC). Proc Am Sot Clin Oncol 2: 147, 1983 (Abstr) 30. Barker GH, Whiltshaw E: Randomized trial comparing low-dose cis-platin and chlorambucil with low-dose cis-platin, chlorambucil and doxorubicin in advanced ovarian carcinoma. Lancet I: 747-750, 1981 31. Bruckner HW, Cohen CJ, Goldberg JD et al: Improved chemotherapy for ovarian cancer with cis-diamminedichloroplatinum and adriamycin. Cancer 47: 2288-2294, 1981 32. Bernath A, Andrews T, Dixon R, et al: Long term follow-up of hexamethylmelamine, adriamycin, cis-platinum versus cyclophosphamide, adriamycin, cis-platinum in alkylating agent resistant advanced ovarian carcinoma. Proc Am Sot Clin Oncol 1: 110, 1982 (Abstr) 33. Neijt JP, ten Bokkel Huinink WW, Hamervma E, et al: Combination chemotherapy including cis-nlatinum in previously treated patients with advanced ovarian carcinoma. Proc Am Sot Clin Oncol 1: iO8, 1982 (Abstr) 34. Vogl SE, Berenzweig M, Kaplan BH, Moukhtar M, Bulkin W: The CHAD and HAD regimens in advanced ovarian cancer: Combination chemotherapy including cyclophosphamide, hexamethylmelamine, adriamycin and cis-dichlorodiammineplatinum (II). Cancer Treat Rep 63: 311-317, 1979 35. Kane R, Harvey H, Andrews T, ef al: Phase II trial of cyclophosphamide, hexamethylmelamine, adriamycin, and cis-dichlorodiammineplatinum (II) combination chemotherapy in advanced ovarian carcinoma. Cancer Treat Rep 63: 307-309, 1979 36. Young RC, von Hoff DD, Gormley P et al: Cis-dichlorodiammineplatinum for the treatment of advanced ovarian cancer. Cancer Treat Rep 63: 15391544, 1979 37. Wiltshaw E, Submarian S, Alexopoulos C, Barker GH: Cancer of the ovary: A summary of experience with cis-dichlorodiammineplatinum at the Royal Marsden Hospital. Cancer Treat Rep 63: 1545-1548, 1979 38. Bruckner HW, Cohen CJ, Kabakow B et al: Ovarian cancer: Secondary cis-platin regimens and prognostic factors. Proc Am Sot Clin Oncol 22: 469, 1981 (Abstr) 39. Decker DC, Fleming TR, Malkasian CD, Webb MJ, Jeffries JA, Edmonson JH: Cyclophosphamide plus cis-Platinum in Combination: Treatment Program for Stage III or IV Ovarian Carcinoma. Obstet Gynecol 60: 481-487, 1982 Trial of the Addition of cis40. Wilbur D, Reutschler R, Wagner R et al: Randomized

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diamminodichloroplatinum(DDP) and/or BCG to Cylcophosphamide (CTX) Chemotherapy for Ovarian Carcinoma. Proc Am Sot Ctin Oncol 2: 147, 1983 (Abstr) Rutledge FN, Smith JP: Management of ovarian carcinoma: Surgery, irradiation and chemotherapy. Am J Obstet Gyaecol 98: 374-386, 1967 Mantel N, Haenszel W: Statistical aspects of the analysis of data from retrospective studies of disease. J Nat1 Cancer Inst 22: 719-748, 1959 Breslow NE, Day NE: StatIstIcal Methods in Cancer Research Vol. 1. The analysis of case control studies. IARC Scientific Publications No. 32, Lyon, 1980; pp. 140-142. Sturgeon JFG, Fine S, Gospodarowicz MK et al: A randomized trial of melphalan alone versus combination chemotherapy in advanced ovarian cancer. Prnc Am But CBn One01 23: 418, 1982 (Abstr) Williams CJ, Mead GM, Green JA et al: A Randomized Study of cis Platin, Adriamycin and Cyclophosphamide (PACe) versus Chloramubucil (CB) in Stage III and IV Ovarian Carcinoma. Proc Am Sot ClIn Oncol 2: 156, 1983 (Abstr) Eraker SA, Sox HC: Assessment of patients’ preferences for therapeutic outcomes. Med Decis Making 1: 30-39, 1981 Raiffa H: Decision Analysis Reading, Mass: Addison-Wesley, 1968. pp. 9, 51-103 Keeney RL, Raiffa H: Decisions with Multiple Objective: Preferences and Value Trade Offs. New York: Wiley, 1976 Johnson EM, Huber GP: The technology of utility assessment. IEEE Trans Sys Sci Cybem. SMC 7: 31 l-325, 1977 McNeil BJ, Weichselbaum R, Pauker SG: Speech and Survival. Tradeoffs between quality and quantity of life. N Engl J Med 305: 982-987, 1981 Tversky A, Kahneman D: The framing of decisions and the psychology of choice. Science 211: 453-458, 1981 McNeil BJ, Pauker SG, Sox HC, Tversky A: On the elicitation of preference for alternative therapies. N Engl J Med 306: 1259-1262, 1982 Der Simonian R, Charette LJ, McPeek B, Mosteller F: Reporting on methods in clinical trials. N Engl J Med 306: 1332-1337, 1982 May GS, DeMets DL, Friedman LM, Furberg C, Passamani E: The randomized clinical trial: bias in analysis. Circulation 64: 669-673, 1981 Pliskin JS, Shepard DS, Weinstein MC: Utility functions for life years and health status. Oper Res 28: 206224, 1980

APPENDIX HEALTH

STATES

1

IN ADVANCED

OVARIAN

CANCER The following descriptions were used to explain the various states of health to the volunteers. The hypothetical patient was a 60-year-old married woman still leading a relatively active and enjoyable life before the diagnosis of ovarian carcinoma. Symptom-free No pain or side effects of therapy. Pain

The pain without any “pain killers” is severe and prevents you carrying on or enjoying normal daily activities. Morphine-like medicine, taken by mouth, controls the pain so that it does not bother you. The medicine makes you less alert (somewhat more vague) than you are normally, but you are able to carry on most of your daily activities. Mild side effects (mild S/E) You experience a loss of appetite and occasional mild nausea after meals. You have less energy than normal, but are still able to carry out most of your daily activities. Moderate-to-severe

side eflects (Mod-sev S/E)

Following each treatment (every 3 weeks) you experience severe vomiting, feel “lousy” and stay in bed for the first day; for the first week after treatment you have occasional vomiting, nausea after meals, and lack energy, spending most of the time resting at home; for the remaining 2 of every 3 weeks you are able to carry out most of your daily activities but still experience loss of appetite and mild fatigue. You lose most or all of your hair while on treatment.

APPENDIX METHODOLOGY

USED

2

FOR DECISION

ANALYSIS

1. Constructing utility curves For this analysis, we assumed the utility function u,(t), for survival to time, t, in health status, i, to be of the form (,‘,(1) = S,(l/4)

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R. JOHN SIMES

where the parameters s,, i = 0, 1, . ., 5 refer to the “percentage value“ of each health state with respect to symptom-free survival for the same period. (The narameter for svmntom-free survival was defined as sn = 100). The-parameter r reflects whether the-individual is-risk-averse (r < 1): risk-neutral (r = 1) or risk-seeking (r > I). For risk-averse individuals, the degree of risk aversion is sometimes described by the proportional risk aversion constant, c = 1 - r, where larger values of c reflect greater risk aversion. The functional form of utility chosen has some desirable properties, as discussed by Pliskin et al. [55], but it also requires a number of assumptions. For example, it assumes that the relative worth of life in two different states of health for the same number of years depends only on the two states and not the number of years involved. The utility scores obtained, using the certainty equivalence method described in Fig. 3a, were used to estimate r. Certainty equivalents of gambles involving symptom-free survival were estimated and plotted for utilities of 50, 25 and 12.5. The estimation procedure then involved choosing r to minimize the sum of squared errors for these 3 points. The estimated utility curve for symptom-free survival was then used to obtain utility scores in each health state for survival of 6 months, 1, 2 and 4 years. This was done, separately, for both the time trade-off and gamble methods as illustrated in Figs 3b and c. The 4 plotted points were then used to estimate J; for each health state. The estimation procedure involved choosing s, to minimize the sum of squared errors on a natural logarithmic scale. In this way, a utility curve was estimated for each health state using each of the two methods of utility assessment. 2. Expected utilities In general, for discrete outcomes, the expected utility E[U], is the sum of the utility of each outcome, U;., multiplied by its probability, Pi of occurrence. E[U] = 2 U;P,.

(1)

For a continuum of outcomes, such as survival. the expected utility becomes an integral: U(r) q(t)dr

E[U] =

J

(2)

0

where U(t) is the utility of dying at time f, and q(t)dt the chance of dying at time t. 3. Aigorithms used In this analysis, we assumed that the survival distribution for each response category, j, was exponential with failure rate, A,, having the survivor function, Q,(r) and density function q,(r) = l,exp(--Ajt)

(3)

This assumption cannot be strictly correct as responders are guaranteed a minimum survival before a response can be observed but it may be a reasonable approximation. Recall that the utility function, L’,(t), for survival to time, t, in health status, i, was assumed to be U,(t) = si(t/4)‘.

(4)

If we define U,(j) to be the expected utility for a patient surviving only in health status, i, having achieved response category, j, then using equations (Z), (3), and (4), one can calculate

U;(t) q,(r)dt

U;(j) =

J = :;r(l

+ r)/(4A,)‘.

For the patient undergoing a change of health status from i to k, the calculation of expected utility was more complicated, and made the assumption that the additional utility at some point in time did not depend on the past history of health status occupied. If we define U,(i 1t) to be the expected (conditional) utility of an individual changing from health status i to k at time t, then we have

u,o’if) =

J

U,(xfq,(x)dx +

[U,(x) - Uk(f) + U,(t)]q,(x)dx

0

=

J

=L

U&)+)dt

+ [u,(x) - U,(h-)lqi(x)dx + Iu,(t) - u,(t)lQ,(t) J

hi)+:[u,W -

kOl(l

+ Q,(f)).

The calculated expected utilities of these outcomes can then be used in equation (1) to calculate the expected utility of a particular treatment strategy.