Frank A. Sonnenberg

Markov Models in Medical Decision Making A Practical Guide

Markov models are useful when a decision problem involves risk that is continuous over time, when the timing of events is important, and when important events may happen more than once. Representing such clinical settings with conventional decision trees is difficult and may require unrealistic simplifying assumptions. Markov models assume that a patient is always in one of a finite number of discrete health states, called Markov states. All events are represented as transitions from one state to another. A Markov model may be evaluated by matrix algebra, as a cohort simulation, or as a Monte Carlo simulation. A newer repre sentation of Markov models, the Markov-cycle tree, uses a tree representation of clinical events and may be evaluated either as a cohort simulation or as a Monte Carlo simulation. The ability of the Markov model to represent repetitive events and the time dependence of both probabilities and utilities allows for more accurate representation of clinical settings that involve these issues. Key words: Markov models; Markov-cycle decision tree; decision mak ing. (Med Decis Making 1993;13:322-338)

Myocardial revascularization for chronic stable angina. Analysis of the role of percutaneous transluminal coronary angioplasty based on data available in 1989.

No prospective, randomized clinical trial comparing coronary artery bypass grafting, percutaneous transluminal coronary angioplasty, and conservative therapy has been reported. To address when revascularization is indicated, we constructed a decision analytic model. Our model incorporates procedure-related mortality and morbidity, coronary artery disease-related mortality, and the benefit of revascularization. We determined the quality-adjusted life expectancy and expected costs for each strategy. Our model suggests that angioplasty is a reasonable alternative to bypass surgery in patients with favorable lesions if angioplasty would provide a comparable degree of revascularization. Our model predicts that patients treated with angioplasty will have more revascularization procedures than will patients treated with bypass surgery but predicts that both treatments will cost the same over the typical patients lifetime. In many patients with severe angina or documented ischemia, angioplasty is indicated for stenosis of a single artery. In patients with two vessel disease that is amenable to angioplasty, angioplasty may be a reasonable alternative to bypass surgery. Even in patients whose three vessel disease can be completely revascularized by angioplasty, bypass surgery, although relatively expensive, is slightly better than angioplasty. In patients with three vessel disease and comorbidities that increase operative risk, angioplasty may be a reasonable alternative to either bypass surgery or medical therapy.

The Will To Live among HIV-Infected Patients

An estimated 650 000 to 900 000 persons in the United States are infected with HIV (1). Recognizing the enormous health burden of HIV and AIDS, researchers are more frequently studying quality of life in HIV-infected patients (2). Two approaches can be used to measure health-related quality of life: health status assessment and health value assessment (also known as utility or preference assessment) (3). Health status measures describe function and the effect of illness on one or more aspects of health, such as physical function or mental health. Most health-related quality-of-life studies of HIV-infected patients have used health status instruments (2). In contrast, health value measures assess the desirability of a state of health by assessing ones willingness to live a shorter but healthier life (the time-tradeoff technique)or risk a bad outcomeusually deathin exchange for a chance at a healthy life (the standard-gamble technique) (3). Only a few studies have assessed the health values of patients with HIV (4-7). Despite compromised health, HIV-infected patients have been shown to exhibit a strong will to live (4, 7). Using life-satisfaction and utility measures, we examined how patients with HIV think about and value their health. Methods Study Design On the basis of results of six focus groups that included 34 HIV-infected patients, we developed a structured questionnaire and conducted in-depth cognitive interviews (8) with 51additional HIV-infected patients. The study took place between October 1996 and May 1997. Patients Patients were recruited at the time of their physician appointment or by telephone from the University of Cincinnati MedicalCenters Infectious Diseases Center, a regional center for HIV and AIDS. We recruited patients who represented various levels of severity of illness and oversampled women and persons from ethnic minority groups (understudied groups in which the prevalence of HIV infection and AIDS is increasing). We obtained informed consent and paid each patient

Cost-effectiveness of the implantable cardioverter-defibrillator: effect of improved battery life and comparison with amiodarone therapy.

25 for participating. By reviewing medical records, we determined the year that HIV infection was diagnosed, HIV stage (asymptomatic, symptomatic but without AIDS, or AIDS), CD4 cell count, history of injection-drug use, and whether the patient was receiving protease inhibitor therapy. Interviews In addition to demographic and clinical questions, the questionnaire included health rating, time-tradeoff, and standard-gamble questions; health status questions (9); a spirituality question; a religiosity question; questions addressing attitudes toward taking risks (10); questions concerning relationships with friends and family; and four life-satisfaction questions, one of which asked patients to compare their lives now with their lives before HIV infection was diagnosed (Appendix). All interviews were audiotaped, and audiotapes were coded for themes. Statistical Analysis We classified the variables into seven categories: demographic characteristics, clinical characteristics, health status, audiotape themes (that is, factors that patients were taking into account when answering the health value questions), spirituality/religiosity, attitude toward risk, and life satisfaction. Next, we determined the univariate relations of those variables to each of four outcome variables: life-satisfaction, rating scale, time-tradeoff, and standard-gamble scores. Proportions were compared by using the chi-square test or the Fisher exact test; continuous variables were compared by using t-tests or Wilcoxon tests, as appropriate. We assessed univariate correlations with outcome measures using Spearman correlation coefficients. Time-tradeoff scores were compared with standard-gamble scores by using the Wilcoxon signed-rank test and Spearman correlations. We conducted multivariable analyses with logistic regression models to determine significant predictors of whether the patient considered life better since contracting HIV. We used linear regression models to determine significant predictors of rating scale, time-tradeoff, and standard-gamble scores. The best predictors from each of the seven categories were considered candidate variables. We dichotomized the response to the spirituality question at the lowest quartile because of its skewed distribution. All analyses were performed by using SAS software, version 6.11(SAS Institute, Inc., Cary, North Carolina). Role of the Funding Source The Agency for Health Care Policy and Research funded the study but had no role in collecting, analyzing, interpreting, or reporting the data or in the decision to submit the paper for publication. Results Patients Table 1 shows the demographic and clinical characteristics of the 51 patients who completed the interviews. Table 1. Patients Who Participated in One-on-One, In-Depth Interviews Spirituality The mean score (SD) on the spirituality question(which used a scale of 0 to 100) was 85.7 26.1. The median score was100 (25th and 75th percentiles, 90 and 100), indicating that more than half of the patients said that they were fully at peace with God and the universe. Twenty-nine patients (57%) stated that religion was very important to them, and14 patients (27%) said that religion was somewhat important. Living with HIV Forty-nine percent of patients (95% CI, 35% to 63%) said that their life was better currently than it was before they were aware that they had HIV. Twenty-nine percent of patients said that life was currently worse at the time of the interview, 18% said that it was about the same, and 4%did not know. In univariate analyses, 73% of women said that their life was better currently compared with 39% of men (P=0.034), and 71% of persons who no longer used injection drugs said that their life was better currently compared with 45% of patients who had never used injection drugs (P>0.2). In addition, nonwhite patients (P=0.07) and unmarried patients (P=0.10) tended to say that life had gotten better. Feelings about whether life had improved since the patient had contracted HIV were unrelated to such factors as stage of HIV disease, number of years since diagnosis, or whether the patient was receiving protease inhibitor therapy. In multivariable analyses, patients who said that their lives were better were more likely to be at peace with God and the universe, to be female, and to have stopped using injection drugs (C-statistic, 0.8) (Table 2). Table 2. Predictors of Life Satisfaction and Health Values Scores on the other three life-satisfaction questions were also high. When asked how they felt their life was going, 71% of patients were mostly satisfied, pleased, or delighted; only 6% were mostly dissatisfied or unhappy. No patient felt that life was terrible. In addition, 41% of patients felt that their life was staying about the same, and 47% of patients felt that life was getting better; the remainder of patients felt that life was getting worse or did not know. Finally, when patients were asked to rate how they were feeling about their life as a whole on a scale from 0 (as bad as things could be) to 100 (as good as things could be), the mean score was 80.0 22.2 (median, 90 [25th and 75th percentiles, 60 and100]). Health Rating Scores On the 0 to 100 health rating scale, the mean score was71.0 18.7 (median, 70 [25th and 75th percentiles, 60 and90]). In univariate analyses, HIV-infected patients without AIDS had higher health ratings than patients with AIDS (mean rating, 77.6 compared with67.0; P=0.058). In multivariable analyses, rating scale scores were related to HIV stage: Asymptomatic patients had higher scores than symptomatic patients and patients with AIDS. Scores were also inversely related to level of fatigue (R 2 =0.44). Time-Tradeoff Scores With a 5-year time frame, the mean time-tradeoff score was 0.95 0.1 (median, 0.99 [25th and 75th percentiles, 0.93 and1.0]), indicating that, on average, patients did not have a clear preference between living 5 years in their current state of health and 4.75 years (0.95 5 years) in excellent health. A total of 24 patients (47%)were unwilling to trade any time at all, and 7 patients (14%) were willing to trade, at most, 9 days of life expectancy for excellent health (utility,0.995). Time-tradeoff scores for patients who did not have AIDS(mean score, 0.96) did not differ from scores for patients with AIDS (mean score, 0.94). Multivariable analyses showed that higher time-tradeoff scores were related to higher scores on the health rating scale, being at peace with God and the universe, male sex, and having children (R 2 =0.27). Standard-Gamble Scores The mean standard-gamble score was 0.80 0.27(median, 0.93 [25th and 75th percentiles, 0.65 and 1.0]), indicating that, on average, patients were willing to take up to a 20% risk ([1 0.80] 100%) for death in exchange for a chance at perfect health. Although 21 patients (41%) were willing to accept no more than 1 chance in 200 (utility 0.995), standard-gamble scores tended to be lower than time-tradeoff scores (P<0.001; r=0.37). Mean standard-gamble scores tended to be higher among patients without AIDS than among patients with AIDS (mean score, 0.90 compared with 0.74; P=0.1). Multivariable analyses showed that standard-gamble scores were inversely related to level of disability and to risk aversion (R 2 =0.33). Discussion Despite advances in treatment, HIV infection and AIDS remain chronic and debilitating, and no cure or vaccine is expected soon. Consequently, two findings from our study are particularly noteworthy. First, half of the patients interviewed indicated that their life with HIV is better than it was before they contracted HIV. Only 29% of patients said that their life was worse. Second, time-tradeoff utilities were especially high; this result indicates that despite their compromised health, patients strongly preferred longevity to excellent health. Factors unrelated to health that contributed to (and confounded) health values included spiritualit

Toward a Peer Review Process for Medical Decision Analysis Models

The implantable cardioverter-defibrillator (ICD) greatly reduces the incidence of sudden cardiac death among patients with recurrent sustained ventricular tachycardia and fibrillation who do not respond to conventional antiarrhythmic therapy. A cost-effectiveness analysis was performed, comparing the ICD, amiodarone and conventional agents. Actual variable costs of hospitalization and follow-up care were used for 21 ICD- and 43 amiodarone-treated patients. Life expectancy and total variable costs were predicted with use of a Markov decision analytic model. Clinical event rates and probabilities were based on published reports or expert opinion. Life expectancy with an ICD (6.1 years) was 50% greater than that associated with treatment with amiodarone (3.9 years) and 2.5 times that associated with conventional treatment (2.5 years). Assuming replacement every 24 months, ICD lifetime treatment costs (in 1989 dollars) for a 55-year old patient are expected to be

Automated Critiquing of Medical Decision Trees

89,600 compared with

An Architecture for Knowledge-based Construction of Decision Models

24,800 for amiodarone and

Distributed decision support using a web-based interface: prevention of sudden cardiac death.

16,100 for conventional therapy, yielding a marginal cost/effectiveness ratio for ICD versus amiodarone therapy of 1f429,200/year of life saved, which is comparable to that of other accepted medical treatments. If technologic improvements extend average battery life to 36 months, the marginal cost/effectiveness ratio would be

Electronic Submission for Medical Decision Making

21,800/year of life saved, and at 96 months it would be

Taking the Helm

13,800/year of life saved. Patient age at implantation did not significantly affect these results. If quality of life on amiodarone therapy is 30% lower than that with the ICD, the marginal cost/effectiveness ratio decreases by 35%. If the quality of life for patients receiving drugs is 40% lower than that of patients treated with an ICD, use of the defibrillator becomes the dominant strategy.