Medical Decision Making

This paper introduces stochastic trees, a new modeling approach for the class of medical decision problems in which risks of mortality and morbidity may extend over time. A stochastic tree may be regarded as a continuous-time version of a Markov-cycle tree, or alternately, as a multi-state DEALE model. Optimal decisions in stochastic trees can be determined by rollback, much in the same fashion as decision trees. The author discusses how age- dependent mortality rates and declining incidence rates may be modeled using stochastic trees. Concepts are illustrated using examples from the medical literature. It is argued that stochastic trees possess important advantages over Markov-cycle trees for medical decision modeling. Key words: stochastic trees; DEALE models; decision analysis; Markov cycle trees. (Med Decis Making 1992;12:163-178)

An ideal method for assessing performance of non-binary diagnostic tests would specify each test's optimal operating point and would tell a diagnostician which of many tests was the best one to use in a particular clinical situation. This article shows how information theory and receiver operating characteristic (ROC) analysis can be combined to evaluate and compare diagnostic tests at their optimum cutoffs once disease prevalence and test properties are specified. Though it is not appropriate for all clinical situations, the method can be used for most diagnostic tests whenever information is desired for its own sake or when reducing uncertainty is the goal of testing. The method also is appropriate in those situations where benefits and costs cannot be specified precisely enough to permit test optimization based on a balancing of anticipated goods and evils. Key words: non-binary diagnostic tests; information theory; receiver operating characteristic curves. (Med Decis Making 1992;12:179- 188)

Modeling of the uncertainty of multiple input variables for a complex decision problem com plicates sensitivity analysis. A method of analysis comprising stochastic simulation of the model and logistic regression of the simulated dichotomous decision variable against all of the input variables yields a direct measure of the importance of input variables to the decision. This method is demonstrated on a previously analyzed clinical decision either to continue observation or to immediately treat with anticoagulants a woman presenting with deep vein thrombosis in the first trimester of pregnancy. A relative measure of the importance of each input variable in causing a change of decision is estimated by calculating the change in the log odds attributable to variation of each input variable over its range of uncertain values compared with the total change of log odds from variation of all input variables. This method is compared with alternative measures of input variable importance, and is found to be a simple yet powerful tool for gaining quantitative insight into the nuances of a decision model. Key words: decision sensitivity; logistic regression; decision model; Monte Carlo technique. (Med Decis Making 1992;12:189-196)

Probability estimates of angiographic coronary artery disease made by experienced, board- certified staff cardiologists were compared with those of cardiologists in training (fellows). In addition, estimates made before coronary angiography were compared with those made several months later based on written clinical summaries of 15 items of objective clinical and test data. Cardiologists were asked to estimate the probabilities of coronary artery disease, multivessel disease, and triple-vessel or left main disease. The study population consisted of 510 consecutive patients without valvular disease referred for the first time for coronary angiography to three hospitals. Both staff and fellows consistently overestimated the pre-angiographic probability of coronary artery disease. The probabilities estimated from patient summaries were always significantly lower than the pre-angiographic assessments. Only staff cardiologists reliably assessed the probabilities of coronary artery disease during the second assessment (p < 0.05). Thus, estimates of disease probability based on clinical judgment vary according to the source of information, and these estimates are more accurate when physicians have objective data on hand and do not know the identities of the patients. Key words: judgment; disease probability; disease estimate; coronary artery disease; clinical assessment; value-induced bias. (Med Decis Making 1992;12:197-203)

The authors developed a method that utilizes logistic regression analysis to 1) calculate the disease probability with confidence intervals at which any specified proportion of physicians reaches a clinical decision, 2) statistically test whether factors other than disease probability affect this clinical decision, and 3) statistically test whether physician decision making in relation to disease probability varies by other factors. They apply the method to analyze the relationship between disease probability and the proportion of physicians who diagnosed coronary artery disease (CAD) in 127 consecutive subjects who completed the treadmill exercise tolerance test (ETT) at two hospitals. Twenty-five percent of the physicians decided that CAD was possible or definite at a post-ETT disease probability of 0.24 (95% CL = 0.07-0.35); 50% at 0.54 (95% CL = 0.43-0.70); and 75% at 0.82 (95% CL = 0.67-1.0). Multivariate logistic regression analysis revealed three factors significantly and independently related to the diagnosis of CAD: post-ETT disease probability, positive ETT result, and cigarette smoking. The proportion of physicians who reached a diagnosis of CAD did not differ by hospital setting (VA versus university), level of training (attending versus housestaff/ fellow), or diagnosing service (cardiology versus other internal medicine). It is concluded that factors other than disease probability may affect physician diagnostic decisions. Key words: medical decision making; decision threshold; logistic regression analysis; stochastic threshold model; exercise treadmill test; ischemic heart disease. (Med Decis Making 1992;12:204-212)

Feedback to physicians about how they use information in making judgments can improve the quality of their judgments, but questions remain about which types of feedback are most effective. The authors conducted a controlled study of feedback in 60 medical students learning to predict the risk of cardiovascular death based on the presence or absence of five risk factors. After a pretest of 40 cases abstracted from patient records, the students worked through 173 computer-simulated cases and a posttest of 40 patient cases. The students received no feedback, probability feedback (correct probability of cardiac death for each case), cognitive feedback (the correct cue weights compared with their own weights derived from the previous set of cases), or both types of feedback. Students who received probability feedback markedly improved both base rate calibration and discrimination. Those who received only cognitive feedback showed no improvement over control on any of the measures of learning. All subjects were highly consistent in their weightings. The superiority of probability feedback differed from previous findings that cognitive feedback was essential for mastery of multiple-cue-probability learning tasks. The information on cue-outcome relationships given by cognitive feedback may be more useful when these relationships are complex and the combining rule is not known, while the precise outcome information provided by probabilistic feedback is more useful when the combining rule is known and the cue- outcome relationships are straightforward. Thus, the optimal method of learning depends on the nature of the task. Key words: risk factors; computer simulations; heart disease. (Med Decis Making 1992;12:213-221)

As part of a validation of a mathematical model of breast cancer, the Health Insurance Plan of Greater New York (HIP) randomized controlled trial of breast cancer screening and the uncontrolled Breast Cancer Detection Demonstration Projects (BCDDP) trial were simulated. Model predictions were in accord with the nine-year survival experience of women in the HIP trial, and, with the exception of women 40-44 years old, with HIP data on 18-year survival. Five-year survival rates of screen-detected cases in the BCDDP were very close to the model's predictions. However, the model did not predict the high survival rate of women who had interval cancers in the BCDDP. By the end of the BCDDP, almost 85% of the participants performed breast self-examination (BSE) regularly. Consistent with this obser vation, an appealing hypothesis to explain the high survival rate of women who had interval cancers is that BSE is of value in detecting breast cancers earlier. Consideration of model outliers can be of value in increasing understanding of the phenomena being modeled. Key words: breast self-examinations; breast cancer screening; mathematical models; model val idation. (Med Decis Making 1992;12:222-228)