Rapid Approximation of Confidence Intervals for Markov Process Decision Models: Applications in Decision Support Systems

Design: Monte Carlo simulation studies of a decision model comparing two treatments for benign prostatic hypertrophy: watchful waiting (WW) and transurethral prostatectomy (TUR). Measurements: The 95% confidence interval (CI) for the mean of the Markov model; the correlation of a linear approximation with the full Markov model; the predictive performance of the approximation; the information index of specific utilities in the model. Results: The 95% CI for the gain in utility with initial TUR was 21.4 to 19.0 quality-adjusted lifemonths. A multivariate linear model had an excellent fit to the predictions of the Markov model (R2 = 0.966). In an independent data set, the linear model also had a high correlation with the full Markov model (R2 = 0.967); its predictions were unbiased (p = 0.597, paired t-test); and, in 96.4% of simulated cases, its treatment recommendation was the same. Conclusion: Using the linear model, it was possible to efficiently compute which health state had the largest contribution to the variance of the decision model. This is the most informative utility value to elicit next. The most informative utility at any point in a sequence changed depending on utilities previously entered into the model. A linear model can be used to approximate the predictions of a Markov process decision model. n J Am Med Inform Assoc. 1997;4:301–312. In the early 1980s the goal of medical decision analysis was to help individual patients make difficult medical decisions. Most medical decision analyses are performed with computers, and computers may be a reasonable tool for conducting decision analytic ‘‘dialogues’’ with the patient. In these dialogues, a meaAffiliations of the authors: Palo Alto Veterans Affairs Health Care System, Palo Alto, CA (DJC); Stanford University School of Medicine, Stanford, CA (LAL). Supported by a grant (LM 05626-02) from the National Library of Medicine and the Ambulatory Care Fellowship, Department of Veterans Affairs. Correspondence and reprints: Leslie A. Lenert, MD, Division of Clinical Pharmacology, MSOB X208, Stanford, CA 94305-5463. Received for publication: 10/7/96; accepted for publication: 2/12/97. sure of the uncertainty of the decision model’s recommendation is important in terms of validity and acceptability. Many decision models, such as Markov or semi-Markov process models, are extremely complex, and methods for confidence interval determination can be computationally expensive, making interactive use of these models impossible. We sought a simple method of summarizing the uncertainty inherent in a Markov process model that could be used on a real-time scale. We introduce a Monte Carlo method for confidence interval calculation for Markov models. Using a previously published Markov model, we show that the results of this Monte Carlo simulation can be summarized accurately using a simple linear model. This model can then be used interactively, with a drastic decrease in computation time, to provide decision support for individual patients. We discuss the advantages of this method over other computational methods for interactive decision support. 302 CHER, LENERT, Rapid Approximation of Confidence Intervals for Markov Decision Models