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Rapid Approximation of Confidence Intervals for Markov Process Decision Models

Applications in Decision Support Systems

Affiliations of the authors: Palo Alto Veterans Affairs Health Care System, Palo Alto, CA (DJC); Stanford University School of Medicine, Stanford, CA (LAL).

Correspondence and reprints: Leslie A. Lenert, MD, Division of Clinical Pharmacology, MSOB X208, Stanford, CA 94305-5463.

Abstract Objective: Develop the methodological foundation for interactive use of Markov process decision models by patients and physicians at the bedside.

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 -1.4 to 19.0 quality-adjusted life-months. 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.