Large-Sample Bayesian Posterior Distributions for Probabilistic Sensitivity Analysis

In probabilistic sensitivity analyses, analysts assign probability distributions to uncertain model parame-ters and use Monte Carlo simulation to estimate the sensitivity of model results to parameter uncertainty. The authors present Bayesian methods for construct-ing large-sample approximate posterior distributions for probabilities, rates, and relative effect parameters, for both controlled and uncontrolled studies, and dis-cuss how to use these posterior distributions in a prob-abilistic sensitivity analysis. These results draw on and extend procedures from the literature on large-sample Bayesian posterior distributions and Bayesian random effects meta-analysis. They improve on stan-dard approaches to probabilistic sensitivity analysis by allowing a proper accounting for heterogene-ity across studies as well as dependence between con-trol and treatment parameters, while still being simple enough to be carried out on a spreadsheet. The authors apply these methods to conduct a probabilis-tic sensitivity analysis for a recently published analy-sis of zidovudine prophylaxis following rapid HIV testing in labor to prevent vertical HIV transmission in pregnant women. Key words: decision analysis; cost-effectiveness analysis; probabilistic sensitivity analy-sis; Bayesian methods; random effects meta-analysis; expected value of perfect information; HIV transmis-sion; zidovudine prophylaxis. (Med Decis Makin