Purpose: In probabilistic sensitivity analyses (PSA), analysts assign probability distributions to uncertain model parameters, and use Monte Carlo simulation to estimate the sensitivity of model results to parameter uncertainty.  Bayesian methods provide convenient means to obtain probability distributions on parameters given data.  We present large-sample approximate Bayesian posterior distributions for probabilities, rates and relative effect parameters, and discuss how to use these in PSA. 

Methods: We use Bayesian random effects meta-analysis, extending procedures summarized by Ades, Lu and Claxton (2004).  We outline procedures for using the resulting posterior distributions in Monte Carlo simulation.

Results and conclusions: We apply these methods to conduct a PSA for a recently published analysis of zidovudine prophylaxis following rapid HIV testing in labor to prevent vertical HIV transmission in pregnant women (Mrus and Tsevat 2004).  Zidovudine prophylaxis is cost saving and has net benefit $557 per pregnancy compared to not testing for HIV, assuming a cost of $50,000 per lost QALY (mother and child).  We based a PSA on the following data from seven studies of vertical HIV transmission, as well as data for 5 other probability parameters:

Given this data, the two parameters (log Risk population mean) and (log Risk Ratio population mean) for vertical HIV transmission have approximate bivariate normal posterior with mean/sd equal to -1.39/0.12 and -1.02/0.23, and correlation -0.108.  Using these and other posterior distributions for all 5 remaining probabilities in a PSA yields zidovudine prophylaxis optimal 94.3% (±0.13%) of the time, and the expected value of perfect information on all 7 relative effects and probabilities equal to $15.13 (±1.35) per pregnancy.  These results concur with Mrus and Tsevat’s conclusion that the choice of rapid HIV testing followed by zidovudine prophylaxis is not a close call.