Parametric sensitivity analysis using large-sample approximate Bayesian posterior distributions

When a decision analyst desires a sensitivity analysis on model parameters that are estimated from data, a natural approach is to vary each parameter within one or two standard errors of its estimate. This approach can be problematic if parameter estimates are correlated or if model structure does not permit obvious standard error estimates. Both of these difficulties can occur when the analysis of time-to-event data – known as survival analysis – plays a significant role in the decision analysis. We suggest that in this situation, a large-sample approximate multivariate normal Bayesian posterior distribution can be fruitfully used to guide either a traditional threshold proximity sensitivity analysis, or a probabilistic sensitivity analysis. The existence of such a large-sample approximation is guaranteed by the so-called Bayesian central limit theorem. We work out the details of this general proposal for a two-parameter cure-rate model, used in survival analysis. We apply our results to conduct both traditional and probabilistic sensitivity analyses for a recently published decision analysis of tamoxifen use for the prevention of breast cancer.