A Novel Bayesian Distribution-Free Survival Analysis

A new Bayesian distribution-free medical survivor analysis is presented that strictly avoids using right-tail censored data. The Bayesian procedure is focused on two population parameters called ${\varphi }_{fc}$ and ${\Omega }_E$ , which are separate metrics of a treatment difference between the two conditions. The ${\varphi }_{fc}$ parameter is the proportion of failures that are from the Control condition, and the ${\Omega }_E$ parameter is a stochastic difference measure associated with longer survival time before a failure for the patients in the Experimental condition. Point and interval estimates along with a Bayes factor are provided for both parameters. Software is provided for implementing the Bayesian analysis. Monte Carlo simulations are also developed to study the interplay between the stop-testing time used in survival analysis with other variables such as effect size and sample size. The simulations also provide information that enable an approach to survival analysis where there is an early decision about the relative effectiveness of the treatments that is based on the Bayes factor value associated with the ${\varphi }_{fc}$ statistic. This decision can be made when there is a high proportion of right-tail censored data. In the limit of times so long that there are all failures-thus no right-tail censoring-the ${\varphi }_{fc}$ metric is not informative, but the ${\Omega }_E$ metric is still a valid measure of the stochastic difference in failure times between the two conditions.