A random walk approach for quantifying uncertainty in group sequential survival trials

The development of group sequential methods has produced multiple criteria that are used to guide the decision of whether a clinical trial should be stopped early given the data observed at the time of an interim analysis. However, the potential for time-varying treatment effects should be considered when monitoring survival endpoints. In order to quantify uncertainty in future treatment effects it is necessary to consider future alternatives which might reasonably be observed conditional upon data collected up to the time of an interim analysis. A method of imputation of future alternatives using a random walk approach that incorporates a Bayesian conditional hazards model and splits the prior distribution for model parameters across regions of sampled and unsampled support is proposed. By providing this flexibility, noninformative priors can be used over regions of sampled data while providing structure to model parameters over future time intervals. The result is that inference over areas of sampled support remains consistent with commonly used frequentist statistics while a rich class of predictive distributions of treatment effect over the maximal duration of a trial are generated to assess potential treatment effects which may be plausibly observed if the trial were to continue. Selected operating characteristics of the proposed method are investigated via simulation and the approach is applied to survival data stemming from trial 002 of the Community Programs for Clinical Research on AIDS (CPCRA) study.