A Bayesian piecewise exponential phase II design for monitoring a time-to-event endpoint

Abstract

A robust Bayesian design is presented for a single-arm phase II trial with an early stopping rule to monitor a time to event endpoint. The assumed model is a piecewise exponential distribution with non-informative gamma priors on the hazard parameters in subintervals of a fixed follow up interval. As an additional comparator, we also define and evaluate a version of the design based on an assumed Weibull distribution. Except for the assumed models, the piecewise exponential and Weibull model based designs are identical to an established design that assumes an exponential event time distribution with an inverse gamma prior on the mean event time. The three designs are compared by simulation under several log-logistic and Weibull distributions having different shape parameters, and for different monitoring schedules. The simulations show that, compared to the exponential inverse gamma model based design, the piecewise exponential design has substantially better performance, with much higher probabilities of correctly stopping the trial early, and shorter and less variable trial duration, when the assumed median event time is unacceptably low. Compared to the Weibull model based design, the piecewise exponential design does a much better job of maintaining small incorrect stopping probabilities in cases where the true median survival time is desirably large.

Keywords: Bayesian adaptive design; futility monitoring; go/no-go decision; interim analysis.

FIGURE 1

Estimation of the survival distribution by the Kaplan–Meier method, or assuming either a Weibull or an exponential distribution

FIGURE 2

Estimation of the progression-free survival distribution by the Kaplan–Meier method, or assuming either a piecewise exponential or exponential distribution

FIGURE 3

User interface for the Shiny application of PE-G method