Weibull prediction of event times in clinical trials

Abstract

In clinical trials with interim analyses planned at pre-specified event counts, one may wish to predict the times of these landmark events as a tool for logistical planning. Currently available methods use either a parametric approach based on an exponential model for survival (Bagiella and Heitjan, Statistics in Medicine 2001; 20:2055) or a non-parametric approach based on the Kaplan-Meier estimate (Ying et al., Clinical Trials 2004; 1:352). Ying et al. (2004) demonstrated the trade-off between bias and variance in these models; the exponential method is highly efficient when its assumptions hold but potentially biased when they do not, whereas the non-parametric method has minimal bias and is well calibrated under a range of survival models but typically gives wider prediction intervals and may fail to produce useful predictions early in the trial. As a potential compromise, we propose here to make predictions under a Weibull survival model. Computations are somewhat more difficult than with the simpler exponential model, but Monte Carlo studies show that predictions are robust under a broader range of assumptions. We demonstrate the method using data from a trial of immunotherapy for chronic granulomatous disease.