Nonparametric prediction of event times in randomized clinical trials

In clinical trials with planned interim analysis, it can be valuable for logistical reasons to predict the times of landmark events such as the 50th and 100th event. Bagiella and Heitjan (Stat Med 2001; 20: 2055-63) proposed a parametric prediction model for failure-time outcomes assuming exponential survival and Poisson enrollment. When little is known about the distributions of interest, there is concern that parametric prediction methods may be biased and inefficient if their underlying distributional assumptions are invalid. We propose nonparametric approaches to make point and interval predictions for landmark dates during the course of the trial. We obtain point predictions using the Kaplan-Meier estimator to extrapolate the survival probability into the future, selecting the time when the expected number of events is equal to the landmark number. To construct prediction intervals, we use a simulation strategy based on the Bayesian bootstrap. Monte Carlo results demonstrate the superiority of the nonparametric method when the assumptions underlying the parametric model are incorrect. We demonstrate the methods using data from a trial of immunotherapy of chronic granulomatous disease.