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Abstract
In clinical trials with planned interim analyses, it can be valuable for a variety of reasons to predict the times of landmark events in advance of their occurrence. Bagiella and Heitjan (2001) proposed a parametric prediction model for failure-time outcomes assuming exponential survival and Poisson enrollment. There is concern that their model has limited application because of the strong distributional assumptions, and that the predictions may be inaccurate if distributional assumptions are wrong.
To address this concern, we first propose a nonparametric approach to making point and interval prediction of 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 the Bayesian bootstrap to generate the predictive distribution of landmark times; predictive intervals are quantiles of this distribution. Monte Carlo simulation results demonstrate the superiority of the nonparametric method when the assumptions underlying the parametric model are incorrect.
Secondly, we generalize the exponential survival model to the two-parameter Weibull model. The survival probability in the future is estimated from the available data and the prior guesses for the values of two Weibull parameters. For interval prediction, we approximate the posterior distribution using the sampling-importance-resampling technique, and generate the predictive distribution of landmark times. Monte Carlo simulation results show that the Weibull prediction model works very well for the Weibull and gamma distributions, but not so well for the lognormal distribution.
Finally, we extend the constant enrollment rate model to a non-homogenous Poisson process model. For the parametric prediction, we use a truncated exponential enrollment model. For non-parametric prediction, we generalize the enrollment model by using weighted sampling from previous enrollment time intervals. Monte Carlo simulation results illustrate the advantage of these generalizations over the constant rate model and their flexibility in predicting enrollment.
We demonstrate these methods using data from a trial in immunotherapy of chronic granulomatous disease.
