Stochastic modeling and prediction for accrual in clinical trials

Patient accrual in clinical trials is a topic of interest for important practical reasons. It has implications in both the initial planning and ongoing monitoring of trials. Slow accrual is of particular concern when it leads to reduced sample size. Although accrual in clinical trials has been studied and its estimation has been proposed and implemented, the existing methods are usually over-simplified by assuming a constant or piecewise constant accrual rate, and more flexible and realistic methods are needed. In this paper, we discuss a principled framework to monitor and predict trial accrual. We model trial accrual using a non-homogeneous Poisson process and model the underlying time-dependent accrual rate using cubic B-splines. The statistical inference and prediction procedure for the model are studied in a Bayesian paradigm. We conduct simulation studies to investigate the performance of the proposed approach and compare with a constant accrual rate model discussed by Gajewski et al. (Statist. Med. 2008; 27: 2328-2340). With satisfactory results, we illustrate the proposed method using accrual data from a real oncology trial. Our results show that the proposed model is more robust and achieves substantially better performance compared with the existing methods.