Additive Cost Modelling in Clinical Trial

Abstract

In the framework of a clinical trial, an important question is how long it takes to recruit a given number n of patients. Until now, most techniques were based on deterministic models and various ad hoc techniques. Using a Poisson process to describe the recruitment process is now an accepted approach. However, in real trials, different centres have different recruitment rates. To mimic this variation, Anisimov and Fedorov (Stat Med 26(27):4958–4975, 2007) used the so-called Poisson-gamma model in which the patients are assumed to arrive at different centres according to Poisson processes with Gamma-distributed rates. Here, we investigate the very first step of a cost model for multicentric clinical trial. This additive model describes the total cost C(t) of the trial at time t assuming patients arrive according to a Poisson-gamma process. To account for loss of patients during screening period, we also assume a patient can drop the trial at arrival with a centre-specific random probability; these probabilities are assumed Beta-distributed among centres. Filtered Poisson processes naturally arise in this model. Although these processes are not semi-martingales, we show we can calculate the expectation $\mathbb{E}[C(\tau )]$ where τ is the (random) first time when the recruitment process reaches n.