Patient recruitment forecasting in clinical trials using time-dependent Poisson-gamma model and homogeneity testing criteria

Clinical trials in the modern era are characterized by their complexity and high costs and usually involve hundreds/thousands of patients to be recruited across multiple clinical centres in many countries, as typically a rather large sample size is required in order to prove the efficiency of a particular drug. As the imperative to recruit vast numbers of patients across multiple clinical centres has become a major challenge, an accurate forecasting of patient recruitment is one of key factors for the operational success of clinical trials. A classic Poisson-gamma (PG) recruitment model assumes time-homogeneous recruitment rates. However, there can be potential time-trends in the recruitment driven by various factors, e.g. seasonal changes, exhaustion of patients on particular treatments in some centres, etc. Recently a few authors considered some extensions of the PG model to time-dependent rates under some particular assumptions. In this paper, a natural generalization of the original PG model to a PG model with non-homogeneous time-dependent rates is introduced. It is also proposed a new analytic methodology for modelling/forecasting patient recruitment using a Poisson-gamma approximation of recruitment processes in different countries and globally. The properties of some tests on homogeneity of the rates (non-parametric one using a Poisson model and two parametric tests using Poisson and PG model) are investigated. The techniques for modeling and simulation of the recruitment using time-dependent model are discussed. For re-projection of the remaining recruitment it is proposed to use a moving window and re-estimating parameters at every interim time. The results are supported by simulation of some artificial data sets.