Modelling/Forecasting Patient Recruitment in Clinical Trials Using Poisson-Gamma Model with Time-Dependent Rates

Modern late-phase clinical trials require hundreds/thousands of patients to be recruited across many clinical sites in different countries. For the operational success of clinical trials it is crucial to predict in real time the recruitment in different countries and globally, the stopping time when the recruitment target will be reached and the probability to recruit in time. A classic Poisson-gamma model developed earlier in the papers of the author and with co-authors for modelling and forecasting patient recruitment assumes time-homogeneous recruitment rates. However, the rates may vary over time due to various reasons, such as seasonal effects, lack of patients in some sites, etc. Therefore, a natural generalization of the original Poisson-gamma model to the Poisson-Gamma model with time-dependent rates is considered. An analytic technique for modelling and predicting over time the country and global recruitment processes is developed. A technique for Monte Carlo simulation is discussed. Two criteria for testing time-dependence, non-parametric Poisson-type criterion and parametric Poissongamma one, are considered. The implementations to predicting recruitment in clinical trials using simulated data-sets are discussed.