Modeling restricted enrollment and optimal cost-efficient design in multicenter clinical trials

Design and forecasting of patient enrollment is among the greatest challenges that the clinical research enterprize faces today, as inefficient enrollment can be a major cause of drug development delays. Therefore, the development of the innovative statistical and artificial intelligence technologies for improving the efficiency of clinical trials operation are of the imperative need. This paper is describing further developments in the innovative statistical methodology for modeling and forecasting patient enrollment. The underlying technique uses a Poisson-gamma enrollment model developed by Anisimov & Fedorov in the previous publications and is extended here to analytic modeling of the enrollment on country/region level. A new analytic technique based on the approximation of the enrollment process in country/region by a Poisson-gamma process with aggregated parameters is developed. Another innovative direction is the development of the analytic technique for modeling the enrollment under some restrictions (enrollment caps in countries). Some discussion on using historic trials for better prediction of the enrollment in the new trials is provided. These results are used for solving the problem of optimal trial cost-efficient enrollment design: find an optimal allocation of sites/countries that minimizes the global trial cost given that the probability to reach an enrollment target in time is no less than some prescribed probability. Different techniques to find an optimal solution for high dimensional optimization problem for the cases of unrestricted and restricted enrollment and for a small and large number of countries are discussed.