  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.
