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

TL;DR

This paper introduces a time-dependent Poisson-gamma model for more accurate patient recruitment forecasting in complex, multi-center clinical trials, addressing the limitations of traditional homogeneous rate models.

Contribution

It extends the classic PG model to incorporate non-homogeneous, time-dependent rates and develops new homogeneity testing methods for improved recruitment prediction accuracy.

Findings

The proposed model captures time-trends in recruitment data.

Homogeneity tests effectively identify rate variations.

Simulation results validate the model's forecasting capabilities.

Abstract

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.