Bayesian modeling and prediction of accrual in multi-regional clinical trials

Abstract

In multi-regional trials, the underlying overall and region-specific accrual rates often do not hold constant over time and different regions could have different start-up times, which combined with initial jump in accrual within each region often leads to a discontinuous overall accrual rate, and these issues associated with multi-regional trials have not been adequately investigated. In this paper, we clarify the implication of the multi-regional nature on modeling and prediction of accrual in clinical trials and investigate a Bayesian approach for accrual modeling and prediction, which models region-specific accrual using a nonhomogeneous Poisson process (NHPP) and allows the underlying Poisson rate in each region to vary over time. The proposed approach can accommodate staggered start-up times and different initial accrual rates across regions/centers. Our numerical studies show that the proposed method improves accuracy and precision of accrual prediction compared to existing methods including the NHPP model that does not model region-specific accrual.

Discussion on the paper “Real-Time Prediction of Clinical Trial Enrollment and Event Counts: A Review”, by DF Heitjan, Z Ge, and GS Ying

“…One is using mixed Poisson processes where the global rate is modelled using different approaches [12,13,16,17]. Another one uses Brownian or fractional Brownian motions [14,18].…”

“…Thus, the predictive processes at different levels are in general non-homogeneous doubly stochastic Poisson processes where the global and individual rates depend on the processes of initiation, closing centers and individual rates. This feature of P-G model profitably differentiates it from the other models for global prediction based on using Poisson models [12,13,17] and Brownian and fractional Brownian motions [14,18], as in these papers it is assumed that the predictive process is time-homogeneous with constant parameters estimated at interim time.…”

“…Therefore, the posterior rates are actually time dependent as depend on interim data. In fact the idea of interim estimation for P-G model is in some sense similar to estimating the enrollment rates in [12] by using spline models and interim data, however the procedure of estimation is different as in P-G model data is used to re-estimate the parameters of gamma distributions of the rates (on global or regional levels), but in [12] data is used to re-estimate the spline parameters of the rates.…”

“…Actually during the stable period the basic models for the mean trend of global enrollment should behave similar. This includes Poisson type models [13,17], models with spline approximation [12], Brownian and fractional Brownian motions [14,18], and P-G model. However, these techniques except P-G model may not be suitable at the trial start-up and during the transient period and also for other types of analysis (enrollment performance, adaptive adjustment, etc.…”

Real-time prediction of clinical trial enrollment and event counts: A review

“…Thus a number of papers have proposed enrollment models that allow the Poisson accrual rate to vary over time. Long and co-authors [51] used spline models to describe the accrual rate against time, incorporating random effects in the spline coefficients when the recruitment system has a hierarchical structure [14]. Tang et al [42,43] proposed a model in which daily accrual starts from a low value and rises gradually to a constant rate.…”