Models for patients' recruitment in clinical trials and sensitivity analysis

Abstract

Taking a decision on the feasibility and estimating the duration of patients' recruitment in a clinical trial are very important but very hard questions to answer, mainly because of the huge variability of the system. The more elaborated works on this topic are those of Anisimov and co-authors, where they investigate modelling of the enrolment period by using Gamma-Poisson processes, which allows to develop statistical tools that can help the manager of the clinical trial to answer these questions and thus help him to plan the trial. The main idea is to consider an ongoing study at an intermediate time, denoted t(1). Data collected on [0,t(1)] allow to calibrate the parameters of the model, which are then used to make predictions on what will happen after t(1). This method allows us to estimate the probability of ending the trial on time and give possible corrective actions to the trial manager especially regarding how many centres have to be open to finish on time. In this paper, we investigate a Pareto-Poisson model, which we compare with the Gamma-Poisson one. We will discuss the accuracy of the estimation of the parameters and compare the models on a set of real case data. We make the comparison on various criteria : the expected recruitment duration, the quality of fitting to the data and its sensitivity to parameter errors. We discuss the influence of the centres opening dates on the estimation of the duration. This is a very important question to deal with in the setting of our data set. In fact, these dates are not known. For this discussion, we consider a uniformly distributed approach. Finally, we study the sensitivity of the expected duration of the trial with respect to the parameters of the model : we calculate to what extent an error on the estimation of the parameters generates an error in the prediction of the duration.

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

“…3.3 [11] that "Mijoule et al [15] proposed replacing the gamma with a Pareto mixture." Actually in [15] the authors investigated further properties of P-G model, compared them with the Pareto-Poisson model using real datasets from [2], and also investigated the feasibility of the model.…”

“…3.3 [11] that "Mijoule et al [15] proposed replacing the gamma with a Pareto mixture." Actually in [15] the authors investigated further properties of P-G model, compared them with the Pareto-Poisson model using real datasets from [2], and also investigated the feasibility of the model. In final conclusions the authors "recommend the use of the Poisson-Gamma, which is easier to handle", and also recommend using a uniform distribution for centers initiation when the opening dates of the centers are not known precisely, which is proposed in [3,4].…”

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

“…Bakhshi et al [7] investigated the model empirically, observing that the parameters of the gamma distribution appear to vary across similar trials; that is, a second level of hierarchy may be needed. Mijoule et al [31] proposed replacing the gamma with a Pareto mixture.…”

“…Thus it may be that so-called "unconditional" accrual modelsthose that ignore center information -will be just as accurate as models that specifically incorporate data on centers. Moreover, models that describe between-center variation as random effects (Anisimov [2][3][4][5], Mijoule [31]) require large numbers of centers to enable precise estimation of the rate parameters. Not all trials have enough centers to render this approach practicable.…”

Simulating Correlated Ordinal and Discrete Variables with Assigned Marginal Distributions

“…Meanwhile, a huge variability of the recruitment process makes the question quite hard to investigate, thus, stochastic modelling has to be developed. There were many investigations on this way and now we are able to claim that the easier to handle and more relevant model is a so-called Poisson-Gamma model (Mijoule et al (2012)) introduced in Anisimov et al (2007). This model assumes that patients arrive at different centres according to Poisson processes where the rates are Γ(α, β)-distributed.…”