Recruitment prediction for multicenter clinical trials based on a hierarchical Poisson-gamma model: Asymptotic analysis and improved intervals

We analyze predictions of future recruitment to a multicenter clinical trial based on a maximum-likelihood fitting of a commonly used hierarchical Poisson-gamma model for recruitments at individual centers. We consider the asymptotic accuracy of quantile predictions in the limit as the number of recruitment centers grows large and find that, in an important sense, the accuracy of the quantiles does not improve as the number of centers increases. When predicting the number of further recruits in an additional time period, the accuracy degrades as the ratio of the additional time to the census time increases, whereas when predicting the amount of additional time to recruit a further n center dot+ patients, the accuracy degrades as the ratio of n center dot+ to the number recruited up to the census period increases. Our analysis suggests an improved quantile predictor. Simulation studies verify that the predicted pattern holds for typical recruitment scenarios in clinical trials and verify the much improved coverage properties of prediction intervals obtained from our quantile predictor. In the process of extending the applicability of our methodology, we show that in terms of the accuracy of all integer moments it is always better to approximate the sum of independent gamma random variables by a single gamma random variable matched on the first two moments than by the moment-matched Gaussian available from the central limit theorem.

Automated summary

This study analyzes predictions of future recruitment in multicenter clinical trials, finding that the accuracy of quantile predictions does not necessarily improve with an increasing number of centers. The accuracy of predicting the number of further recruits declines with increasing ratio of additional time to census time, while the accuracy of predicting the time to recruit a certain number of patients degrades with increasing ratio of patients to total recruited. Simulation studies confirm the predicted patterns and improved coverage properties of prediction intervals.