Recruitment prediction for multi-centre clinical trials based on a hierarchical Poisson-gamma model: asymptotic analysis and improved intervals
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We analyse predictions of future recruitment to a multi-centre clinical trial based on a maximum-likelihood fitting of a commonly used hierarchical Poisson-Gamma model for recruitments at individual centres by a particular census time. We consider the asymptotic accuracy of quantile predictions in the limit as the number of recruitment centres, C, grows large and find that, in an important sense, the accuracy of the quantiles does not improve as the number of centres 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^+ patients, the accuracy degrades as the ratio of n^+ 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. Further studies show substantial improvement even outside the range of scenarios for which our results strictly hold.
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