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We analyse predictions of future recruitment to a multi-centre clinical trialbased on a maximum-likelihood fitting of a commonly used hierarchicalPoisson-Gamma model for recruitments at individual centres. We consider theasymptotic accuracy of quantile predictions in the limit as the number ofrecruitment centres grows large and find that, in an important sense, theaccuracy 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 timeincreases, whereas when predicting the amount of additional time to recruit afurther $n^+_\bullet$ patients, the accuracy degrades as the ratio of$n^+_\bullet$ to the number recruited up to the census period increases. Ouranalysis suggests an improved quantile predictor. Simulation studies verifythat the predicted pattern holds for typical recruitment scenarios in clinicaltrials and verify the much improved coverage properties of prediction intervalsobtained from our quantile predictor. In the process of extending theapplicability of our methodology, we show that in terms of the accuracy of allinteger moments it is always better to approximate the sum of independent gammarandom variables by a single gamma random variable matched on the first twomoments than by the moment-matched Gaussian available from the central limittheorem.

Recruitment prediction for multi-centre clinical trials based on a hierarchical Poisson-gamma model: asymptotic analysis and improved intervals