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 $n_{•}^{+}$n+∙$n_{•}^{+}$ patients, the accuracy degrades as the ratio of $n_{•}^{+}$n+∙$n_{•}^{+}$ 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. 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.

中文翻译：

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基于分层泊松-伽玛模型的多中心临床试验招募预测：渐近分析和改进区间

我们基于对单个中心招募的常用分层泊松伽玛模型的最大似然拟合来分析对多中心临床试验未来招募的预测。随着招聘中心数量的增加，我们考虑了分位数预测的渐近精度，并发现，在一个重要的意义上，分位数的精度并没有随着中心数量的增加而提高。当预测在额外时间段内进一步招募的人数时，准确性会随着额外时间与人口普查时间的比率增加而降低，而在预测额外时间以招募更多人时，准确性会降低。$n_{•}^{+}$n+∙$n_{•}^{+}$患者，准确度下降的比率$n_{•}^{+}$n+∙$n_{•}^{+}$到普查期招募的人数增加。我们的分析表明改进的分位数预测器。模拟研究验证了预测模式适用于临床试验中的典型招募场景，并验证了从我们的分位数预测器获得的预测区间的覆盖率大大提高。在扩展我们方法的适用性的过程中，我们表明，就所有整数矩的准确性而言，通过在前两个矩上匹配的单个 gamma 随机变量来近似独立 gamma 随机变量的总和总是比通过从中心极限定理得到的矩匹配高斯。