TY - JOUR

T1 - Recruitment prediction for multicenter clinical trials based on a hierarchical Poisson–gamma model

T2 - Asymptotic analysis and improved intervals

AU - Mountain, Rachael

AU - Sherlock, Chris

N1 - This is the peer reviewed version of the following article: Rachael Mountain, Chris Sherlock (2021), Recruitment prediction for multicenter clinical trials based on a hierarchical Poisson–gamma model: Asymptotic analysis and improved intervals. BIOMETRIC METHODOLOGY. doi: 10.1111/biom.13447 which has been published in final form at https://onlinelibrary.wiley.com/doi/full/10.1111/biom.13447 This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.

PY - 2022/6/30

Y1 - 2022/6/30

N2 - 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+• 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. 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

AB - 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+• 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. 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

KW - asymptotic analysis

KW - asymptotic correction

KW - clinical trial recruitment

KW - multicenter clinical trial

KW - Poisson process

KW - recruitment prediction interval

U2 - 10.1111/biom.13447

DO - 10.1111/biom.13447

M3 - Journal article

VL - 78

SP - 636

EP - 648

JO - Biometrics

JF - Biometrics

SN - 0006-341X

IS - 2

ER -