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

Research output: Contribution to journalJournal articlepeer-review

<mark>Journal publication date</mark>5/02/2021
Publication StatusAccepted/In press
<mark>Original language</mark>English


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. We consider the asymptotic accuracy
of quantile predictions in the limit as the number of recruitment centres 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 $n^+_\bullet$ patients, the accuracy degrades as the ratio of $n^+_\bullet$ 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.

Bibliographic note

Accepted for publication in February 2021.