Prediction intervals for overdispersed binomial endpoints and their application to toxicological historical control data

TL;DR

This paper introduces four new prediction intervals for overdispersed binomial data in toxicology, demonstrating their superior control of error rates over traditional heuristics through extensive simulations and real data application.

Contribution

The paper develops and compares four novel prediction intervals, including Bayesian and frequentist methods, tailored for overdispersed binomial data in toxicology, improving control of type-1-error.

Findings

Frequentist bootstrap calibrated prediction intervals best control type-1-error.

Bayesian generalized linear mixed model intervals are practically applicable.

Heuristic methods fail to control type-1-error in simulations.

Abstract

For toxicology studies, the validation of the concurrent control group by historical control data (HCD) has become requirements. This validation is usually done by historical control limits (HCL), which should cover the observations of the concurrent control with a predefined level of confidence. In many applications, HCL are applied to dichotomous data, e.g. the number of rats with a tumor vs. the number of rats without a tumor (carcinogenicity studies) or the number of cells with a micronucleus out of a total number of cells. Dichotomous HCD may be overdispersed and can be heavily right- (or left-) skewed, which is usually not taken into account in the practical applications of HCL. To overcome this problem, four different prediction intervals (two frequentist, two Bayesian), that can be applied to such data, are proposed. Based on comprehensive Monte-Carlo simulations, the coverage probabilities of the proposed prediction intervals were compared to heuristical HCL typically used in daily toxicological routine (historical range, limits of the np-chart, mean plus minus 2 SD). Our simulations reveal, that frequentist bootstrap calibrated prediction intervals control the type-1-error best, but, also prediction intervals calculated based on Bayesian generalized linear mixed models appear to be practically applicable. Contrary, all heuristics fail to control the type-1-error. The application of HCL is demonstrated based on a real life data set containing historical controls from long-term carcinogenicity studies run on behalf of the U.S. National Toxicology Program. The proposed frequentist prediction intervals are publicly available from the R package predint, whereas R code for the computation of the two Bayesian prediction intervals is provided via GitHub.