Prediction intervals for overdispersed binomial data with application to historical controls

Bioassays are highly standardized trials for assessing the impact of a chemical compound on a model organism. In that context, it is standard to compare several treatment groups with an untreated control. If the same type of bioassay is carried out several times, the amount of information about the historical controls rises with every new study. This information can be applied to predict the outcome of one future control using a prediction interval. Since the observations are counts of success out of a given sample size, like mortality or histopathological findings, the data can be assumed to be binomial but may exhibit overdispersion caused by the variability between historical studies. We describe two approaches that account for overdispersion: asymptotic prediction intervals using the quasi-binomial assumption and prediction intervals based on the quantiles of the beta-binomial distribution. Both interval types were α-calibrated using bootstrap methods. For an assessment of the intervals coverage probabilities, a simulation study based on various numbers of historical studies and sample sizes as well as different binomial proportions and varying levels of overdispersion was run. It could be shown that α-calibration can improve the coverage probabilities of both interval types. The coverage probability of the calibrated intervals, calculated based on at least 10 historical studies, was satisfactory close to the nominal 95%. In a last step, the intervals were computed based on a real data set from the NTP homepage, using historical controls from bioassays with the mice strain B6C3F1.