  In toxicology, the validation of the concurrent control by historical control
data (HCD) has become requirements. This validation is usually done by
historical control limits (HCL) which in practice are often graphically
displayed in a Sheward control chart like manner. 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. Comprehensive Monte-Carlo
simulations assessing the coverage probabilities of seven different methods for
HCL calculation reveal, that frequentist bootstrap calibrated prediction
intervals control the type-1-error best. Heuristics traditionally used in
control charts (e.g. the limits in Sheward np-charts or the mean plus minus 2
SD) as well a the historical range fail to control a pre-specified coverage
probability. 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 Bayesian prediction intervals is provided via
GitHub.
