The R package predint: Prediction intervals for overdispersed binomial and Poisson data or based on linear random effects models in R

A prediction interval is a statistical interval that should encompass one (or more) future observation(s) with a given coverage probability and is usually computed based on historical control data. The application of prediction intervals is discussed in many fields of research, such as toxicology, pre-clinical statistics, engineering, assay validation or for the assessment of replication studies. Anyhow, the prediction intervals implemented in predint descent from previous work that was done in the context of toxicology and pre-clinical applications. Hence the implemented methodology reflects the data structures that are common in these fields of research. In toxicology the historical data is often comprised of dichotomous or counted endpoints. Hence it seems natural to model these kind of data based on the binomial or the Poisson distribution. Anyhow, the historical control data is usually comprised of several studies. These clustering gives rise to possible overdispersion which has to be reflected for interval calculation. In pre-clinical statistics, the endpoints are often assumed to be normal distributed, but usually are not independent from each other due to the experimental design (cross-classified and/or hierarchical structures). These dependencies can be modeled based on linear random effects models. Hence, predint provides functions for the calculation of prediction intervals and one-sided bounds for overdispersed binomial data, for overdispersed Poisson data and for data that is modeled by linear random effects models.