The application of extreme value theory to pharmacometrics

Clinical trials are often analyzed by examining the means, e.g., what is the mean treatment effect or what is the mean treatment difference, but there are times when analysis of the maximums (or minimums) are of interest. For instance, what is the highest heart rate that could be observed or what the smallest treatment effect that could be expected? While inference on the means is based on the central limit theorem, the corresponding theorem for maximums or minimums is the Fisher-Tippett theorem, also called the extreme value theorem (EVT). This manuscript will introduce EVT to pharmacometricians, particularly block maxima analysis and peak over threshold analysis, and provide examples for how it can be applied to pharmacometric data, particularly the analysis of pharmacokinetics and ECG safety data, like QTcF intervals.