Applying Beta Distribution in Analyzing Bounded Outcome Score Data

Disease status is often measured with bounded outcome scores (BOS) which report a discrete set of values on a finite range. The distribution of such data is often non-standard, such as J- or U-shaped, for which standard analysis methods assuming normal distribution become inappropriate. Most BOS analysis methods aim to either predict the data within its natural range or accommodate data skewness, but not both. In addition, a frequent modeling objective is to predict clinical response of treatment using derived disease endpoints, defined as meeting certain criteria of improvement from baseline in disease status. This objective has not yet been addressed in existing BOS data analyses. This manuscript compares a recently proposed beta distribution–based approach with the standard continuous analysis approach, using an established mechanism-based longitudinal exposure-response model to analyze data from two phase 3 clinical studies in psoriatic patients. The beta distribution–based approach is shown to be superior in describing the BOS data and in predicting the derived endpoints, along with predicting the response time course of a highly sensitive subpopulation.