Quantifying and Estimating Regression to the Mean Effect for Bivariate Beta-Binomial Distribution

Abstract

ABSTRACT Subjects with initially extreme observations upon remeasurement are found closer to the population mean. This tendency of observations toward the mean is called regression to the mean (RTM) and can make natural variation in repeated data look like real change. Studies, where subjects are selected on a baseline criterion, should be guarded against the RTM effect to avoid erroneous conclusions. In an intervention study, the difference between pre-post variables is the combined effect of intervention/treatment and RTM. Thus, accounting for RTM is essential to accurately estimate the intervention effect. Many real-life examples are better modeled by a bivariate binomial model with varying probability of success. In this article, a bivariate beta-binomial distribution is used that allows the probability of success to vary from subject to subject. Expressions for the total, RTM, and treatment effect are derived, and their behavior is demonstrated graphically. Maximum likelihood estimators of RTM are derived, and their statistical properties are studied via Monte Carlo simulation. The proposed techniques are employed to estimate the RTM effect by utilizing data related to the Countway WM-class circulation.