Effect of bivariate regression toward the mean in uncontrolled clinical trials

Estimating treatment effects in the presence of regression toward the mean is a problem arising in truncated distributions and is being recognized with increasing interest in recent literature. Any extraneous source of variability such as within-subject variability and measurement errors can contribute to the magnitude of regression toward the mean. In investigations where subjects are selected for study based on preliminary measurements on two characteristics of interest, truncation and regression toward the mean may occur on both variates. The effects of regression toward the mean depend on the process used to select subjects for study which in turn determines how the underlying distribution is truncated. In this paper we consider the expected regression toward the mean under different selection processes based on a bivariate normal random variable.