A method for quantifying the regression to the mean effect applied to bivariate binary outcomes in the presence of limited baseline data

Abstract

In studies lacking a control group, a crucial step in estimating the study effect is to tease apart the proportion of the total observed change in key outcomes which are due to study participation, from that which is caused by regression to the mean (RTM). We developed novel methods for quantifying RTM effects which jointly model bivariate binary data, while accommodating situations in which baseline data on a representative sample is available for only one of the binary variables. We conducted simulations testing various aspects of our joint model, including cases when modeling assumptions were not met. Using data from a longitudinal cohort study of women at risk for HIV, we then applied our joint model separately to three pairs of bivariate binary outcome measures. We found that weak correlation resulted in a higher proportion of change attributable to study participation for the variable that was not directly selected for, likely due to a lower RTM effect as a result of less predictable selection pressure. Enhanced estimation of RTM effects in non-randomized studies can be obtained using methods which make use of all available data.