Estimating the effect of regression toward the mean under stochastic censoring

This investigation estimated regression toward the mean in the evaluation of a blood cholesterol educational program in which the probability of return for a follow-up measure was positively related to the initial measure--a situation the authors term "stochastic censoring." The situation in which selection is by a fixed cutpoint is well known. The authors estimate the extent of regression toward the mean when selection is probabilistically related to an initially higher blood cholesterol level. A Monte Carlo method is proposed, conditional on the observed data, for estimating the regression toward the mean and its precision. In 106 simulations, regression toward the mean was estimated to be 0.012 mmol/liter (standard deviation (SD), 0.032 mmol/liter). Similar estimates were obtained using Empirical Bayes shrinkage estimates of baseline cholesterol (regression toward the mean = 0.0106 mmol/liter) and numeric integration (0.0109 mmol/liter). The observed reduction in blood cholesterol was 0.271 mmol/liter (SD, 0.061 mmol/liter); after correction for regression toward the mean, the estimate of the true educational effect was 0.259 mmol/liter (SD, 0.069 mmol/liter). Functions are presented that will enable investigators to predict regression toward the mean and its standard deviation under the conditions that errors are gaussian and stochastic censoring can be approximated by a logistic model.