A more flexible regression-to-the-mean model with possible stratification

We consider a regression-to-the-mean model that includes both additive and multiplicative treatment effects. We allow either or both of these treatment effects to be stratified by ranges of the first measurement. We focus on the situation where there is a very large sample on the first measurement and a relatively small subsample for the second measurement is selected, which often occurs in screening trials. We propose some asymptotically efficient estimators for the parameters of the model that are very simple to compute. We begin with a discussion of the full model, and more on tests and estimation for reduced models follows. An example from a large screening trial is discussed.