Causal Interpretation of Between-Within Models for Twin Research

Abstract The between-within (BW) model is a popular regression model for twin data. Despite its popularity, the properties of the BW model have not yet been thoroughly investigated, and most reviews are largely heuristic. The aim of this paper is to provide a formal guide to the causal interpretation of BW models. First, we show that the BW model produces a specific subpopulation causal effect, in the absense of non-shared confounding. Second, we discuss how to adjust for non-shared confounders in the BW model. We show that if the adjustment is done in a `standard fashion', then the desired causal interpretation is lost. We further show that the causal interpretation can be retrieved with a minor modification of the model.