Graphical Models for Surrogates

Recently, it has been demonstrated that graphical models promise some potential for expressing causal concepts, see for example Pearl (2000), Lauritzen (2001), or Dawid (2002). The causal interpretation is most direct in models based on directed acyclic graphs, whereas causal interpretation for chain graph models generally is more subtle and complex (Lauritzen and Richardson 2002). In the articles cited, such concepts as confounding, partial compliance, causal sufficiency of covariates, and prediction of treatment effects were discussed and illuminated. In this article we will use graphical models to illustrate and analyse the notion of a surrogate outcome, such as also discussed e.g. in Frangakis and Rubin (2002).