Reasoning about data with directed graphs

Abstract

This paper constructs graphical models for two important analysis problems to demonstrate how graphs can clearly represent complex relationships. A powerful property of graphical models called d-separation describes the statistical associations in a given graphical model. This allows the effects of unmeasured variables to be predicted, and suggests conditional analyses which can distinguish conjectured models. If an assumption called quasi-linearity is made, further conclusions can be drawn based on the structure of the graph and d-separation. Making the quasi-linearity assumption explicit also contributes to our understanding of which aspects of our causal intuition are based on linearity assumptions. The examples that we consider are the scientific interpretation of interventions and the evaluation of the validity of candidate surrogate endpoints for clinical trials. Intervention studies can be plagued by non-compliance with assigned treatment and ambiguity in interpreting results when treatment assignment manipulates multiple factors. We show graphically the conclusions that can be drawn under various assumptions. The topic of surrogate endpoints is addressed in causal terms and modelled graphically.