Model averaging for improving inference from causal diagrams

Abstract

Model selection is an integral, yet contentious, component of epidemiologic research. Unfortunately, there remains no consensus on how to identify a single, best model among multiple candidate models. Researchers may be prone to selecting the model that best supports their a priori, preferred result; a phenomenon referred to as “wish bias”. Directed acyclic graphs (DAGs), based on background causal and substantive knowledge, are a useful tool for specifying a subset of adjustment variables to obtain a causal effect estimate. In many cases, however, a DAG will support multiple, sufficient or minimally-sufficient adjustment sets. Even though all of these may theoretically produce unbiased effect estimates they may, in practice, yield somewhat distinct values, and the need to select between these models once again makes the research enterprise vulnerable to wish bias. In this work, we suggest combining adjustment sets with model averaging techniques to obtain causal estimates based on multiple, theoretically-unbiased models. We use three techniques for averaging the results among multiple candidate models: information criteria weighting, inverse variance weighting, and bootstrapping. We illustrate these approaches with an example from the Pregnancy, Infection, and Nutrition (PIN) study. We show that each averaging technique returns similar, model averaged causal estimates. An a priori strategy of model averaging provides a means of integrating uncertainty in selection among candidate, causal models, while also avoiding the temptation to report the most attractive estimate from a suite of equally valid alternatives.