Abstract

The problem of how to best select variables for confounding adjustment forms one of the key challenges in the evaluation of exposure or treatment effects in observational studies. Routine practice is often based on stepwise selection procedures that use hypothesis testing, change-in-estimate assessments or the lasso, which have all been criticised for not giving sufficient priority to the selection of confounders. This has prompted vigorous recent activity in developing procedures that prioritise the selection of confounders, while preventing the selection of so-called instrumental variables that are associated with exposure but not outcome (after adjustment for the exposure). A major drawback of all these procedures is that there is no finite sample size at which they are guaranteed to deliver treatment effect estimators and associated confidence intervals with adequate performance. This is the result of the estimator jumping back and forth between different selected models, and standard confidence intervals ignoring the resulting model selection uncertainty.

In this talk, I will develop insight into this by evaluating the finite-sample distribution of the exposure effect estimator in linear regression, under a number of the aforementioned confounder selection procedures. I will then propose a simple and generic solution in the context of generalised linear models, which overcomes this concern (under weaker conditions than competing proposals).