Arvid Sjölander: Doubly robust estimation in generalized linear models

A common aim of epidemiological research is to assess the association between a particular exposure and a particular outcome, controlling for a set of measured covariates. This is often done by using a regression model for the outcome. A commonly used class of models is the generalized linear models (GLMs), and the model parameters are typically estimated through maximum likelihood. If the model is correct, then the maximum likelihood estimator is consistent, but may otherwise be inconsistent. Recently, a new class of estimators has been developed, known as doubly robust (DR) estimators. These estimators use two regression models, one for the outcome and one for the exposure, and are consistent if either model is correct, not necessarily both. Thus, DR estimators give the analyst two chances, instead of only one, to make valid inference. In this talk we present (some of) the theory for DR estimation in GLMs. We motivate the theory with an example from the National March Cohort. We also present a new Stata command, drglm, that implements the most common DR estimators for GLMs.