Impact of Outcome Model Misspecification on Regression and Doubly-Robust Inverse Probability Weighting to Estimate Causal Effect

Estimating treatment effects with observational data requires adjustment for confounding at the analysis stage. This is typically done by including the measured confounders along with the treatment covariate into a regression model for the outcome. Alternatively, it is also possible to adjust for confounding by taking into account the propensity of an individual to receive treatment, with inverse probability weighting (IPW). In the class of IPW estimators, the so-called doubly-robust estimator also requires the specification of the outcome regression model, in addition to the propensity model. The aim of this paper is to investigate the impact of misspecification of the outcome model on the performances of the usual regression and doubly-robust IPW estimators for estimating treatment effects. We examine the performances of the estimators across the parameter space for different scenarios of model misspecification using large-sample theory. We find that for small-to-moderate sample sizes, the regression estimator compares favorably to the IPW doubly-robust estimator. Finally we argue, both conceptually and on the basis of our results, that treatment-confounder interactions should be included in the outcome regression model.