Causal regression with imputed estimating equations

Literature on causal inference has emphasized the average causal effect, defined as the mean difference in potential outcomes under different treatment conditions. We consider marginal regression models that describe how causal effects vary in relation to covariates. To estimate parameters, we replace missing potential outcomes in estimating functions with fitted values from imputation models that include confounders and prognostic variables as predictors. When the imputation and analytic models are linear, our procedure is equivalent to maximum likelihood for normally distributed outcomes and covariates. Robustness to misspecification of the imputation models is enhanced by including functions of propensity scores as regressors. In simulations where the analytic, imputation, and propensity models are misspecified, the method performs better than inverse-propensity weighting. Using data from the National Longitudinal Study of Adolescent Health, we analyze the effects of dieting on emotional distress in the population of girls who diet, taking into account the study's complex sample design.