Covariate association eliminating weights: a unified weighting framework for causal effect estimation

Weighting methods offer an approach to estimating causal treatment effects in observational studies. However, if weights are estimated by maximum likelihood, misspecification of the treatment assignment model can lead to weighted estimators with substantial bias and variance. In this paper, we propose a unified framework for constructing weights such that a set of measured pretreatment covariates is unassociated with treatment assignment after weighting. We derive conditions for weight estimation by eliminating the associations between these covariates and treatment assignment characterized in a chosen treatment assignment model after weighting. The moment conditions in covariate balancing weight methods for binary, categorical and continuous treatments in cross-sectional settings are special cases of the conditions in our framework, which extends to longitudinal settings. Simulation shows that our method gives treatment effect estimates with smaller biases and variances than the maximum likelihood approach under treatment assignment model misspecification. We illustrate our method with an application to systemic lupus erythematosus data.