In observational studies the overall aim when fitting a model for the propensity score is to reduce bias for an estimator of the causal effect. For this purpose guidelines for covariate selection for propensity score models have been proposed in the causal inference literature. To make the...

In the causal inference literature a class of semi-parametric estimators is called robust if the estimator has desirable properties under the assumption that at least one of the working models is correctly specified. A standard example is a doubly robust estimator that specifies parametric...

An estimand of interest in empirical studies with observational data is the average treatment effect of a multi-valued treatment in the treated subpopulation. We demonstrate three estimation approaches: outcome regression, inverse probability weighting and inverse probability weighted...