  Estimating a causal effect from observational data can be biased if we do not
control for self-selection. This selection is based on confounding variables
that affect the treatment assignment and the outcome. Propensity score methods
aim to correct for confounding. However, not all covariates are confounders. We
propose the outcome-adaptive random forest (OARF) that only includes desirable
variables for estimating the propensity score to decrease bias and variance.
Our approach works in high-dimensional datasets and if the outcome and
propensity score model are non-linear and potentially complicated. The OARF
excludes covariates that are not associated with the outcome, even in the
presence of a large number of spurious variables. Simulation results suggest
that the OARF produces unbiased estimates, has a smaller variance and is
superior in variable selection compared to other approaches. The results from
two empirical examples, the effect of right heart catheterization on mortality
and the effect of maternal smoking during pregnancy on birth weight, show
comparable treatment effects to previous findings but tighter confidence
intervals and more plausible selected variables.
