Adjusting for a balancing score is sufficient for bias reduction when estimating causal effects including the average treatment effect and effect among the treated. Estimators that adjust for the propensity score in a nonparametric way, such as matching on an estimate of the propensity score, can be consistent when the estimated propensity score is not consistent for the true propensity score but converges to some other balancing score. We call this property the balancing score property, and discuss a class of estimators that have this property. We introduce a targeted minimum loss-based estimator (TMLE) for a treatment specific mean with the balancing score property that is additionally locally efficient and doubly robust. We investigate the new estimator's performance relative to other estimators, including another TMLE, a propensity score matching estimator, an inverse probability of treatment weighted estimator, and a regression based estimator in simulation studies.
Biostatistics | Statistical Methodology | Statistical Theory
Lendle, Samuel D.; Fireman, Bruce; and van der Laan, Mark J., "Balancing Score Adjusted Targeted Minimum Loss-based Estimation" (May 2013). U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 311.