Comment: Understanding OR, PS and DR

We congratulate Kang and Schafer (KS) on their excellent article comparing various estimators of a population mean in the presence of missing data, and thank the Editor for organizing the discussion.In this communication, we systematically examine the propensity score (PS) and the outcome regression (OR) approaches and doubly robust (DR) estimation, which are all discussed by KS.The aim is to clarify and better our understanding of the three interrelated subjects.Sections 1 and 2 contain the following main points, respectively.(a) OR and PS are two approaches with different characteristics, and one does not necessarily dominate the other.The OR approach suffers the problem of implicitly making extrapolation.The PS-weighting approach tends to yield large weights, explicitly indicating uncertainty in the estimate.(b) It seems more constructive to view DR estimation in the PS approach by incorporating an OR model rather than in the OR approach by incorporating a PS model.Tan's (2006) DR estimator can be used to improve upon any initial PS-weighting estimator with both variance and bias reduction.Finally, Section 3 presents miscellaneous comments. UNDERSTANDING OR AND PSFor a population, let X be a vector of (pretreatment) covariates, T be the treatment status, Y be the observed outcome given by (1 -T )Y 0 + T Y 1 , where (Y 0 , Y 1 ) are potential outcomes.The observed data consist of independent and identically distributed copies (X i , T i , Y i ), i = 1, . . ., n. Assume that T and (Y 0 , Y 1 ) are conditionally independent given X.The objective is to estimate