The Pursuit of Efficiency versus Robustness: A Learning Experience from Analyzing a Semiparametric Nonignorable Propensity Score Model

Rosenbaum and Rubin’s pioneering work on “The Central Role of the Propensity Score in Observational Studies for Causal Effects” has shaped the landscape of the literature in causal inference and missing data analysis. In the past decades, the concept of propensity score has been used not only under ignorability assumption, but also under nonignorability assumption. The nice properties of double robustness and semiparametric efficiency are well known under ignorability; however, the situation is a lot more sophisticated under nonignorability. In this paper, we summarize what we have learnt from analyzing a semiparametric nonignorable propensity score model. It turns out that, under nonignorability, the efficient estimator for the quantity of interest might be too complicated to be practically implemented. On the other hand, by sacrificing the efficiency to some extent, one type of robust estimators is much easier to derive and implement; hence is recommended. This is a general tradeoff between efficiency and robustness in a typical semiparametric model.