Abstract: The theoretical results in Robins, Rotnitzky and Zhao (1994) and Robins and Rotnitzky (1992) are revisited for semiparametric regression models with missing data. The main results provide a more relevant format for the calculations of efficient score functions. The intuition behind those abstract results and major steps of their proofs are discussed. The surrogate outcome regression problem is studied as a new application. Beyond the derivation of its efficient score function, an estimating method based on the efficient score function is proposed. A set of regularity conditions is given that provides desirable large sample properties for the proposed method.
Key words and phrases: Double robustness, efficient score, projection, missing at random, score function, semiparametric regression models, surrogate outcome, tangent space.