Improving semiparametric estimation using surrogate data

This paper considers estimating a parameter that denes an estimating function U(y; x; ) for an outcome variable y and its covariate x when the outcome is missing in some of the observations. We assume that, in addition to the outcome and the covariate, a surrogate outcome is available in every observation. The eciency of existing estimators for depend critically on correctly specifying the conditional expectation of U given the surrogate and the covariate. When the conditional expectation is not correctly specied, which is the most likely scenario in practice, the estimation eciency can be severely compromised even if the propensity function (of missingness) is correctly specied. We propose an estimator that is robust against the choice of the conditional expectation via an empirical likelihood. We demonstrate that the proposed estimator achieves eciency gain whether the conditional score is correctly specied or not. When the conditional score is correctly specied, the estimator reaches the semiparametric variance bound within the class of estimating functions generated by U. The practical performance of the estimator is evaluated using simulation and a dataset based on the 1996 U.S. presidential election