Improving semiparametric estimation by using surrogate data

• Published in: Journal of the Royal Statistical Society. Series B, Statistical methodology Statistical methodology, 2008-09, Vol.70 (4), p.803-823
• Main Authors: Chen, Song Xi, Leung, Denis H. Y., Qin, Jing
• Format: Article
• Language: English
• Subjects: 9130; Analytical estimating; Binary system; Binomials; Data collection; Distribution theory; Efficiency; Empirical likelihood; Estimating equations; Estimating techniques; Estimation; Estimation methods; Estimators; Exact sciences and technology; General topics; Linear inference, regression; Mathematics; Missing data; Missing values; Model testing; Preliminary estimates; Presidential elections; Probability and statistics; Sciences and techniques of general use; Selection bias; Simulation; Statistical methods; Statistical models; Statistical variance; Statistics; Studies; Surrogate outcome; U.S.A; Unbiased estimators; Voting
• ISSN: 1369-7412; 1467-9868
• DOI: 10.1111/j.1467-9868.2008.00662.x

The paper considers estimating a parameter β that defines an estimating function U(y,x,β) 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 efficiency of existing estimators for β depends critically on correctly specifying the conditional expectation of U given the surrogate and the covariate. When the conditional expectation is not correctly specified, which is the most likely scenario in practice, the efficiency of estimation can be severely compromised even if the propensity function (of missingness) is correctly specified. We propose an estimator that is robust against the choice of the conditional expectation via an empirical likelihood. We demonstrate that the estimator proposed achieves a gain in efficiency whether the conditional score is correctly specified or not. When the conditional score is correctly specified, the estimator reaches the semiparametric variance bound within the class of estimating functions that are generated by U. The practical performance of the estimator is evaluated by using simulation and a data set that is based on the 1996 US presidential election.