Empirical likelihood in missing data problems

Missing data is a ubiquitous problem in medical and social sciences. It is well known that inferences based only on the complete data may not only lose efficiency, but may also lead to biased results if the data is not missing completely at random (MCAR). The inverse-probability weighting method proposed by Horvitz and Thompson (1952) is a popular alternative when the data is not MCAR. The Horvitz-Thompson method, however, is sensitive to the inverse weights and may suffer from loss of efficiency. In this paper, we propose a unified empirical likelihood approach to missing data problems and explore the use of empirical likelihood to effectively combine unbiased estimating equations when the number of estimating equations is greater than the number of unknown parameters. One important feature of this approach is the separation of the complete data unbiased estimating equations from the incomplete data unbiased estimating equations. The proposed method can achieve semiparametric efficiency if the probability of missingness is correctly specified. Simulation results show that the proposed method has better finite sample performance than its competitors. Supplemental materials for this paper, including proofs of the main theoretical results and the R code used for the NHANES example, are available online on the journal website. KEY WORDS: Empirical likelihood; Estimating functions; Missing data: Surrogate end point.