Conditional Empirical Likelihood Approach to Statistical Analysis with Missing Data.

Abstract

This dissertation focuses on the development of conditional empirical likelihood (CEL) based methods for mean regression analysis when the outcome is subject to missingness. It considers the cases of cross-sectional data, longitudinal data with dropout, and unbalanced longitudinal data. Unlike the existing estimating functions based estimators, the proposed estimators do not require to model any higher order moments of the data beyond the missingness mechanism and the conditional mean of the outcome. In both cases of cross-sectional data and longitudinal data with dropout, under the missing at random (MAR) mechanism and certain regularity conditions, the proposed CEL based augmented inverse probability weighted (CEL-AIPW) estimator is doubly robust and locally efficient. Specifically, the CEL-AIPW estimator is consistent if either the missingness mechanism or the conditional mean of the outcome given the observed data at each level of missingness is correctly modeled, and attains the semiparametric efficiency bound when both quantities are correctly modeled. In the case of unbalanced longitudinal data, the unbalanced follow-up visits are dealt with via stratification according to distinctive follow-up patterns. Such a strategy implicitly assumes the missing completely at random (MCAR) mechanism, the same mechanism assumed by the popular generalized estimating equations (GEE) method. The proposed CEL estimator achieves the same efficiency as that of the GEE estimator obtained employing the true variance-covariance matrix of the longitudinal outcomes. In all three cases, the proposed estimators are implemented through a nested optimization, and the detailed Newton-Raphson algorithm is described for each case. Certain issues related to the numerical implementation are also discussed. The asymptotic distributions of all proposed estimators are derived, and the finite sample performances with comparisons to some existing estimators are examined using simulation experiments. As for the application in the three cases, we analyze the data collected from an intervention study for adolescents of parents with HIV, the data from the national cooperative gallstone study, and the data from the Kenya primary school nutritional intervention study, respectively.PhDBiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/99966/1/peisong_1.pd