Kernel-Profile Efficient Estimation in Generalized Partially Linear Models with Missing Outcomes in Longitudinal Studies

We consider a generalized partially linear model with missing outcomes in longitudinal studies.Our proposed method, the longitudinal augmented inverse probability weighted kernel-profile estimating equations, employs kernel estimating equations for the nonparametric part and profile estimating equations for the parametric part.Auxiliary variables are used to model both the missingness and the conditional mean.The resulting estimators for both the parametric and nonparametric parts are doubly robust.To further understand these estimators, we derive the semiparametric efficiency bound and the asymptotic properties of the proposed estimators.We find that the estimator for the parametric part attains the semiparametric efficiency bound under the multivariate normal assumption.We demonstrate the empirical performance of the proposed method through simulation studies and an application to CD4 count data.