Kernel estimation in semiparametric mixed effect longitudinal modeling

Abstract

HIV damages the immune system by targeting the CD4 cells. Hence CD4 count data modeling is important in the analysis of HIV infection. This paper considers a semiparametric mixed effects model for the analysis of CD4 longitudinal data. The model is a natural extension to the linear mixed and semiparametric models that uses parametric linear model to present the covariate effects and an arbitrary nonparametric smooth function to model the time effect and account for the within subject correlation using random effects. We approximate the nonparametric function by the profile kernel method, and make use of the weighted least squares to estimate the regression coefficients. Under some regularity conditions, the asymptotic normality of the resulting estimator is established and the performance is compared with the backfitting method. Although, two estimators share the same asymptotic variance matrix for independent data, it is shown that, backfitting often produces larger bias and variance than the profile-kernel method, asymptotically. Consequently, the use of backfitting method is no longer advised in semiparametric mixed effect longitudinal model. For practical implementation and also improve efficiency, the estimation of the covariance function is accomplished using an iterative algorithm. Performance of the proposed methods are compared through a simulation study and the analysis of CD4 data.