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The theory and methods for measurement errors and missing data problems in semiparametric nonlinear mixed-effects models Liu, Wei

Abstract

Semiparametric nonlinear mixed-effects (NLME) models are flexible for modelling complex longitudinal data. Covariates are usually introduced in the models to partially explain inter-individual variations. Some covariates, however, may be measured with substantial errors. Moreover, the responses may be missing and the missingness may be nonignorable. In this thesis, we develop approximate maximum likelihood inference in the following three problems: (1) semiparametric NLME models with measurement errors and missing data in time-varying covariates; (2) semiparametric NLME models with covariate measurement errors and outcome-based informative missing responses; (3) semiparametric NLME models with covariate measurement errors and random-effect-based informative missing responses. Measurement errors, dropouts, and missing data are addressed simultaneously in a unified way. For each problem, we propose two joint model methods to simultaneously obtain approximate maximum likelihood estimates (MLEs) of all model parameters. Some asymptotic properties of the estimates are discussed. The proposed methods are illustrated in a HIV data example. Simulation results show that all proposed methods perform better than the commonly used two-step method and the naive method.

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