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Joint inference of NLME and GLMM models with informative censoring Zhang, Hongbin


Non-linear mixed effects models (NLME) and generalized linear mixed effects models (GLMM) are commonly used to model longitudinal process. This thesis goes beyond the single process modelling and focuses on jointly modelling multiple longitudinal processes with different types of variables. In particular, we investigate methods on joint inference of NLME and GLMM models for the following three problems: (1) joint models of NLME and GLMM for complete data with NLME for the time-dependent mis-measured covariate and GLMM for discrete longitudinal response; (2) joint models with covariate subject to informative left censoring; and (3) joint models with informative right censoring with respect to both response and covariate. For each problem, we propose two joint modelling methods to obtain "exact" and approximate maximum likelihood estimates (MLEs) of all model parameters. Measurement errors and missing data are addressed simultaneously in a unified way. Some asymptotic results are also developed. The proposed methods are illustrated with a HIV data. Simulation results show that the joint modelling methods perform better than the commonly used naive method and two-step method.

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