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Nonlinear mixed effects models with dropout and missing covariates when the dropout depends on the random effects Song, Shijun

Abstract

Nonlinear mixed effects models (NLMEs) are very popular in many longitudinal studies such as HIV viral dynamic studies, pharmacokinetics analyses, and studies of growth and decay. In these studies, however, missing data problems often arise, which make some statistical analyses complicated. In this thesis, we proposed an exact method and an approximate method for NLMEs with random-effects based informative dropouts and missing covariates, and propose methods for simultaneous inference. Monte Carlo E M algorithms are used in both methods. The approximate method, which is based on a Taylor series expansion, avoids sampling the random effects in the E-step and thus reduces the computation burden substantially. To illustrate the proposed methods, we analyze two real datasets. The exact method is applied to a dataset with covariates and a dataset without covariates. The approximate method is applied to the dataset without covariates. The result shows that, for both datasets, dropouts may be correlated with individual random effects. Ignoring the missingness or assuming ignorable missingness may lead to unreliable inferences. A simulation study is performed to evaluate the two proposed methods under various situations.

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