Prediction of random effects in mixed effects models under violations of the normality assumption for the random-effects and a graphical approach to detect violations
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Issue Date
2019-12-31Author
Wang, Zhiwen
Publisher
University of Kansas
Format
187 pages
Type
Dissertation
Degree Level
Ph.D.
Discipline
Biostatistics
Rights
Copyright held by the author.
Metadata
Show full item recordAbstract
In longitudinal data analysis, the introduction of random effects provides statisticians with a convenient tool for modeling repeated measurements. Mixed effects linear models extend linear and generalized linear models for non-repeated measures to repeated measures or longitudinal data. One important assumption of these models is that the random effects are normally distributed. In this dissertation, we investigated via simulations the impact of violations of this assumption on the prediction of the random effects, by comparing the prediction accuracy and robustness of two methods: the empirical Bayes method and a semi-parametric method based on quadratic inference functions. Chapter 1 explores this impact for continuous responses modeled with the random effects linear model and Chapter 2 explore this impact for the random-effects logistic regression model. Finally, Chapter 3 proposes and examines a graphical method to examine this assumption in the context of two-dimensional time-dependent personalized medicine models with continuous responses that track the trajectories of patients’ disease severities and individual treatment benefits when the patients are under medical or behavioral treatments. One important conclusion of these investigations is that the empirical Bayes approach is very robust to violations of the normality assumption. The EB approach has non-inferior but usually higher accuracy in random effects prediction, and is computational, numerical and algebraic simply. Thus, it is more recommendable for random-effects prediction than the method based on quadratic inference functions in statistical practice. Finally, our graphical approach successfully detected departures from the normality assumption and worked efficiently even with small and moderate sample sizes.
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