Defense Date

2012

Document Type

Dissertation

Degree Name

Doctor of Philosophy

Department

Biostatistics

First Advisor

Yongyun Shin

Abstract

This dissertation has multiple aims in studying hierarchical linear models in biomedical data analysis. In Chapter 1, the novel idea of studying the durations of adolescent growth spurts as a predictor of adulthood obesity is defined, established, and illustrated. The concept of contextual effects modeling is introduced in this first section as we study secular trend of adulthood obesity and how this trend is mitigated by the durations of individual adolescent growth spurts and the secular average length of adolescent growth spurts. It is found that individuals with longer periods of fast height growth in adolescence are more prone to having favorable BMI profiles in adulthood. In Chapter 2 we study the estimation of contextual effects in a hierarchical generalized linear model (HGLM). We simulate data and study the effects using the higher level group sample mean as the estimate for the true mean versus using an Empirical Bayes (EB) approach (Shin and Raudenbush 2010). We study this comparison for logistic, probit, log-linear, ordinal and nominal regression models. We find that in general the EB estimate lends a parameter estimate much closer to the true value, except for cases with very small variability in the upper level, where it is a more complicated situation and there is likely no need for contextual effects analysis. In Chapter 3 the HGLM studies are made clearer with large-scale simulations. These large scale simulations are shown for logistic regression and probit regression models for binary outcome data. With repetition we are able to establish coverage percentages of the confidence intervals of the true contextual effect. Coverage percentages show the percentage of simulations that have confidence intervals containing the true parameter values. Results confirm observations from the preliminary simulations in the previous section of this paper, and an accompanying example of adulthood hypertension shows how these results can be used in an application.

Rights

© The Author

Is Part Of

VCU University Archives

Is Part Of

VCU Theses and Dissertations

Date of Submission

June 2012

Included in

Biostatistics Commons

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