DOI

10.17077/etd.kyudwswa

Document Type

Dissertation

Date of Degree

Fall 2015

Degree Name

PhD (Doctor of Philosophy)

Degree In

Biostatistics

First Advisor

Cavanaugh, Joseph

First Committee Member

Clarke, William

Second Committee Member

Oleson, Jacob

Third Committee Member

Foster, Eric

Fourth Committee Member

Ramirez, Marizen

Abstract

This manuscript consists of three papers which formulate novel generalized linear model methodologies.

In Chapter 1, we introduce a variant of the traditional concordance statistic that is associated with logistic regression. This adjusted c − statistic as we call it utilizes the differences in predicted probabilities as weights for each event/non- event observation pair. We highlight an extensive comparison of the adjusted and traditional c-statistics using simulations and apply these measures in a modeling application.

In Chapter 2, we feature the development and investigation of three model selection criteria based on cross-validatory c-statistics: Model Misspecification Pre- diction Error, Fitting Sample Prediction Error, and Sum of Prediction Errors. We examine the properties of the corresponding selection criteria based on the cross- validatory analogues of the traditional and adjusted c-statistics via simulation and illustrate these criteria in a modeling application.

In Chapter 3, we propose and investigate an alternate approach to pseudo- likelihood model selection in the generalized linear mixed model framework. After outlining the problem with the pseudo-likelihood model selection criteria found using the natural approach to generalized linear mixed modeling, we feature an alternate approach, implemented using a SAS macro, that obtains and applies the pseudo-data from the full model for fitting all candidate models. We justify the propriety of the resulting pseudo-likelihood selection criteria using simulations and implement this new method in a modeling application.

Keywords

Biostatistics, Generalized linear models, Model selection

Pages

xvi, 124 pages

Bibliography

Includes bibliographical references (pages 121-124).

Copyright

Copyright © 2015 Patrick Ten Eyck

Included in

Biostatistics Commons

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