Degree Type

Dissertation

Date of Award

1998

Degree Name

Doctor of Philosophy

Department

Statistics

First Advisor

Kenneth J. Koehler

Abstract

This thesis examines approaches for analyzing interval censored survival data, where it is only known that an event occurred between two inspection points. The first paper adapts methods for continuous lifetime data to interval censored data. Partial likelihood estimation for proportional hazards models, which relies on the unique ordering of event times provided by continuous data, is modified to handle tied failure times arising from interval censoring. Alternatively, the second paper examines estimation methods based on the discrete distribution of the counts observed in the inspection intervals;Four methods for modifying partial likelihood analysis of proportional hazards models to deal with interval censored event times are compared in a simulation study. The Efron approximation is shown to be superior to the Breslow approximation, but both methods tend to break down as either the number of tied event times created by interval censoring increases or treatment effects increase. Estimated treatment effects tend to be biased toward zero for both methods. The Efron approximation is shown to closely approximate the geometric mean of the partial likelihoods for all possible orderings of tied event times, while maximizing the arithmetic mean of all possible likelihoods more closely approximates results that would be obtained if the exact event times were known. Geometric and arithmetic means of random samples of possible partial likelihoods are considered for situations with larger numbers of tied failure times;In the second paper, estimation methods are developed for interval censored event time data where members of a cohort may provide correlated response times and different cohorts may be subjected to different inspection schedules are discussed. Initially any correlations among response times are ignored and a multinomial model is applied to the counts observed in the inspection intervals. Non-homogeneous inspection schedules require estimation methods for incompletely classified multinomial data. Robust variance estimation is used to obtain consistent estimates of covariance matrices for parameter estimates. Parametric models for multinomial probabilities are also considered, and tests for comparing the fit of nested models are developed. An application to modeling the development rate of bean leaf beetle eggs is discussed.

DOI

https://doi.org/10.31274/rtd-180813-4991

Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/

Copyright Owner

Rebecca Jean Benner

Language

en

Proquest ID

AAI9826516

File Format

application/pdf

File Size

137 pages

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