Date of Award

Spring 1984

Project Type

Dissertation

Program or Major

Mathematics

Degree Name

Doctor of Philosophy

Abstract

The experimental systems studied in this dissertation are designed to investigate the effect of diet on incidence rates of cancer. These investigations involve the chemical induction of tumors in experimental animals in order to test the chemopreventative effects of various substances. Both tumor number and rate of tumor development are important in evaluating the effects of a chemopreventative agent. This is made difficult, when multiple tumors occur, by the confounding of the number of induced tumors and their time of detection. This confounding occurs because experiments are terminated before all induced tumors have been detected. Fewer tumors observed in one treatment group, as compared to another, may be the result of a decreased number of induced tumors, a slowing of tumor growth rate, or both. Current statistical procedures do not consider this factor and therefore, do not reliably discriminate between these biologically different possibilities.

This study provides the cancer researcher with statistical procedures which directly address this problem of confounding of tumor number and detection time distributions. The method of maximum likelihood is used to simultaneously estimate the parameters characterizing these two confounded distributions. In order to compare treatments the likelihood ratio test is used to detect overall group differences and a technique is described to isolate which factor(s) (tumor number and/or rate of development) is(are) contributing to a group difference. Numerical results are used to discuss the sensitivity of the estimation procedure subject to changes in the experimenter controlled variables in order to design more accurate and efficient experiments and better utilize resources.

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