Date of Award

12-1991

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Dr. McKean

Second Advisor

Dr. Naranjo

Third Advisor

Dr. Sievers

Fourth Advisor

Dr. Stoline

Abstract

Dose response assessment using quantal bioassay is a useful statistical procedure, especially in pharmaceutical science. The problem can be written in terms of a generalized linear model. The response of a subject is often dichotomous; that is, either the response or the absence of a response is recorded. The probability of response is related to the dose through a link function. A frequently used link function is the logistic. Statistical problems include fitting the model, confirming the existence of a dose response, and estimation of the ED50, the value of the dose at which the probability of response is 50%.

Traditional maximum likelihood procedures appear to be sensitive to slight departures from the under lying model. In this dissertation, we explore robust procedures which are less sensitive to such departures while yielding results similar to the likelihood methods when the data follow the model. Some work has been done on robust estimation of the parameters in this model. Robust hypothesis testing methods, however, have been relatively unexplored. This is the main topic of this dissertation.

We investigate procedures based on signed rank statistics for the generalized linear model based on a logistic link function. Methods based on signed rank statistics are robust in the linear model and they appear to be robust for these generalized linear models, also. We derive some of the asymptotic properties for signed rank procedures for the logistic model. This derivation is partially based on the projection technique which we have extended from its use in linear models to these generalized linear models. We use these asymptotic properties to establish several test statistics for confirming the existence of a dose response relationship in a first order logistic model. Several examples are used to illustrate the performance of these tests. We also explore the use of robust diagnostic procedure in these examples to identify outlying and influential cases.

Comments

Fifth Advisor: Dr. Vidmar

Access Setting

Dissertation-Open Access

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