Logistic regression for the modeling of low-dose radiation effects.

Abstract

The primary goal of this thesis is to examine statistical procedures that determine if a nonlinear threshold dose effect occurs in cancer incidence in animal experiments. This is to say, does there exist a level of radiation which does not increase the risk of cancer in animals? This question will be explored on data over several species of animals (beagles, rats, and mice) and several different sources of radiation (e.g. radium, or plutonium). Here we consider experiments with several groups of animals at several dose levels In mathematical terms, this thesis will determine if a "knee" fit to a logistic regression models the data better than a simple logistic regression curve. The knee is a non-linear kink in the dose response relationship at a specific dose. If there is evidence to support the knee model hypothesis, it can be interpreted to mean that there is evidence of a threshold effect in the dose response. A secondary goal is to determine if two knees will suffice for data sets of this nature. The motivation behind this goal, is that a two knee model should be able to model both a low dose threshold and a high dose drop-off (due to over exposure to radiation, past the Maximally Tolerated Dose, MTD). Any knees above two will generally only contribute to overfitting of the model. Another goal is to give guidelines on the design of experiments, that will assist researchers in determining if a threshold does in fact exist.