The equal slopes test: A statistical method for evaluating modifying factors in quantitative risk analysis

In quantitative risk analysis, making inferences on the magnitude of the risks associated with low-dose exposure from the risks estimated at higher doses is accomplished by extrapolation procedures. This dissertation introduces a statistical method into the process of extrapolation to provide guidance on the selection of an extrapolation procedure that is supported by the observed data trend. A statistical test, called the Equal Slopes Test, that is a special case of general hypothesis testing in Generalized Nonlinear Models, is developed to compare the trend of the observed data in the region of high dose to the extrapolation-induced trend of dose-response in the region of low dose. The behaviors of the test statistics in Generalized Nonlinear Models are investigated. Asymptotically, these statistics converge in distribution to non-central chi-square distributions. But for fixed sample size, this dissertation shows, through both theoretical derivation and simulated examples, that power functions based on the asymptotic non-central chi-square distribution are non-monotonic with respect to the alternative parameter values, causing the power of certain tests to eventually return to the significance level. The Wald's statistic behaves similarly to the power function, rising initially but eventually decreasing as the alternative parameter value moves further away from the null value. The likelihood ratio statistic, by comparison, is always monotonic, suggesting that the non-central chi-square distribution may be a poor approximation to the behavior of the likelihood ratio statistic. In addition, this dissertation develops numerical approximating methods for implementing the Equal Slopes Test when dose-risk functions are complex, such as those that are used in dynamic pharmacokinetic models.