ABSTRACT
The majority of approaches in this book are tests on dose-response relationships, such as the Williams trend test. Alternatively, parametric non-linear models for a dose-response relationship can be used. The difference between a qualitative factor dose (assumed in testing) and the quantitative covariate (assumed in modeling) are: i) the relationship between the administered dose and the concentration at the target tissue is commonly unknown, and therefore the less stringent dose level, e.g., zero-dose control and low, medium, high dose may be appropriate, ii) the choice of a particular dose-response model may be more problematic compared with just the assumption of monotonicity when using trend tests, iii) the impact of a particular model function on increased power (in the case of an appropriate model choice) or reduced robustness (otherwise) can be serious, iv) the model fit for designs with only few doses (such as the common 2 to 3 doses) may be problematic. In this chapter three applications will be discussed: i) estimation of ED50 (also denoted as EC50, LD50, IC50), ii) the estimation of the relative potency between two or more parallel dose-response curves, and iii) the estimation of the benchmark dose (BMD) together with its lower confidence limits. The choice and fit of parametric non-linear models for both normally distributed variables, such as weight, and proportions, such as tumor rates, are shown.
