Statistical inferences on nonconstant relative potency with quantal response data

Relative potency is widely used in toxicological and pharmacological studies to characterize potency of chemicals. The relative potency of a test chemical compared to a standard chemical is defined as the ratio of equally effective doses (standard divided by test). This classical concept relies on the assumption that the two chemicals are toxicologically similar-that is, they have parallel dose-response curves on log-dose scale-and thus have constant relative potency. Nevertheless, investigators are often faced with situations where the similarity assumption is deemed unreasonable, and hence the classical idea of constant relative potency fails to hold; in such cases, simply reporting a single constant value for relative potency can produce misleading conclusions. Relative potency functions, describing relative potency as a function of the mean response (or other quantities), is seen as a useful tool for handling nonconstant relative potency in the absence of similarity. Often, investigators are interested in assessing nonconstant relative potency at a finite set of some specific response levels for various regulatory concerns, rather than the entire relative potency function; this simultaneous assessment gives rise to multiplicity, which calls for efficient statistical inference procedures with multiplicity adjusted methods. In this paper, we discuss the estimation of relative potency at multiple response levels using the relative potency function, under the log-logistic dose-response model. We further propose and evaluate three approaches to calculating multiplicity-adjusted confidence limits as statistical inference procedures for assessing nonconstant relative potency. Monte Carlo simulations are conducted to evaluate the characteristics of the simultaneous limits.