Dose-response and thresholds in mutagenicity studies: a statistical testing approach

The analysis of dose-response relationships is an important objective in toxicology, and one in which both modelling and testing approaches are used. One particular question is whether a threshold exists at low doses. The concept of a pragmatic threshold is used, i.e. low doses with biologically unimportant effects are assumed to be threshold doses. "Biologically unimportant" means, in statistical terms, a lower effect than the effect of the negative control, or at least a just-tolerable margin delta higher than the effect of the negative control. Therefore, threshold doses can be tested in terms of a one-sided hypothesis of equivalence. A new approach is proposed, assuming, at the least, that the low dose is a threshold dose, and the highest dose is superior to the negative control. By analogy to the k-fold rule commonly used in mutagenicity studies, tests on ratio-to-control are used. The a priori definition of the threshold margin is inherently needed. A further approach proposes the analysis of dose-response relationships by means of order-restricted inference (the so-called trend test). A modification of a multiple-contrast test is used, in which only those contrasts are included that are sensitive for no effects at low doses. A further modification treats the complicated, but real, problem of simultaneous existence of a threshold, a monotonic increase, and a downturn effect at high dose(s). A parametric procedure is considered, together with an extension for proportions. The important problem of a priori sample size definition is discussed. The approaches are demonstrated by means of examples based on real data.