Log-Likelihood Ratio Tests for Comparing Dose-Response Data Fitted to the Logistic Function

摘要

In bioassays, logistic and probit functions are commonly used to describe quantal dose response and to estimate median concentrations of toxicant that cause an effect (i.e., TLm, ED50, LD50); however, the bioassayist must still decide whether dose response varies significantly between two or more treatments. The paper demonstrates tests of homogeneity that are based on likelihood ratios. The logistic function is used to model the probability of response as a function of concentration. The hypotheses considered here are (1) independent dose responses for each treatment, (2) a common median effective dose for all treatments, (3) a common dispersion of responses around each median effective dose, and (4) a common dose response for all treatments.