Weighted logistic regression and robust analysis of diverse toxicology data

Single toxin dose-response models revisited

The goal of this paper is to offer a rigorous analysis of the sigmoid shape single toxin dose-response relationship. The toxin efficacy function is introduced and four special points, including maximum toxin efficacy and inflection points, on the dose-response curve are defined. The special points define three phases of the toxin effect on mortality: (1) toxin concentrations smaller than the first inflection point or (2) larger then the second inflection point imply low mortality rate, and (3) concentrations between the first and the second inflection points imply high mortality rate. Probabilistic interpretation and mathematical analysis for each of the four models, Hill, logit, probit, and Weibull is provided. Two general model extensions are introduced: (1) the multi-target hit model that accounts for the existence of several vital receptors affected by the toxin, and (2) model with a nonzero mortality at zero concentration to account for natural mortality. Special attention is given to statistical estimation in the framework of the generalized linear model with the binomial dependent variable as the mortality count in each experiment, contrary to the widespread nonlinear regression treating the mortality rate as continuous variable. The models are illustrated using standard EPA Daphnia acute (48h) toxicity tests with mortality as a function of NiCl or CuSO₄ toxin.

Categorical regression analysis of acute exposure to tetrachloroethylene

Exposure-response analysis of acute noncancer risks should consider both concentration (C) and duration (T) of exposure, as well as severity of response. Stratified categorical regression is a form of meta-analysis that addresses these needs by combining studies and analyzing response data expressed as ordinal severity categories. A generalized linear model for ordinal data was used to estimate the probability of response associated with exposure and severity category. Stratification of the regression model addresses systematic differences among studies by allowing one or more model parameters to vary across strata defined, for example, by species and sex. The ability to treat partial information addresses the difficulties in assigning consistent severity scores. Studies containing information on acute effects of tetrachloroethylene in rats, mice, and humans were analyzed. The mouse data were highly uncertain due to lack of data on effects of low concentrations and were excluded from the analysis. A model with species-specific concentration intercept terms for rat and human central nervous system data improved fit to the data compared with the base model (combined species). More complex models with strata defined by sex and species did not improve the fit. The stratified regression model allows human effect levels to be identified more confidently by basing the intercept on human data and the slope parameters on the combined data (on a C x T plot). This analysis provides an exposure-response function for acute exposures to tetrachloroethylene using categorical regression analysis.