THRESHOLD MODELS FOR COMBINATION DATA FROM REPRODUCTIVE AND DEVELOPMENTAL EXPERIMENTS

In risk assessment, thresholds are generally believed to exist for tox ic reproductive and developmental agents. Therefore, dose combinations exist below the threshold where the response is not distinguishable f rom background and above the threshold where a dose-response trend res ults, Because data from combination experiments are more reflective of human exposure to environmental agents, threshold models that incorpo rate the effect of interactions among these agents are developed. For s agents acting in combination, the threshold is an s-dimensional surf ace, More specifically, for a combination of two agents, the threshold is a two-dimensional contour of dose combinations, and for a single a gent, the threshold is represented by a single dose value, not necessa rily a dose level used in the experiment. In toxicological experiments designed to investigate the reproductive or developmental effects of a chemical on laboratory animals, litter effects typically are present , yielding overdispersion. Instead of assuming a particular distributi onal form for the binary responses, quasi-likelihood methods often are used where parameters are introduced to measure the overdispersion. T his article describes threshold models for combination reproductive an d developmental experiments and develops parameter estimation techniqu es using quasi-likelihood methods. Once parameters are estimated, a hy pothesis test for an overall dose-response relationship is performed u sing a quasi-likelihood ratio statistic. Next, a confidence interval a bout the threshold parameter is constructed using a quasi-likelihood r atio statistic, and finally, a confidence region is constructed about the threshold surface, Illustrative examples are presented that use si ngle-agent reproductive data from the National Toxicology Program and three-agent combination developmental data from the Environmental Prot ection Agency and Man Tech Environmental Technology, Inc.