An Asymptotic Confidence Region for the ED 100p From the Logistic Response Surface for a Combination of Agents

When viewed in light of the simplicity of the solution in a single variable, it is not surprising that the estimation of the ED10op in combinations has received little attention in the statistical literature. As a result of the increasing interest in the effects of combinations of agents either as the result of treatment or environmental exposure, however, consideration of the estimation of the ED1oop in combinations is warranted. [Skarin, Canellos, Rosenthal, Case, Maclntyre, Pinkus, Moloney, and Frei (1983) reported on the use of a combination of six drugs in the treatment of lymphoma, and Lang, Kurzepa, Cole, and Loper (1980) indicated that several known or suspected carcinogens were identified among the many compounds present in drinking water.] Confidence bands on the logistic response curve were considered by Hauck (1983) and Brand, Pinnock, and Jackson (1973). One of the advantages claimed by Hauck is that his method is not restricted to a single explanatory variable, as is the approach taken by Brand et al. In their paper, however, Brand et al. discussed placing confidence bands about points on the inverse response curve, for example, the ED1oop, a topic not discussed by Hauck. It is the purpose of this article to develop and illustrate a method for estimating a large sample confidence region about the ED1oOP from the logistic curve in the case of multiple explanatory variables. 2. BACKGROUND