The estimation of individual dose-response coefficients from joint toxicity information

Statistical methods for the analysis of joint-action data require that dose-response information is available for each stimulus individually and in combination with all other stimuli. However, it may be necessary to estimate the dose-response equation for an individual stimulus from combination data when dose-response information for that stimulus alone is unavailable.; A sequential estimation procedure is developed for two stimuli which combine in an additive fashion. First, a likelihood ratio test is used to determine from combination data whether the individual dose-response equations of the two stimuli are parallel or nonparallel. The logistic model of Berkson is then parameterized in terms of new dose metameters called equivalence doses which allows the logit of response to be written as an explicit function of the ln dose for both the parallel and nonparallel models. Coefficient estimates for the individual dose-response equation of interest are obtained by maximizing the ln-likelihood parameterized in terms of the parallel or nonparallel Equivalence Model.; Simulation studies were used to evaluate this procedure over a wide range of dose-response conditions. The procedure performs best when the individual dose-response equations for both stimuli are parallel. When the dose-response equations are not parallel, the performance of the procedure is difficult to assess.