Incorporating extra information in experimental design for bioassay

In a bioassay, under certain experimental circumstances, information on concentration (dose rate) and time to response for some subjects can be combined in a single analysis. An underlying logistic random variable is assumed and the resulting mixed- (continuous-quantal) response model is analyzed by likelihood methods. The estimation procedure for the mean and the variance is described, and expressions for asymptotic variances are obtained. A comparison of results from the mixed model and from the standard quantal-response model shows that there is a substantial reduction in the variance of the estimators for the mixed model. On the basis of the table of asymptotic variances, some design implications are discussed. An example from insect pheromone research is used to illustrate the main ideas.