Robust Procedures for Drug Combination Problems with Quantal Responses

Two drugs are administered to groups of animals at various combined dosages and the number of animals that respond is recorded. After a brief consideration of experimental designs for this problem, we discuss modelling it as a generalized linear model in which the response surface is connected to the joint lethality of the drugs via a link function. Questions concerning the interaction of the drugs can then be phrased in terms of the surface parameters. Through examples and a Monte Carlo study, we show that the usual maximum likelihood estimation (MLE) analysis is quite sensitive to slight amounts of contamination in these models. As an alternative analysis, we propose a robust analysis based on a robust fit of the model. The robust fit is quite similar to the MLE fit in that one norm is substituted for another; hence, interpretation of the robust analysis is similar to that of the MLE analysis. The robust analysis appears to be less sensitive to contamination than the MLE analysis and to have high efficiency for a logit model. We discuss the use of the jackknife for these models. Besides being useful in the construction of informative diagnostics concerning the model, the jackknife can be used to form stable analyses for contaminated models.