Testing for ordered group effects in binary and continuous outcomes

A likelihood ratio test is proposed for the detection of an ordered group effect on bivariate responses where one response is binary and the other is continuous. The procedure is based on a conditional logistic model for the binary response given the continuous outcome. We also develop a likelihood ratio test for simultaneously determining the goodness of fit of the ordering assumption on both responses. Our approach is motivated by a particular toxicity study application involving laboratory animals that focused on the effect of a food color additive on the development of reticuloendothelial (RE) tumors. A brief discussion on extensions to the methodology introduced here is also given, along with a comparison of the approach with a marginal strategy where the presence of an ordered group effect is assessed independently for each of the two responses.