Testing for Ordered Group Effects in Binary and Continuous Outcomes

Abstract

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.

Constrained statistical inference in generalized linear, and mixed models with incomplete data

“…In addition, joint likelihood analysis and tests of heterogeneity may be performed. Farrell and Park (2007) proposed a constrained likelihood ratio tests for ordered group effects with one binary and one continuous response. Their method was shown to follow a chi-bar-square distribution asymptotically.…”

Testing for and against an order restriction among bivariate populations

“…Various examples of this type can be found in clinical trials, econometrics, psychology and many other areas. Farrell and Park (2007) [11] proposed a likelihood ratio test for the detection of an ordered group effect on bivariate responses based on a conditional logistic model. However, this thesis aims to develop a testing procedure to detect such an ordering effect in a joint model constructed using the concept of latent variables.…”