On the use of stochastic ordering to test for treatment related trend with clustered discrete data
by
Kyeongmi Cheon
University of Memphis
Coauthors: Aniko Szabo , E. Segun George

The definition of treatment related trend has always been ambiguous in studies with clustered data. Usually, treatment effect is defined either in terms of per cluster member response rate or in terms of per whole cluster response rate. In the former case, response function is usually modeled by the use of a linear link response function for the marginal response probability for a cluster member. In the latter, several options have recently been suggested by Kuk (2004) in the context of risk assessment of developmental toxicity studies. In this paper, we propose an approach which defines trend in the effect of treatment in terms of multivariate stochastic ordering of toxicology endpoints. Most existing definitions, including those of Kuk are special cases of this definition, therefore it is robust and incorporates various forms of monotone responses. Using death/resorption and malformation as endpoints and assuming multinomial exchangeability for each litter, we use a saturated model representation of the multinomial exchangeable distribution by George, et al. (2007) to model the joint distribution of these endpoints. The saturated model representation ensures that our procedure is essentially nonparametric. We address the problem of sparseness and augment data using the marginal compatibility assumption of Zhang and Kuk (Biometrics, 2007). To construct a likelihood ratio test for trend we device an EM algorithm that adapts the works of Lindsay ( Ann. of Stat, 1983) and Hoff (J. of Comp. and Graphical Stat., 2000) for MLE computation under stochastic ordering. Our work can be easily generalized for multinomial clustered data that involve more than three end points

Date received: February 27, 2008