ORDER-RESTRICTED TESTS FOR STRATIFIED COMPARISONS OF BINOMIAL PROPORTIONS

The data set presented relates a binomial response to ordered levels o f an explanatory variable, representing doses of a drug, with data col lected at several centers. A study goal is to test independence of the response and the ordinal factor, assuming under the alternative only that the binomial parameter is a monotonically increasing function of the ordinal predictor. We present two likelihood-ratio tests that are sensitive to order-restricted alternatives. Simulating the exact distr ibutions of the test statistics yields nearly exact P-values. We also discuss related analyses for comparing two groups on an ordinal respon se, and we propose a test that is sensitive to a stochastic ordering a lternative.