Abstract
This article concerns the testing and estimation of a dose-response effect in medical studies. We study the statistical test of homogeneity against umbrella alternatives in a sequence of Poisson distributions associated with an ordered dose variable. We propose a test similar to Cochran-Armitage’s trend test and study the asymptotic null distribution and the power of the test. We also propose an estimator to the vertex point when the umbrella pattern is confirmed and study the performance of the estimator. A real data set pertaining to the number of visible revertant colonies associated with different doses of test agents in an in vitro mutagenicity assay is used to demonstrate the test and estimation process. (α C statistic, maximum likelihood estimate, monotone trend test, Poisson distribution,
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