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Ulm, Kurt and Dannegger, Felix and Becker, Ursula (1998): Tests for Trends in Binary Response. Collaborative Research Center 386, Discussion Paper 115
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Abstract

Tests for trend in binary response are especially important when analyzing animal experiments where the response in various dose--groups is of interest. Among the nonparametric tests the approach of Cochran and Armitage is the one which is most commonly used. This test (CA-test) is actually a test for a linear trend. The result of this test is highly dependent on the quantification of the dose. Varying score assignments can lead to totally different results. As an alternative isotonic regression is proposed. The result of this approach is independent of any monotonic transformation of the dose. The p--value related with the isotonic regression can be obtained either from considering all possible combinations of the total number of events in the dose--groups or by analyzing a random sample of all permutations. Both tests are compared within a simulation--study and on data from an experiment considering whether a certain type of fibre, para--aramid, is carcinogenic. The result of the commonly used CA--test is highly dependent on the event rate in the lowest and highest dose--group. Based on our analyses we recommend to use the isotonic regression instead of the test proposed by Cochran and Armitage.