Tests for Trends in Binary Response

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.