Significance Levels of Randomization Trend Tests in the Event of Rare Occurrences

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Abstract
In the statistical evaluation of data from a dose‐response experiment, it is frequently of interest to test for dose‐related trend: an increasing trend in response with increasing dose. The randomization trend test, a generalization of Fisher's exact test, has been recommended for animal tumorigenicity testing when the numbers of tumor occurrences are small. This paper examines the type I error of the randomization trend test, and the Cochran‐Armitage and Mantel‐Haenszel tests. Simulation results show that when the tumor incidence rates are less than 10%, the randomization test is conservative; the test becomes very conservative when the incidence rate is less than 5%. The Cochran‐Armitage and Mantel‐Haenszel tests are slightly anti‐conservative (liberal) when the incidence rates are larger than 3%. Further, we propose a less conservatived method of calculating the p‐value of the randomization trend test by excluding some permutations whose probabilities of occurrence are greater than the probability of the the observed outcome.

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