Testing for trend with count data.

Among the tests that can be used to detect dose-related trends in count data from toxicological studies are nonparametric tests such as the Jonckheere-Terpstra and likelihood-based tests, for example, based on a Poisson model. This paper was motivated by a data set of tumor counts in which conflicting conclusions were obtained using these two tests. To define situations where one test may be preferable, we compared the small and large sample performance of these two tests as well as a robust and conditional version of the likelihood-based test in the absence and presence of a dose-related trend for both Poisson and overdispersed Poisson data. Based on our results, we suggest using the Poisson test when little overdispersion is present in the data. For more overdispersed data, we recommend using the robust Poisson test for highly discrete data (response rate lower than 2-3) and the robust Poisson test or the Jonckheere-Terpstra test for moderately discrete or continuous data (average responses larger than 2 or 3). We also studied the effects of dose metameter misspecification. A clear effect on efficiency was seen when the 'wrong' dose metameter was used to compute the test statistic. In general, unless there is strong reason to do otherwise, we recommend the use of equally spaced dose levels when applying the Poisson or robust Poisson test for trend.