Testing trend for count data with extra-Poisson variability. (English) Zbl 1210.62140
Summary: Trend tests for monotone trend or umbrella trend (monotone upward changing to monotone downward or vise versa) in count data are proposed when the data exhibit extra-Poisson variability. The proposed tests, which are called the GS1 test and the GS2 test, are constructed by applying an orthonormal score vector to a generalized score test under an \(r\)th-order log-linear model. These tests are compared by simulation with the Cochran-Armitage test and the quasi-likelihood test of W.W. Piegorsch and A.J. Bailer [Statistics for enuiron, mental biology and toxicology. (1997)]. It is shown that the Cochran-Armitage test should not be used under the existence of extra-Poisson variability; that, for detecting monotone trend, the GS1 test is superior to the others; and that the GS2 test has high power to detect an umbrella response.
MSC:
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
| 62G10 | Nonparametric hypothesis testing |
| 65C60 | Computational problems in statistics (MSC2010) |
Keywords:
Cochran-Armitage test; generalized score test; negative binomial distribution; orthonormal score vector; toxicologyReferences:
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