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On tests of linearity for dose response data: Asymptotic, exact conditional and exact unconditional tests

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  • Man-Lai Tang

Abstract

The approximate chi-square statistic, X 2 Q , which is calculated as the difference between the usual chi-square statistic for heterogeneity and the Cochran-Armitage trend test statistic, has been widely applied to test the linearity assumption for dose-response data. This statistic can be shown to be asymptotically distributed as chi-square with K - 2 degrees of freedom. However, this asymptotic property could be quite questionable if the sample size is small, or if there is a high degree of sparseness or imbalance in the data. In this article, we consider how exact tests based on this X 2 Q statistic can be performed. Both the exact conditional and unconditional versions will be studied. Interesting findings include: (i) the exact conditional test is extremely sensitive to a small change in dosages, which may eventually produce a degenerate exact conditional distribution; and (ii) the exact unconditional test avoids the problem of degenerate distribution and is shown to be less sensitive to the change in dosages. A real example involving an animal carcinogenesis experiment as well as a fictitious data set will be used for illustration purposes.

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  • Man-Lai Tang, 2000. "On tests of linearity for dose response data: Asymptotic, exact conditional and exact unconditional tests," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(7), pages 871-880.
    • Handle: RePEc:taf:japsta:v:27:y:2000:i:7:p:871-880
    DOI: 10.1080/02664760050120551
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    1. Leonard Bayer & Christopher Cox, 1979. "Exact Tests of Significance in Binary Regression Models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 28(3), pages 319-324, November.
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