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Trend tests for nonlinear response in proportion are proposed under binomial and extra-binomial variabilities for dose-response developmental toxicology data. The proposed test under binomial variabil...ity is constructed by applying orthonormal dose vector to score test under logistic model, and the test for extra binomial variability is constructed by applying the same idea to generalized score test. It is shown that the test for data with binomial variability is asymptotically equivalent to the $ Q_r $ test proposed by Jayasekara et al. (1999); and that the proposed test for data with overdispersion has higher powers than the generalized Cochran-Armitage test for detecting nonlinear response. It is also shown by simulation that the trend tests for binomial variability should not be used when the data exhibit extra binomial variability since it inflates the type I error substantially.続きを見る
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