Trend tests in proportion are developed under binomial and extra-binomial variability for linear and non-linear dose-responses. Those tests employ orthonormal dose vectors and are proved to be score test, or generalized score test. They are applied for designing biological monitoring systems using water snails to detect the emergence of a toxic chemical in fresh water. Specifically, they are used for selecting a cut-off category for sensitive detection of a toxic chemical when dose responses are observed by means of categories.

Keywords: Down-tern of dose response curve; Cochran-Armitage test; Generalized score test; Over dispersion

Biography: Takashi Yanagawa is the founder of the graduate program of Biostatistics at Kurume University, Japan. He is an elected member of the ISI. He was a member of Science Council, Japan and was the Regional President of the International Biometric Society, Japanese Region. He is the author or co-author of 120 scienticic papers in major journals such as Biometrika, Biometrics, Journal of the American Statistical Assiciation, Statistics in medicine, Environmetrics and others.