Abstract
In Chap. 2, we used isotonic regression to estimate the order- restricted means. Chapter 3 is devoted to order-restricted inference in a dose-response setting. We formulate the null hypothesis and the ordered alternatives and we discuss the test statistics proposed by Williams (Biometrics 27:103–117, 1971; Biometrics 28:519–531, 1972) and Marcus (Biometrika 63:177–83, 1976); both are “t-test”-type test statistics that can be used to compare each nonzero dose level to the zero dose (i.e., the control) under order constraints. In the last part of the chapter we discuss the likelihood ratio test (Barlow et al., Statistical inference under order restriction. Wiley, New York, 1972; Robertson et al., Order restricted statistical inference. Wiley, New York, 1988).
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