Order-restricted dose-related trend tests.

Methods of isotonic regression are proposed to increase the power of common trend tests in situations where a monotonicity constraint is imposed upon the dose-response function. Isotonic versions of Cochran-Armitage type trend tests for binary response data are developed, and the bootstrap method is used in finding the empirical distributions of the test statistics and their critical values. The isotonic likelihood ratio test with a survival adjustment is also proposed. This survival adjustment can be applied to the likelihood ratio test for either the order-restricted or unrestricted parameter cases. To achieve the isotonic modifications, an amalgamation algorithm is applied when the observed dose-response is non-monotonic. A Monte Carlo simulation study comparing these trend tests shows the advantages of the isotonic modifications and survival adjustment. By applying the proposed methods to data from a toxicology and carcinogenesis study conducted as part of the National Toxicology Program, the effect of CI Pigment Red 23 is investigated. Copyright 2001 John Wiley & Sons, Ltd.