Consonant closed likelihood ratio test procedures with application to dose-response study

Coherence and Consonance are two important concepts in multiple testing procedures (MTP). Closed test is a well-known coherent hypothesis testing procedure, which is not necessarily consonant. In this paper, we propose two consonant closed likelihood ratio tests which are compared with the step-down Dunnett test (SD) and Dunnett-Tamhane step-up test (SU) in several aspects. Simulation and dose-response study examples show that the new procedures have certain advantages over the SD and SU test. For example, the rejection region of our new procedures is larger than that of the SD test particularly when most of the null hypotheses are false. The new procedures control the family-wise error rate (FWER) strongly without the equal correlation assumption, which is a necessary condition for the SU test. In terms of computing effort, the new procedures require similar moderate computation for critical constants as the SU test and they follow the same steps as any closed test procedures. We also provide guideline in applying consonance adjustment in multivariate analysis with mixed model and repeated measurements.