UC Riverside

In the past century, several multiple testing procedures have been developed based on the closure principle. Procedures following the closure principle are called closed test and they find individual tests for intersection hypotheses in the family and collates the results to control the familywise error rate. Almost all popular closed tests use the union-intersection method for their intersection hypotheses. However, due to computational issue, likelihood ratio test has not yet received much attention in closed testing. Moreover, not being a union-intersection method, the likelihood ratio test will not satisfy the logical consistency requirement of consonance.

In this dissertation, a general solution (consonance adjustment) to the consistency problem in multiple hypotheses testing is proposed under the framework of closure principle and partitioning principle. Simulation examples are used to show its advantages.

Besides a general framework, also provided in this dissertation is a special form of the consonant test in the context of multiple comparisons with a control. Using likelihood ratio test with the closure principle and a consonance adjustment step, the consonant closed likelihood ratio test is introduced. The rejection region, shortcut and steps in critical constants calculation are discussed. Extensive simulation studies and pre-clinical trial example are provided.

More recently, testing for efficacy in multiple endpoints has emerged as a challenging statistical problem in clinical trials. Current approaches to this problem are based on closed testing or partition testing, which test the efficacy in certain dose-endpoint combinations and collate the results. Partition testing is in general a more powerful approach since it tests fewer hypotheses to avoid unnecessary power loss. However, all current approaches are still based on various union-intersection tests. In my dissertation, I generalize the decision path principle proposed by Liu and Hsu (2009) to the cases with multiple primary endpoints. Then propose a new partition testing approach based on consonance adjusted likelihood ratio test. The new procedure provides consistent inferences and yet it is still conservative and does not rely on the estimation of endpoint correlations or independence assumption which might be challenged by the regulatory agencies.