Doctoral Dissertation Defense: Bo Liu

Title:  Univariate and Multivariate Equivalence Testing in Some Biomedical Applications

Abstract 
The topic of equivalence testing came into prominence in the context of assessing bioequivalence; i.e., testing if a generic drug is similar to a brand name drug. Following the extensive literature (including books) on the topic of bioequivalence testing, the topic has diversified into a variety of other applications where the data can be univariate or multivariate. The present work investigates a few such univariate and multivariate equivalence testing problems, motivated by specific applications. The applications considered include (i) Equivalence testing of the dose-response relationships between two groups, (ii) Equivalence testing of several population means under unequal variances, (iii) Equivalence testing of two intra-subject covariance matrices under crossover designs, and (iv) Equivalence testing for food safety assessment.

In each case, we have developed the necessary criteria for declaring equivalence. We believe our criteria are well motivated: they are based on the form of the likelihood ratio test (LRT) statistic or the overlap coefficient (OVL); the latter quantifies the intersection between two probability density functions, so that a large overlap is evidence of similarity between the two distributions. The proposed criteria are between zero and one, with values close to one indicative of equivalence. Our criteria go beyond the usual (and sometimes ad hoc) criteria based on means and variances, often used in bioequivalence assessment. Both the LRT statistic based and OVL based criteria involve all of the population parameters, so that equivalence can be concluded in a comprehensive manner.

We have pursued two approaches for the development of tests based on the criteria: a parametric bootstrap and a fiducial methodology. The performance of the proposed solutions have been assessed using simulations, and have been illustrated using real data analysis. We believe that we have developed a framework for equivalence assessment in both univariate and multivariate problems relevant to many applications.