This thesis mainly investigates statistical methods for quantile-based equivalence testing, with applications in clinical trials and pharmaceutical development. In many settings, treatment effects cannot be adequately characterized by mean comparisons alone, making equivalence assessment at specific quantiles a valuable alternative for evaluating efficacy and safety.

The thesis considers equivalence testing for a single quantile in two independent Gaussian populations with unequal variances. Existing methods based on the Two One-Sided Tests procedure for quantiles (qTOST) are often conservative in finite samples, resulting in reduced statistical power. To address this issue, a finite-sample adjustment procedure is proposed. Theoretical results and simulation studies show that the proposed method maintains the nominal significance level while achieving uniformly higher power than qTOST.

The proposed method extends the framework to simultaneous equivalence testing of multiple quantiles. Novel size-matched procedures are developed to overcome the conservativeness of conventional approaches. The proposed methods provide accurate type I error control while substantially improving power and reducing sample size requirements, particularly in unbalanced and heteroscedastic settings.

Computational tools and reproducible software are developed to support practical implementation. Simulation studies and pharmaceutical applications demonstrate the effectiveness and applicability of the proposed methods.