ABSTRACT
ABSTRACT Equivalence trials aim to demonstrate that new and standard treatments are equivalent within predened clinically relevant limits. In the presence of unspecied variances, methods such as the likelihood ratio test use sample estimates for those variances; Bayesian models integrate them out in the posterior distribution. These methods limit the knowledge of the extent that equivalence is affected by variability of the parameter of interest. In this chapter, we propose a likelihood approach that retains the unspeci-ed variances in the model and partitions the likelihood function into two
CONTENTS
7.1 Introduction ................................................................................................ 134 7.1.1 Motivation ....................................................................................... 134 7.1.2 Outline ............................................................................................. 135
7.2 Likelihood Method .................................................................................... 135 7.2.1 Crossover Design ........................................................................... 136
7.2.1.1 Hypothesis and Likelihood Ratio Test......................... 136 7.2.1.2 Fieller Condence Set ..................................................... 136 7.2.1.3 Proposed Likelihood Function ..................................... 137
7.2.2 Parallel Design ............................................................................... 138 7.3 Bayesian Approach .................................................................................... 140
7.3.1 Crossover Design ........................................................................... 140 7.3.2 Parallel Design ............................................................................... 141
7.4 Inference on Equivalence Affected by Unspecied Variances ........... 142 7.4.1 Normal Dataset and Likelihood Ratio Test Result ................... 142 7.4.2 Standardized Prole Likelihood ................................................. 143 7.4.3 Inference about Equivalence Affected by γ ............................... 145 7.4.4 Inference about Equivalence Affected by σ and ρ .................... 147
7.5 Comparison of Different Approaches in Crossover Design ................ 147 7.6 Conclusion and Discussion ...................................................................... 151 References ............................................................................................................. 152
components: F-statistic function for variances and t-statistic function for the ratio of two means. By incorporating unspecied variances, the proposed method can help identify a numeric range of variances where equivalence is more likely to be achieved, which cannot be accomplished by current analysis methods. By partitioning the likelihood function into two components, the proposed method provides more inference information than a method that relies solely on one component. We recommend the proposed likelihood method as a better alternative than current analysis methods for equivalence inference.
