In this dissertation a methodology is proposed for simultaneously evaluating the population bioequivalence (PBE) of a generic drug to a pre-licensed drug, or the bioequivalence of two formulations of a drug using multiple correlated pharmacokinetic metrics. The univariate criterion that is accepted by the food and drug administration (FDA) for testing population bioequivalence is generalized. Very few approaches for testing multivariate extensions of PBE have appeared in the literature. One method uses the trace of the covariance matrix as a measure of total variability, and another uses a pooled variance instead of the reference variance. The former ignores the correlation between the measurements while the later is not equivalent to the criterion proposed by the FDA in the univariate case, unless the variances of the test and reference are identical, which reduces the PBE to the average bioequivalence. The confidence interval approach is used to test the multivariate population bioequivalence by using a parametric bootstrap method to evaluate the 100% (1-alpha) confidence interval. The performance of the multivariate criterion is evaluated by a simulation study. The size and power of testing for bioequivalence using this multivariate criterion are evaluated in a simulation study by altering the mean differences, the variances, correlations between pharmacokinetic variables and sample size. A comparison between the two published approaches and the proposed criterion is demonstrated. Using nonlinear models and nonlinear mixed effects models, the multivariate population bioequivalence is examined. Finally, the proposed methods are illustrated by simultaneously testing the population bioequivalence for AUC and Cmax in two datasets.

人的一生避免不了大小病痛，一但身體不適、罹患疾病，就須由醫師診斷、服用藥物；而藥物之生產首重有效與安全，要能有效的治療疾病，也要限制其毒性不超過安全限制以避免危害人體。 　　藥品之開發需要極為龐大之成本，故而各藥廠對於可以節省開發成本的藥品新劑型與學名藥之研究深感興趣；相對的，也就對於如何證明藥品新劑型（或學名藥）與原廠藥為生體相等可互用的方法多加探討。 　　美國FDA對於生體相等之評估準則，擬由過去的平均生體相等轉換成為個體生體相等評估準則；更改後的準則考慮面向較為完整周全，但是其應用卻須要更為繁複的試驗方式與更多的成本來配合，為了保留新準則之評估概念並簡化試驗與降低評估成本，本篇論文試圖找出新、舊評估準則之關聯，並以舊有準則為基礎做調整，盼能透過對舊準則之調整達到與新準則相類似之評估結果。如此一來，可沿用舊有試驗方法完成新準則所欲進行之評估，降低此評估研究之耗資，同時確保藥品新劑型（或學名藥）與原廠藥為生體相等可互用，具有相同療效與安全保證。

Bioequivalence determines if two drugs are alike. The three kinds of bioequivalence are Average, Population, and Individual Bioequivalence. These Bioequivalence criteria can be evaluated using aggregate and disaggregate methods. Considerable work assessing bioequivalence in a frequentist method exists, but the advantages of Bayesian methods for Bioequivalence have been recently explored. Variance parameters are essential to any of theses existing Bayesian Bioequivalence metrics. Usually, the prior distributions for model parameters use either informative priors or vague priors. The Bioequivalence inference may be sensitive to the prior distribution on the variances. Recently, there have been questions about the routine use of inverse gamma priors for variance parameters. In this paper we examine the effect that changing the prior distribution of the variance parameters has on Bayesian models for assessing Bioequivalence and the carry-over effect. We explore our method with some real data sets from the FDA.