在一般藥品及臨床試驗上，經常使用對等性檢定(Equivalence Test)來評估原廠藥與專利藥之間的差異是否顯著，透過雙單尾檢定(Two one-sided tests procedure, TOST)，以檢定兩種處理的對等性，而當兩個處理之間差異不為0且在對等界線內時，其檢定力函數(Power function)為非對稱型分配，故過去所提出的方法只能算出近似的樣本數，使其所計算出來的檢定力發生不足或是過多的現象，雖然過去曾提出簡單的迭代方法來改善此問題，但其檢定力函數的積分上下限包含了樣本標準差(s)，為一個隨機變數，透過給定其為常數，所得之樣本數亦為近似的結果。
本論文所提出的方法考慮了樣本標準差的分配，為一精確方法來決定樣本數，此外，討論兩個藥物動力學反應值所需的樣本數，透過正交對角化共變異矩陣，得到一個新的分配使得兩個變數之間為獨立，再應用所提出的方法於兩變數的樣本數決定，並呈現計算出來的樣本數進行比較與分析。

The equivalence test is a hypothesis to confirm whether the new test product conforms to the standard reference product. It has many applications such as evaluation of GMO crop and its conventional crop, or generic drugs and their innovative drugs. The equivalence hypothesis can be decomposed into the non-inferiority (NI) and non-superiority (NS) hypothesis. The two one-sided tests (TOST) procedure is usually proposed to test the difference between two treatments. When the difference in population means between two treatments is not 0 but within the equivalence limits, the proportion of the type II error rate allocated to each of the two tails of the central t-distribution cannot be analytically determined. Hence, no close form of the exact sample size for the equivalence hypothesis is available.
Current methods provide the sample sizes by assuming the sample standard deviation as a constant. In fact, the lower and upper limits for the power calculation contains s, which is a random variable. By integrating the probability density function of s, the power can be computed. We suggest a method with consideration of type II error rates for both one-sided hypotheses to determine the sample size for the equivalence hypothesis, by treating the sample standard deviation as a random variable.
In addition, the covariance matrix of multiple responses was transformed by orthogonal diagonalization. We obtained a new distribution in which multiple responses are independent of each other. Consequently, we apply the proposed method to the determination of the sample size for multiple responses. Numerical examples illustrate the applications of the proposed method.

誌謝 iii
中文摘要 iv
Abstract v
Contents vii
List of Figures viii
List of Tables ix
Chapter 1 Introduction 1
Chapter 2 Review of the Current Methods 4
2.1 Current Methods of Sample Size Determination 7
2.2 A Simplified Approach to Sample Size Determination 11
2.2.1 A Simplified Approach to Sample Size Determination for one PK response 11
2.2.2 A Simplified Approach to Sample Size Determination for multiple PK responses 12
Chapter 3 The Proposed Methods 16
3.1 Sample size determination of one response 16
3.2 Sample size determination of two independent responses 19
3.3 Sample size determination of two correlated responses 22
Chapter 4 Numerical Studies 35
4.1 Numerical Studies for One PK Response 35
4.2 Numerical Studies for Two PK Responses 35
4.2.1 Numerical Studies for two independent PK Responses 36
4.2.2 Numerical Studies for two correlated PK Responses 36
4.3 Numerical Examples 38
4.3.1 Numerical Examples for one PK response 39
4.3.2 Numerical Examples for two PK responses 39
Chapter 5 Discussion and Conclusion 86
References 88
Appendix A. R program Codes for sample size Determination 91
Appendix B. R program Codes for Numerical Examples 102

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