A Geometric Mean Approach to Sampling Size Determination for the Equivalence Hypothesis

一般使用對等性假設檢定(Equivalence hypothesis)來評估原廠學名藥與專利藥品在檢定上是否有差異，另外對等性假設檢定也常應用於一般藥品及臨床上檢驗。雙單尾檢定(Two one-sided tests procedure, TOST)常常被使用於作對等性假設檢定上來檢定兩種處理差異，當兩處理之間的差異不為0時，其檢定力函數(Power function)即非對稱型分配，故一般在對等性假設檢定中只有近似的公式可計算出樣本數，其計算出來的樣本數會使檢定力(power)產生不足或是過多的現象，為求改善此點，本論文建議在對等性假設檢定中使用幾何平均的概念來推估所需樣本數。並將本論文及過去其他方法計算出的樣本數表列做比較。其中兩處理差異範圍包含常應用於生物相等性的對數尺度及臨床相等性的原始尺度。最後並針對在對等性假設檢定中不同方法所對應計算出的樣本數給予建議與其應用的資料類型。Equivalence hypothesis is the correct hypothesis to confirm whether the newly developed product conforms to the current standard product. It has great applications to evaluation of generic drug products and other new clinical modalities. Two one-sided tests (TOST) procedure was proposed to test the equivalence hypothesis for two treatments. When the difference in population means between two treatments is not 0, the power function is not symmetric, hence only approximate formulas are proposed to determine the sample size for the equivalence hypothesis. The resulting sample sizes may provide either insufficient power or unnecessarily high power. We suggest geometric mean approaches to determination of the sample size for equivalence hypothesis. A numerical study was conducted to compare the performance of our proposed method with other current methods. Numerical examples illustrate the applications to bioequivalence on the logarithmic scale and to clinical equivalence on the original scale. Remarks on the usage of different methods for sample size determination for equivalence hypothesis are made