| 摘要: | 檢定k 個常態母體平均數是否相等, 通常用傳統統計檢定虛無假設H0 : .i = .j (所有i ?= j) 及其對立假設H1 : .i ?= .j (某些i; j) 。但許多研究考慮類似問題時, 採用比較符合實際的區間假設檢定, 如: H0 : .. ? .. ? d 及對立假設 Ha : .. ?.. > d; 此處.. = max {.1; · · · ; .k} 與.. = min {.1; · · · ; .k}, 且虛無假設為複合假設。然而更為有用的區間假設檢定應是生體等效性檢定, 檢定一般製藥公司所生產的學名藥(generic drugs) 其療效必須與正廠生產的藥品等效(或等價, equivalence)。本研究計畫的目的, 考慮一種基於平均生體相容性的生體等效性檢定H0 : .. ?.. ? d 及對立假設Ha : .. ?.. < d: 在母體變異數(.2) 已知且相等, 及母體變異數未知且相等的情形下, 參考Chen 和Hsu (2011) 的方法, 預期能推導出概度比檢定程序(likelihood ratio test), 來處理以上生體等效性檢定的問題。本研究計畫亦將探討其統計理論性質, 如檢定不偏性, 均勻最強檢定力不偏或不變檢定, 偏離常態之穩健性等。且更近一步, 使用數值比較方法評估概度比檢定程序。
Testing the homogeneity of k normal population means usually refers to testing the standard null hypothesis H0 : μi = μj for all i 6= j against the hypothesis H1 : μi 6= μj for some i and j. Some authors consider a more realistic analogue of the null hypothesis in that H0 is replaced by the interval hypothesis, say, H0 : μ. ? μ. ? d against Ha : μ. ? μ. > d, where μ. = max {μ1, · · · , μk} and μ. = min {μ1, · · · , μk} . Note that H0 is a composite hypothesis. A more useful interval hypotheses is referred to as the hypothesis of bioequivalence in medical studies because the objective is to demonstrate the equivalence of the generic version of a drug to the brand name’s formulation. In this project we consider a special form of equivalence based on average bioavailability for approval of generic drug products: H0 : μ.?μ. ? d vs. Ha : μ.?μ. < d. We will derive likelihood ratio (LR) tests for this bioequivalence hypothesis for the cases of the common known variance and common but unknown variance, using the similar approach employed by Chen and Hsu (2011). We will also investigate more theoretical statistics properties, such as unbiasedness of the test, optimal properties such as uniformly most powerful unbiased or invariant test, and robustness to the departure of normality. Numerical comparisons to other methods will be also performed in order to evaluate the proposed procedure. |
