多變量離群值的統計鑑定及在生物對等性評估上之研究

Abstract

在生物對等性研究中，最常見的試驗設計，是二期雙序列的交叉設計( )；此交叉設計是在建立在線性混合效應模型之下，應用於平均生物對等性評估的統計推斷。離群者所指，乃是接受測試藥品之受試者，其生物可用率反應值(test formulation)遠高於或遠低於其參照藥品的生物可用率反應值(reference formulation)，亦或是對測試藥品、參照藥品的反應值，與其他受試者呈現出極端差距者。在平均生物對等性研究中，離群者的排除或納入，在往後的統計分析中可能歸納出不同的結論。概似距離檢定、估計距離檢定和Hotelling T2檢定，為現已提出做為檢定離群者的方法。然而，這些檢定方法並沒有根據中央卡方隨機變數的最大值，或是根據其模擬數據得出的經驗臨界值來完成檢定。為了克服上述缺點，我們根據Fisher-Tippett定理，得出其Hotelling T2統計值最大值的漸進分布，並導出檢定離群者的統計檢定之推論；我們進行模擬研究，以型I誤差機率和檢定力來研究和比較我們所提出方法之表現有何差異。實際資料則用來說明我們所提出方法的運用。

The most commonly employed design for bioequivalence studies is the two-sequence and two-period ( ) crossover design under which a linear mixed-effects model is applied to make statistical inference of evaluation of average bioequivalence (ABE). Outlying subjects are unusual subjects with extremely high or low bioavailability of the test formulation relative to the reference formulation; or with extreme bioavailabilities to both formulations as compared to other subjects. Inclusion or exclusion of outlying subjects may lead to a completely difference conclusion of ABE. Likelihood distance (LD), Estimates distance (ED) and Hotelling T2 (HT) have been proposed for detection of outlying subject. However, these methods are not based on the maximum of the central chi-square random variables or they are based on empirical critical values obtained from the simulations. To overcome these drawbacks, based on the Fisher-Tippett theorem, we derived the asymptotic distribution of the maximum of Hotelling T2 statistic for the inference of detection of an outlying subjects. Simulation studies were conducted to investigate and compare the performance, in terms of size and power, of our proposed procedure. Real data illustrate the application of our proposed method.