在2x2交叉設計下進行藥物動力學(pharmacokinetic)的研究中，本文考慮以直接比較平均藥物濃度-時間側寫(drug concentration-time profile)的角度評估參照藥品與測試藥品的平均生物相等性(average bioequivalence)。本文首先假設藥物濃度服從廣義伽瑪分配，在平均藥物濃度-時間側寫為一階單區藥物動力模式(one-compartment model)下提出藥物濃度的參數藥物動力學模型。除收集藥物濃度資料外，亦包含與受試者生理狀態相關的共變數，本文在參數藥物動力學模型中考慮引入線性共變數效應解釋受試者之間的差異性。本文進一步考慮半參數藥物動力學模型，在不假設特定藥物動力學模式下，以自然立方樣條估計(natural cubic spline)平均藥物濃度-時間側寫，並考慮非線性共變數效應及共變數之間的交互作用。除討論各模型參數之估計、模式評估及應用外，並根據模型估計之平均側寫建構多重生物相等性檢定。本文使用蒙地卡羅(Monte Carlo)方法模擬各種實務中參照藥品及測試藥品的藥物濃度-時間側寫可能出現的情況，以及不同的藥物濃度分配，藉以研究本文所提多重檢定的型一誤差率及檢定力的表現。最後，藉分析兩筆生物相等性研究的資料說明本文所提各種方法的應用。 To evaluate globally the average bioequivalence of a test drug to a reference drug in a pharmacokinetic study under a 2x2 crossover design, we consider directly comparing the associated drug concentration-time curves. Statistical models for the drug concentrations are suggested when the concentrations measured at different time points are distributed according to a generalized gamma distribution and the mean concentrations over time are described by a one-compartment pharmacokinetic model. A multiple test based on the supreme distance between the two curves over the time interval under study is then proposed for testing the equivalence of the two drug concentration-time curves. We also propose a semi-parametric model for drug concentrations in blood or plasma over time. The semi-parametric model primarily includes smooth mean drug concentration-time curves that can be estimated by using natural cubic splines. Based on the difference of the two estimated natural cubic splines, we then suggest a test for the bioequivalence of the two drugs. The robustness of the level and power performances of the suggested tests are further investigated in a simulation study. Finally, we illustrate two datasets for the bioequivalence study by using the proposed models and tests.
