本文在單期單序列或是多期單序列設計之下的口服藥藥物動力(pharmacokinetic，簡稱為PK)研究，針對受試者的藥物濃度-時間側寫建立乘法混合效應PK統計模型，其中使用第一階吸收與代謝的單區模型(one-compartment model)描述平均藥物濃度-時間側寫。另外，為考慮受試者之間的差異性，將模型中的藥物動力參數視為一個具有厚尾的多維斜線分配隨機向量，並且引用高斯關聯結構連結廣義伽瑪分配描述受試者重複測量的藥物濃度之聯合分配。在多期單序列設計之下，上述PK參數除受試者之間的變異，也包含受試者之內的變異。然後本文根據估計的統計模型，建立暴露參數的信賴區間，其中暴露參數包含藥物濃度-時間側寫下的面積、最大藥物濃度值、達最大藥物濃度所需時間與代謝半衰期。本文進一步使用蒙地卡羅(Monte Carlo)方法模擬上述信賴區間的涵蓋機率及期望長度，藉以探討本文所提模型與其他模型的優劣。最後，本文使用兩筆真實資料，展示本文所提方法的應用。

In this thesis, we consider multiplicative nonlinear mixed effects statistical models for orally administered drug concentration-time profiles obtained in a pharmacokinetic (PK) study under a one period/one sequence and multiple periods/one sequence designs, respectively. In the proposed models, the mean concentration-time curve is described by the one-compartment PK model with first-order absorption and elimination. To take into account the between-subject variability, the logarithms of PK parameters-variables in the proposed models are regarded as a multivariate slash random variable. Moreover, a multivariate generalized gamma distribution is developed for the joint distribution of the drug concentrations that are repeatedly measured from the same subject. Under the multiple periods/one sequence design, the PK parameters- variables also include the with-subject variation. Based on the fitted PK statistical models, we then construct confidence sets for the exposure parameters, such as the area under the drug concentration-time curve, the associated maximum drug concentration, the time to maximum concentration and the elimination half-life. A simulation study is also implemented to investigate the coverage probability and expected length of the proposed confidence sets. Finally, the proposed statistical PK models and the associated inferences are then applied to illustrate two real data sets.

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