在新藥研發的過程中，第二期臨床試驗的目的為初步觀察新藥物之療效與安全性，以確定適當的治療劑量與範圍，並提供是否進入臨床試驗第三期之參考。為了避免給予多數病人無效的新藥物，臨床上常使用二階段設計來進行試驗。Conway和Petroni (1995) 提出雙變量二項反應變數的二階段臨床試驗流程。在第一個階段中，如果服用新藥之後，具療效反應的人數大於或等於某一特定值且發生副作用的人數小於或等於某一特定值，才會進行第二階段的試驗，且唯有當試驗進行到第二階段，試驗所得到的資料才會予以分析。此時，第一階段觀察到具療效反應的人數大於或等於某一特定值 且發生副作用的人數小於或等於某一特定值 ，即服從一聯合截斷分配。針對二階段設計，若忽略截斷的影響，採用試驗中具療效反應比例(樣本百分比)予以估計，會高估新藥物的療效；同理，若採用試驗中發生副作用的比例則低估新藥物的危險性。所以本論文建議採用最大概似估計法來修正截斷的影響，並採用Sterne (1954) 區間估計的概念建立二階段臨床試驗設計中有效性與安全性的聯合信賴區域。

In a drug development process, the primary goal of phase II clinical trials is to determine whether there is sufficient evidence of efficacy and safety to make it worth further study in a phase III clinical trial. Most often, drug experiments employ a two-stage design, such as Conway and Petroni’s design (1995), in order to avoid giving patients an ineffective drug. Due to the nature of two-stage designs, the estimates of response rates should not be computed as if the data were obtained in a single stage. Therefore, this thesis derived bias-reduced estimators for two-stage designs based on bivariate endpoints when the second stage is allowed to continue. In addition, Sterne’s procedure is employed to obtain confidence region for bivariate response rates based on truncated bivariate binomial distribution.

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