在臨床試驗中，選擇適合的藥物是一個非常重要的工作。為了檢驗藥物的安全性、療效性、副作用等，醫學界制訂了四期不同的臨床試驗，其中在第二期臨床試驗中，Cheng-Shiun Leu、Herbert Robbins與 Bruce Levin 提出一個篩選藥物之實驗程序，名為LRL逐次選取程序，分為non-adaptive (無調適)及adaptive (調適)兩種LRL 程序，能有效率地篩選出較佳藥效之藥物，減少受試者人數，來降低實驗成本。他們把服藥後的治療結果視為治療成功或失敗，透過逐次程序選出較佳的藥物；然而，有些藥物的治療結果並不是只有兩種情況，像是降血壓、降血糖等藥物，其反應為一個連續變數，故本文將延續Nga-Ting Chan 所提出的常態反應下之逐次選取程序，名為Normal Distribution Design ( NDD程序)，針對藥效反應服從常態分配之情況，使用貝氏估計的概念而假設藥效參數服從三種不同的beta分布，提出成本函數與逐次選取程序，探討先驗分布、逐次選取程序及選藥情況對成本函數的影響。最後經電腦模擬驗證，證實在藥效反應服從常態分配和其藥效參數服從beta分配下，使用調適程序比使用無調適程序之實驗，更能夠減少實驗成本。

In clinical trials, selecting the appropriate medicines is a significant task. In order to testdrug effects, the medical field has developed four different phases. Cheng-Shiun Leu,Herbert Robbins, and Bruce Levin have designed a procedure, for selecting medicines inphase-Ⅱ, which is called Levin-Robbins-Leu binomial subset selection procedure andwhich is divided into adaptive design and non-adaptive design. It aims not only to selectthe medicines efficiently with better efficacy but also to reduce the sample size and costsof the experiments. The drug responses in LRL procedure are assumed to be Bernoullidistributed. We can select the best medicines through LRL procedure; however, there aresome medicines, such as hypoglycemic agents and hypotensive drug, whose response hasnot only two results but a continuous variable. In this thesis, we extend the sequentialselection procedure with normal responses called the Normal Distribution Design andprovided by Nga-Ting Chan. Focusing on normal responses, we use the view of Bayesianestimation to assume that the drug parameters can be three different beta distribution andpropose the cost function and sequential selecting procedures (adaptive and non-adaptive)to studying how much the prior distributions and procedures affect the cost function. Bythe computer simulations, we can verify that adaptive procedure reduces more the costfunction than non-adaptive one does.

參考文獻
[1] Leu, C.S. and Levin, B. (1999a). On the probability of correct selection in the Levin-Robbins sequential elimination procedure. Statistica Sinica 9, 879-891.
[2] Leu, C.S. and Levin, B. (1999b). Proof of a lower bound formula for the expected reward in the Levin-Robbins sequential elimination procedure. Sequential Analysis 18, 81-105.
[3] Leu, C.S. and Levin, B. (2007). A comparison of two procedures to select the best binomial population with sequential elimination of inferior populations. Journal of Statistical Planning and Inference 137, 245-263.
[4] Leu, C.S. and Levin, B. (2008a). A generalization of the Levin-Robbins procedure for binomial subset selection and recruitment problems. Statistica Sinica 18, 203-218.
[5] Leu, C.S. and Levin, B. (2008b). On a conjecture of Bechhofer, Kiefer, and Sobel for the Levin-Robbins-Leu binomial subset Selection procedures. Sequential Analysis 27, 106-125.
[6] Chan, N.T. (2015). Sequential Selection Procedures with Normal Responses. Master
dissertation. Hsinchu：Tsing Hua University, Taiwan.