Abstract
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.