臨床試驗的實驗設計是醫學統計領域中一個重要議題。其試驗過程是利用適當的樣本數及統計方法來檢驗開發中藥物的安全性及有效性。這也是美國食品及藥物管理局（FDA）批准藥品上市前的必要程序。本研究的第一部份，探討有關臨床試驗中藥物治療率的比較問題，著重在發展中的新藥與目前標準治療方法間成功率的比較，並探討二階段檢定設計之策略。在樣本數相同的條件下，以兩群間成功個數的差距為檢定統計量，比較傳統單一階段與二階段設計的優劣，並用數值結果及檢力函數的圖形，來說明並展示二階段設計的性質。文中所討論的三種檢定設計，也應用在Cardenal et al. (1999) 所討論的臨床試驗問題，並從所需試驗樣本數與檢力的觀點給出適當的建議。此外，標準化之檢定統計量，亦是文獻中常使用之檢定統計量。之後亦檢視三種檢定設計在使用標準統計量下之呈現，並與Pocock (1977) 及 O'Brien & Fleming (1979) 所提出的方法比較。
本文的第二部分，我們考慮手術房的排程問題，這也是醫學研究中很重要的議題之一。臺灣的全民健保制度從1995年實施以來，健保局持續不斷改善健保制度，並嘗試對不同的薪資階層建立合理的費率標準。為配合健保制度的調整，醫院必須更加注意營運成本的控管。由於手術房的營收是醫院主要的收入來源之一，為了維持收支平衡，手術房的有效管理是當務之急。
為了控制營運成本並提升手術房的使用率，我們對手術時間配適分佈，利用統計方法建立手術時間之預測模型，之後配合手術時間預測來設計可行且有效的手術房排程策略，以期達到節省手術房超時成本之目的。本文以南部某醫學中心婦產科手術房的資料為例，利用對數常態及混合對數常態分佈來配適手術時間，並以最佳配適分佈來評估某些手術組合的超時機率是否與該組合由資料估計的超時機率近似。其中，最佳配適分佈的選擇是透過一些模型選擇的標準，包括資訊準則及拔靴法概似比檢定的評估。為了簡化排程的程序，並建立一套標準的排程方式，我們將手術依時間分成三類，且依各手術的困難度，再將每個手術分成三個階段。基於分類的結果，每類給定一適當的分數並提出一套排程的方式，稱為最小分數排程策略。依據此策略重排後的結果與原始排程比較發現，新提出的排程方式可大幅降低超時的人力成本。

The design of clinical trials is one of the important problems in medical statistics. Its main purpose is to determine the methodology and the sample size required of a testing study to examine the safety and efficacy of drugs. It is also a part of the Food and Drug Administration approval process. In this thesis, we first study the comparison of the efficacy of drugs in clinical trials. We focus on the two-sample comparison of proportions to investigate testing strategies based on two-stage design. The properties and advantages of the procedures from the proposed testing designs are demonstrated by numerical results, where comparison with the classical method is made under the same sample size. A real example discussed in Cardenal et al. (1999) is provided to explain how the methods may be used in practice. Some figures are also presented to illustrate the pattern changes of the power functions of these methods. In addition, the proposed procedure is also compared with the Pocock (1997) and O’Brien and Fleming (1979) tests based on the standardized statistics.
In the second part of this work, the operating room scheduling problem is considered, which is also important in medical studies. The national health insurance system has been conducted more than ten years in Taiwan. The Bureau of National Health Insurance continues to improve the national health insurance system and try to establish a reasonable fee ratio for people in different income ranges. In accordance to the adjustment of the national health insurance system, hospitals must pay more attention to control the running cost. One of the major hospital's revenues is generated by its surgery center operations. In order to maintain financial balance, effective operating room management is necessary.
For this topic, this study focuses on the model fitting of operating times and operating room scheduling. Log-normal and mixture log-normal distributions are identified to be acceptable statistically in describing these operating times. The procedure is illustrated through analysis of thirteen operations performed in the gynecology department of a major teaching hospital in southern Taiwan. The best fitting distributions are used to evaluate performances of some operating combinations on daily schedule, which occurred in real data. The fitted distributions are selected through certain information criteria and bootstrapping the log-likelihood ratio test. Moreover, we also classify the operations into three different categories as well as three stages for each operation. Then based on the classification, a strategy of efficient scheduling is proposed. The benefits of rescheduling based on the proposed strategy are compared with the original scheduling observed.

1 Introduction 1
1.1 Designs for clinical trials 2
1.2 Operating time prediction and operating room scheduling 3
2 Preliminaries 5
2.1 Group sequential design 5
2.1.1 Pocock's Test 5
2.1.2 O'Brien-Fleming's test 7
2.1.3 Simon's two stage design 8
2.2 Finite mixture models 10
2.2.1 Mixtures with normal components 11
2.2.2 Assessing the number of components in mixture models 12
2.3 Strategies of operating room scheduling 14
3 Two stage designs for two-sample proportion test 17
3.1 Introduction 17
3.2 Testing procedure based on integer difference of responses 19
3.2.1 Classical single-stage testing design (CS) 20
3.2.2 Two-stage testing with early rejection of H0 (TS) 21
3.2.3 Mixed single- and two-stage testing design (MS) 22
3.2.4 Optimality criteria 23
3.2.5 Numerical results of optimal testing designs 24
3.2.6 Application 28
3.3 Comparisons with the results based on the standardized statistics 32
3.4 Two-stage group sequential test for two treatments with normal responses 36
3.4.1 Test procedure 36
3.4.2 Determination of $N_2(S_1^2 )$ 38
3.4.3 Power function of test 38
3.5 Discussion and conclusion 40
Appendix A 41
A.1 Phases of clinical development 41
A.2 Normal approximation 43
A.3 Proof of Theorem 3.1 44
4 Surgical operating time modeling and combinations for scheduling with
mixture log-normal distributions 47
4.1 Introduction 47
4.2 Model fitting and model selection 50
4.2.1 Normal mixture distribution and density estimation 51
4.2.2 Models selection for the operating time distribution 51
4.3 Evaluation of the fitted models 53
4.3.1 Probability of exceeding time and confidence interval 53
4.3.2 Results of some specified operation combinations 54
4.4 The classification of operations based on operating time 55
4.4.1 Kruskal-Wallis test and multiple comparison 55
4.4.2 Evaluation of combinations based on classification results 56
4.4.3 Minimum grading scheduling strategy 59
4.5 Discussion and conclusion 61
Appendix B 63
B.1 Tables and Figures for Section 4.2 63
B.2 Tables and Figures for Section 4.3 65
B.3 Tables and Figures for Section 4.4 70
Reference 78

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