使用R軟體計算Simon二階段第二期癌症臨床試驗設計的樣本數

Using R to Determine Sample Sizes for Simon Two-Stage Phase II Cancer Clinical Trial Designs

林千斐(Cian-Fei Lin)

指導教授 ： 吳建華

中原大學/理學院/應用數學研究所/碩士(2009年)

https://doi.org/10.6840/cycu200900836

摘要

本篇論文分成五大章節，第一章為緒論，主要說明研究背景及目的；第二章為文獻探討，探討與Simon提出的兩個二階段設計有關之文獻；第三章為研究方法，說明本篇論文的理論推導；第四章為結果分析，分析其演算法結果；最後一章為本篇論文的結論。
　　在新藥研究中，二階段設計扮演一個很重要的角色。Simon在1989年提出最佳化（optimal）和minimax兩個設計，由於Simon在文獻中只有顯示其結果的表格，其中包含在特定的顯著水準 和檢定力 之下所算出來的各階段預先設定值 與樣本數 ，但並沒有清楚描述最佳化和minimax兩個設計的樣本數是如何計算出來，在本篇論文中第二章針對相關文獻探討並整理，因此得知最佳化二階段設計是基於期望樣本數 而得到；而minimax二階段設計則是考慮最大樣本數 和期望樣本數 ，其中 為可容忍的最低有效治療率。
在臨床試驗的研究中，如何有效地取得適當的樣本數是備受關注的。以往的研究者依據Simon在文獻中的表格去做臨床試驗，但常受限於其所給定的顯著水準和檢定力條件與特定的樣本數，當這些特定的參數一旦改變，便無法得知所需的樣本數與各階段的預先設定值。且從過去的文獻中得知，其樣本數的計算是極為複雜且較沒效率，因此本篇論文的主要目的就是使用統計軟體R來計算樣本數，在此提供一個演算法是可以在給定任意的顯著水準和期望檢定力之下，透過電腦做精確的計算來得到樣本數。

關鍵字

二階段設計 ； 最佳化設計 ； minimax設計 ； 樣本數

並列摘要

This paper consists of five chapters. The first chapter is the introduction; it explains the research background and the purpose of the study. Chapter two is the literature review; it explores the literatures related to two Simon’s two-stage designs. Chapter three is the research method, it derives the theory of this research. Chapter four is the result of this study according to the algorithm. The last chapter is the conclusion.
Two-stage designs play a very important role in the study of new drugs. Simon(1989) proposed “optimal” and “minimax” two-stage designs. But Simon(1989) only showed the results form in the literature, containing pre-set value and sample size of every stage, which are calculated under particular significance level and power. But Simon(1989) didn’t clearly described how the sample size of ”optimal” and “minimax” two-stage designs is calculated. Chapter two is aimed at the discussion of literatures related to Simon’s two-stage designs. The optimal two-stage design is based on expected sample size , and the minimax two-stage design can be considered for the maximal sample size and expected sample size , where is the lowest treating rate effectively that can be tolerated.
In the study of clinical trial, how to effectively obtain the appropriate sample size is a major concern. The past researcher have done the clinical trial according to Simon’s form in the literature, but it’s often limited to the given significance level and power and particular sample size, as these particular parameters changes, it is unable to learn the sample size and pre-set value of every stage. According to the past literature, the calculation of sample size is extremely complicated and inefficiently, so the main purpose of this paper is using statistical software R to calculate the sample size. An algorithm of this paper can get the sample size through accurate computation of computer under a given arbitrary significance level and expected power.

並列關鍵字

optimal design ； two-stage design ； sample size ； minimax design

參考文獻

2.Koyama Tatsuki and Chen Heidi（2008）：Proper inference from Simon’s two–stage designs. Stat Med,27:3145-3154.

3.Simon R（1989）：Optimal Two-Stage Designs for Phase II Clinical Trials. Controlled Clinical Trials, 10, 1-10.

5.何錫勳（2006）：二階段設計中母體平均數之估計.國立成功大學統計學系碩士論文

7.林盛峰（2008）：二元反應臨床試驗的二階段設計之實務考量.國立台北大學統計學系碩士論文

1.Groulx Adrienne, Moon Kyung-hee (Kelly), Chung St. Clare（2007）：Using SAS® to Determine Sample Sizes for Traditional 2-Stage and Adaptive 2-Stage Phase II Cancer Clinical Trial Designs.