Statistical Analysis of play-the-winner Design for Continuous Response

• Main Authors: Shi-Qiang Chen, 陳時強
• Other Authors: Chien-Hua Wu
• Format: Others
• Language: zh-TW
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/25516892788834998976

碩士 === 中原大學 === 應用數學研究所 === 99 === In this paper, according to the two response adaptive designs established by Anastasia Ivanova, Atanu Biswas and Anna Lurie in 2005, both designs were followed the new rule called drop-the-loser rule. The rule was evolved from play-the-winner rule. Two designs were used in a trial comparing and assign treatments. From the initial two treatments are used in equal allocation, and then re-assigned to two treatments. The goal is to assign more subjects to the better treatment on average. Assume that treatment outcomes are normally distribution T1~N(mu1,sigma1),T2~N(mu2,sigma2)and mu1>=mu2. This means treatment one is better than treatment two. Using E(T)(means the average response over two treatments) and pi0(allocation proportion to treatment one) to see whether it reached the goal. E(T) is a measurement of central tendency, and it can be seen from the result that every designed E(T) will tend to mu1, it means that assign subjects to treatment one is more than treatment two. And pi0 is the allocation proportion to treatment one, all pi0 are greater than 0.5. The result in E(T) and pi0 is the same. Therefore, the result and the goal is the same.