臺灣博碩士論文加值系統

現今的臨床實驗大多是在比較新藥和舊藥的療效是否有差異，當臨床實驗結果新藥的療效比舊藥來的好，則藥廠才能把新藥上市。療效通常定義為有效及無效或成功及失敗等二元變項。要檢定療效是否有差異的檢定方法有許多種，例如：兩獨立樣本常態比例檢定、皮爾森卡方檢定及概似率檢定。從以往的經驗可以知道，在實驗設計裡加入共變數時，可以不用像上述的檢定方法，需要那麼多的樣本數，就得到相同的檢定力，也就是說，在相同的樣本數之下，有加入共變數的檢定方法，其檢定力會較高。
本論文將共變數加入檢定方法內，並利用羅吉斯迴歸模型來估計二個實驗組別的療效，亦即實驗成功的機率，但由此模型計算出的機率為給定共變數下的條件機率，為了計算出邊際成功機率，分別用二種方式來估計共變數的密度函數，進而推導出邊際成功機率的估計式，由此產生出二個新的檢定統計量，並由泰勒展開式及Delta方法導出統計量的近似分配。
為了檢驗二個新方法的可行性及適用性，將新的檢定方法與傳統檢定方法，針對不同的情況，利用蒙地卡羅模擬生成出的連續型共變數及二元應變數資料，進行檢定力及型一誤差比較分析。由模擬結果可以知道，新方法的檢定力相對於傳統方法的檢定力都有較高的趨勢。

Many clinical trials are conducted to develop a new drug or a new treatment comparing to an existing drug or a placebo. Usually, a new drug or a new treatment has to be proved to be more effective than that for the existing drug or placebo before practicing the new treatment or marketing the new drug. Suppose the effectiveness of a new drug is measured as a success (S) or a failure (F). There are many existing tests can be used to examine the effectiveness of the new drug for a binary response variable. For instance, a two independent sample Z test for proportions, the Pearson chi-square test, and the Likelihood ratio test. From the previous result, the power can be promoted by introducing the covariate into the experimental design under the same sample size. Thus, the purpose of this paper is to derive new tests that implying the information from a covariate. We use the logistic regression to construct the probability of success to construct the new test. Using the Monte Carlo simulations, the proposed methods have better powers than that for the conventional methods. Both proposed methods and conventional methods do not always preserve the type I errors.

1 前言
2 研究方法
2.1 傳統方法
2.1.1 皮爾森卡方檢定
2.1.2 概似率檢定
2.1.3 兩獨立樣本常態比例檢定
2.2 新方法
2.2.1 方法1
2.2.2 方法2
3 模擬分析
3.1 模擬方法
3.2 結果比較
4 討論
5 附錄 定理2-4証明
5.1 定理2証明
5.2 定理3証明
5.3 定理4証明
6 表格

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