本篇論文的研究目的是在三臂非劣性試驗下，針對主要終點為存活時間的右設限資料，計算三組治療組別不同比例所需的樣本數，並探討在何種比例下會得出最佳樣本數，同時確保最佳樣本數下的型一誤差和檢定力達到我們所設定的目標。研究將資料應用在不同的半母數模型來進行模擬，包括Cox迴歸模型、AFT模型和PO模型，其中假設生存時間為參數模型，包含Weibull、Rayleigh、Loglogistic、Pareto四種分配，我們以三組治療組別作為共變異數，利用模型估計迴歸係數，再利用大樣本的分布計算出樣本數和檢定力。最後，將此方法應用於結腸癌資料的研究中，以驗證其效果和可靠性。;The purpose of this study is to calculate the required sample size for three treatment groups in a three-arm non-inferiority trial, where the primary endpoint is survival time with right-censored data. We aim to determine the optimal sample size under different proportions of the three treatment groups, ensuring that the Type I error rate and power meet our predetermined targets. The study involves applying data to various semiparametric models for simulation, including the Cox regression model, Accelerated Failure Time (AFT) model, and Proportional Odds (PO) model. The survival time is assumed to follow parametric models, which include Weibull, Rayleigh, Loglogistic, and Pareto distributions. Using the three treatment groups as covariates, we estimate the regression coefficients with these models and then calculate the sample size and power using large-sample distributions. Finally, this method is applied to a colon cancer dataset to verify its effectiveness and reliability.
