本篇的研究目的為在三臂非劣性試驗下，計算三組治療組不同比例的樣本數，探討在何種比例下有最佳樣本數，以及最佳樣本數的檢定力是否有達到我們所設定的目標。三臂非劣性試驗包含實驗組、對照組和安慰劑組，也稱為黃金標準試驗，用於右設限資料，其中考慮到行政設限和失去追蹤設限，將資料應用在不同的半母數模型進行模擬，本研究採用的半母數模型包括Cox迴歸模型、AFT模型和PO模型(Proportional Odds Model)在相同條件下做比較。我們以三組治療組來當作共變異數，使用模型來估計迴歸係數，得以了解治療組之間的藥效差異，再利用大樣本的分佈計算樣本數與檢定力。最後，我們將發展的方法運用在膀胱癌復發的研究上。;The purpose of this study is to calculate the sample sizes for different allocation to three treatment groups in a three-arm non-inferiority trial. The aim is to determine the optimal sample size for each allocation and assess whether the achieved power meets our predefined target. The three-arm non-inferiority trial consists of an experimental group, a control group, and a placebo group, also known as a gold standard trial. It is designed for right-censored survival data, considering administrative censoring and lost to follow-up. The semiparametric models employed in this study include the Cox proportional hazards model, the accelerated failure time model, and the proportional odds model, which are compared under the same conditions. The three treatment groups are treated as covariates, and the models are used to estimate the coefficients, providing insights into the differences in treatment effects among the groups. The sample sizes and desired power are calculated based on the distribution of a large sample. Finally, the developed methodology is applied to a study on bladder cancer recurrence.
