此篇研究提出了一種統計方法，用於規劃和評估非劣性臨床試驗的樣本數，採用黃金標準設計，用於具有右設限的事件發生數據，其中，黃金標準設計包括實驗藥物、活性對照要與安慰劑，另外，在右設限的部分，行政設限與失去追蹤設限都有被考慮進去。本文的研究目的是計算三臂非劣性試驗的最佳的樣本數以及對於各治療組別的最佳分配，同時，在對立假設下，可以達到所希望的檢定力。使用的方法是一種半參數的方法，使用的模型為AFT模型，並假設試驗終點指標分別為Weibull、Loglogistic以及Lognormal分配去做討論，這三個分配都是在醫學研究中常用的分配。另外，我們也跟Karola等人在2013年提出的方法做比較，他們使用的模型為Cox迴歸模型，此模型具有比例風險的假設，並且假設試驗終點指標為Weibull，根據我們的結果，發現Cox迴歸模型在固定個樣本數的分配比例下的最佳樣本數不會受到Weibull的形狀參數影響；反之，AFT模型則會受到Weibull的形狀參數的改變而改變。最後，我們將提出的方法應用到膀胱癌復發的臨床試驗上，並與參數模型、Cox迴歸模型作比較。

This study presents a statistical method for planning and evaluating sample sizes for non-inferiority clinical trials using a gold-standard design for time-to-event data with right-censored data, where the gold-standard design includes an experimental treatment, an active control and a placebo. Additionally, in the right-censored data, both administrative and lost to follow-up were taken into account. The purpose of this study is to calculate the optimal sample size for a three-arm non-inferiority trial and the optimal allocation to each treatment group, and at the same time, a desired power can be attained under the alternative hypothesis. The method used is a semiparametric approach, and the model used is the AFT model. It is assumed that the endpoints of the trial are Weibull, Loglogistic, and Lognormal distribution, which are commonly used in medical research. In addition, we also compare with the method proposed by Karola et al. in 2013. The model they used is Cox proportional hazards model, which has a proportional hazards assumption and assumes that the endpoints to be Weibull distributed. According to our results, it is found that the optimal number of sample size of the Cox proportional hazards model under the fixed proportion sample size of each treatment will not be affected by the shape parameter of Weibull; conversely, the AFT model will be changed by the change of the shape parameter of Weibull. Finally, we applied the proposed method to a clinical trial of bladder cancer recurrence and compared it with a parametric model and a Cox proportional hazards model.

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