本研究主要目在於探討於右設限資料下，不做存活分布設定達成三臂非劣性檢定所需的最小樣本數，並進一步分析在何種樣本分配比例下，三個治療組別的配置最接近理論上的最佳比例。此外，亦評估在最佳樣本配置下，型一誤差與檢定力是否能達到預設水準。研究中採用三種半母數模型進行分析，分別為 Cox 比例風險模型（Cox PH model）、加速失敗時間模型（AFT model），以及比例勝算模型（PO model）。本研究採用兩種無母數方法——核密度估計（KDE）與 B-spline hazard 方法，來進行樣本分配的估計，進而推估迴歸係數的變異數與共變異數，並比較兩者在估計表現上的優劣。本研究將所提出的方法應用於一筆非小細胞肺癌（NSCLC）臨床試驗資料中，最後與先前的參數方法來做比較，以驗證其實用性。;This study aims to determine the minimum required sample size to achieve a three-arm non-inferiority test under right-censored survival data without assuming a specific survival distribution. Furthermore, it investigates the sample allocation ratios under which the configuration of the three treatment groups most closely approximates the theoretical optimal allocation. In addition, the study evaluates whether, under the optimal allocation, the type I error rate and statistical power can achieve the prespecified levels. Three semiparametric models are employed for analysis: the Cox proportional hazards model (Cox PH model), the accelerated failure time model (AFT model), and the proportional odds model (PO model). In this study, two nonparametric methods—Kernel Density Estimation (KDE) and the B-spline hazard method—are employed to estimate the sample allocation. Based on this, the variances and covariances of the regression coefficients are derived. A comparative analysis is then conducted to assess which method yields superior estimation accuracy. The proposed methods are then applied to a real clinical trial dataset on non-small cell lung cancer (NSCLC), and the results are compared with those from previous parametric approaches to validate their effectiveness and practical utility.
