本研究的主要目的是深入探討淨效應(net effect)與比例效應(fraction effect)在三臂非劣性試驗中的表現，並確定所需的樣本數，以確保型一誤差及檢定力達到預期水平。三臂非劣性試驗包括了實驗組、對照組和安慰劑組，這有助於更全面地評估新藥物的效果。在研究中我們考慮主要終點為右設限的存活資料，包括行政設限與失去追蹤設限，在模型的部分，我們採用了三種半母數模型，分別是Cox比例風險模型、加速失效時間模型(AFT模型)和Proportional Odds模型(PO模型)，針對這三個模型進行各種不同分配比例的最佳樣本數分析。最終，我們將研究成果應用於膀胱癌復發的實際資料中，計算各組別在不同情境下所需的樣本數。;The main objective of this study is to delve into the performance of net effect and fraction effect in three-arm non-inferiority trials, and to determine the required sample size to ensure that Type I error and power reach the expected levels. Three-arm non-inferiority trials, encompass experimental, control, and placebo arms, aiding in a more comprehensive evaluation of the efficacy of new drugs. In this study, we consider the primary endpoint as right-censored survival data, including administrative censoring and loss to follow-up censoring. In terms of modeling, we employ three semi-parametric models, namely the Cox proportional hazards model, Accelerated Failure Time (AFT) model, and Proportional Odds (PO) model, conducting various analyses to determine the optimal sample size for each model under different allocation ratios. Ultimately, we apply the findings of the study to real data on bladder cancer recurrence, calculating the required sample sizes for each group under different scenarios.
