Gu Tianyuan, Chen Zhaojin, Soon Yu Yang, Wee Joseph, Tai Bee-Choo
Saw Swee Hock School of Public Health, National University of Singapore and National University Health System, 12 Science Drive, #10-01, Singapore, 117549, Singapore.
Department of Radiation Oncology, National University Cancer Institute, National University Hospital, Singapore, 119074, Singapore.
BMC Med Res Methodol. 2025 Jul 1;25(1):164. doi: 10.1186/s12874-025-02608-z.
Although the Cox time-varying coefficient (TVC) model has been developed to address non-proportional hazard (PH), its use remains underexplored. Instead, the restricted mean survival time (RMST) has been widely used in non-PH settings to quantify treatment effects using life expectancy ratio (LER) and life expectancy difference (LED).
This study explores a novel extension of the Cox TVC model under non-PH to generate LER and LED to enable a direct comparison with RMST based on flexible parametric survival model (FPM). An intensive simulation study was conducted to compare the performance of FPM to the Cox TVC model under PH and non-PH assumptions. The survival time t was assumed to follow the Piecewise Exponential distribution with various censoring patterns generated from the Uniform distribution. Both methods were evaluated via a randomised clinical trial of nasopharyngeal cancer exhibiting increasing treatment benefit.
Intensive simulations showed Cox TVC outperformed FPM under non-PH in terms of bias and coverage, with generally higher power observed in scenarios of crossing or diverging curves under low censoring. In real-world data, the FPM produced slightly larger LER and LED estimates than Cox TVC. Cox TVC has the advantage of assessing treatment effect at different milestones and detecting earlier difference when estimating using hazard ratio (HR).
Overall, Cox TVC is a viable option for summarising treatment effect using LER and LED under non-PH conditions. It would be beneficial to complement the reporting by providing estimates of HR at specific milestone to detect early differences.
尽管已开发出Cox时变系数（TVC）模型来处理非比例风险（PH）问题，但其应用仍未得到充分探索。相反，受限平均生存时间（RMST）已广泛用于非PH环境中，以使用预期寿命比（LER）和预期寿命差（LED）来量化治疗效果。
本研究探索了非PH条件下Cox TVC模型的一种新扩展，以生成LER和LED，从而能够与基于灵活参数生存模型（FPM）的RMST进行直接比较。进行了一项深入的模拟研究，以比较PH和非PH假设下FPM与Cox TVC模型的性能。假设生存时间t服从分段指数分布，并具有从均匀分布生成的各种删失模式。两种方法均通过一项显示治疗益处增加的鼻咽癌随机临床试验进行评估。
深入模拟显示，在非PH条件下，Cox TVC在偏差和覆盖率方面优于FPM，在低删失情况下交叉或发散曲线的场景中观察到的功效通常更高。在实际数据中，FPM产生的LER和LED估计值略大于Cox TVC。Cox TVC的优势在于能够在不同里程碑评估治疗效果，并在使用风险比（HR）进行估计时检测到更早的差异。
总体而言，Cox TVC是在非PH条件下使用LER和LED总结治疗效果的可行选择。通过提供特定里程碑处的HR估计值来检测早期差异，对补充报告将是有益的。
