INSERM U1219 (Biostatistics team), ISPED, Université de Bordeaux, Bordeaux, France.
Department of Information Management, Chang Gung University, Guishan District, Taoyuan City, Taiwan.
Biom J. 2021 Feb;63(2):423-446. doi: 10.1002/bimj.201900306. Epub 2020 Oct 1.
In a meta-analysis framework, the classical approach for the validation of time-to-event surrogate endpoint is based on a two-step analysis. This approach often raises estimation issues. Recently, we proposed a one-step validation approach based on a joint frailty model. This approach was quite time consuming, despite parallel computing, due to individual-level frailties used to take into account heterogeneity in the data at the individual level. We now propose an alternative one-step approach for evaluating surrogacy, using a joint frailty-copula model. The model includes two correlated random effects treatment-by-trial interaction and a shared random effect associated with the baseline risks. At the individual level, the joint survivor functions of time-to-event endpoints are linked using copula functions. We used splines for the baseline hazard functions. We estimated parameters and hazard function using a semiparametric penalized marginal likelihood method, considering various numerical integration methods. Both individual-level and trial-level surrogacy were evaluated using Kendall's tau and coefficient of determination. The performance of the estimators was evaluated using simulation studies. The model was applied to individual patient data meta-analyses in advanced ovarian cancer to assess progression-free survival as a surrogate for overall survival, as part of the evaluation of new therapy. The model showed good performance and was quite robust regarding the integration methods and data variation, regardless of the surrogacy evaluation criteria. Kendall's Tau was better estimated using the Clayton copula model compared to the joint frailty model. The proposed model reduces the convergence and model estimation issues encountered in the two-step approach.
在荟萃分析框架中，验证生存时间替代终点的经典方法基于两步分析。这种方法经常会引起估计问题。最近，我们提出了一种基于联合脆弱性模型的一步验证方法。尽管采用了并行计算，但由于个体脆弱性用于考虑个体水平数据的异质性，因此该方法非常耗时。现在，我们提出了一种替代的一步方法来评估替代关系，使用联合脆弱性 - Copula 模型。该模型包括两个相关的随机效应治疗 - 试验交互作用和一个与基线风险相关的共享随机效应。在个体水平上，使用 Copula 函数链接生存时间终点的联合幸存者函数。我们使用样条函数来表示基线风险函数。我们使用半参数惩罚边际似然方法来估计参数和风险函数，同时考虑了各种数值积分方法。使用 Kendall's tau 和决定系数来评估个体水平和试验水平的替代关系。通过模拟研究评估了估计器的性能。该模型应用于晚期卵巢癌的个体患者数据荟萃分析中，以评估无进展生存期作为总生存期的替代指标，作为新疗法评估的一部分。该模型表现良好，并且无论替代关系评估标准如何，对于积分方法和数据变化都具有很强的稳健性。与联合脆弱性模型相比，Clayton Copula 模型更好地估计了 Kendall's Tau。与两步法相比，所提出的模型减少了收敛性和模型估计问题。
