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.

中文翻译：

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用于临床试验中失败时间替代终点的元分析验证的联合脆弱联结模型

在元分析框架中，验证事件时间替代终点的经典方法基于两步分析。这种方法通常会引发估计问题。最近，我们提出了一种基于联合脆弱模型的一步验证方法。尽管进行了并行计算，但这种方法非常耗时，因为用于考虑个体层面数据异质性的个体层面的弱点。我们现在提出了一种替代的一步法来评估代孕，使用联合脆弱联结模型。该模型包括两个相关的随机效应治疗-试验相互作用和与基线风险相关的共享随机效应。在个人层面，时间到事件端点的联合幸存者函数使用 copula 函数链接。我们使用样条作为基线危险函数。考虑到各种数值积分方法，我们使用半参数惩罚边际似然法估计参数和风险函数。使用 Kendall 的 tau 和决定系数评估个人水平和试验水平的代孕。使用模拟研究评估估计器的性能。该模型被应用于晚期卵巢癌的个体患者数据荟萃分析，以评估无进展生存期作为总生存期的替代指标，作为评估新疗法的一部分。无论代孕评估标准如何，该模型都表现出良好的性能，并且在整合方法和数据变化方面非常稳健。肯德尔 与关节脆弱模型相比，使用 Clayton copula 模型可以更好地估计 s Tau。所提出的模型减少了两步法中遇到的收敛和模型估计问题。