We propose a two-stage estimation procedure for a copula-based model with semi-competing risks data, where the non-terminal event is subject to dependent censoring by the terminal event, and both events are subject to independent censoring. Under a copula-based model, the marginal survival functions of individual event times are specified by semiparametric transformation models, and the dependence between the bivariate event times is specified by a parametric copula function. For the estimation procedure, in the first stage, the parameters associated with the marginal of the terminal event are estimated only using the corresponding observed outcomes, and in the second stage, the marginal parameters for the non-terminal event time and the copula parameter are estimated via maximizing a pseudo-likelihood function based on the joint distribution of the bivariate event times. We derived the asymptotic properties of the proposed estimator and provided an analytic variance estimator for inference. Through simulation studies, we showed that our approach leads to consistent estimates with less computational cost and more robustness compared to the one-stage procedure developed in Chen (2012), where all parameters were estimated simultaneously. In addition, our approach demonstrates more desirable finite-sample performances over another existing two-stage estimation method proposed in Zhu et al. (2021).

翻译：本文针对半竞争风险数据提出一种两阶段估计方法，其中非终止事件受终止事件的相关删失影响，而两类事件均受独立删失影响。在基于Copula的模型中，各事件时间的边际生存函数由半参数变换模型指定，二元事件时间之间的相关性由参数化Copula函数刻画。估计过程分为两阶段：第一阶段仅利用终止事件对应的观测结果估计其边际参数；第二阶段通过最大化基于二元事件时间联合分布的伪似然函数，同时估计非终止事件时间的边际参数与Copula参数。我们推导了所提估计量的渐近性质，并给出了用于推断的解析方差估计量。模拟研究表明，与Chen（2012）提出的所有参数同时估计的单阶段方法相比，本文方法在计算成本更低、稳健性更强的情况下仍能得到一致估计量。此外，相较于Zhu等（2021）提出的另一种现有两阶段估计方法，本文方法在有限样本下展现出更优的绩效表现。