Modelling multivariate survival data is complicated by the complex association structure among the responses. To balance model flexibility and interpretability, we propose a semiparametric copula model to modulate multivariate survival data, with the marginal distributions of the response components described by semiparametric linear transformation models. To conduct inference about the model parameters, we develop a two-stage maximum likelihood method and a three-stage pseudo-likelihood estimation procedure. We investigate the impact of model misspecification on the estimation of covariate effects and identify a scenario in which consistent estimation of the marginal parameters is retained even when the copula model is misspecified. The proposed methods are justified both theoretically and empirically. An application to a real dataset is provided to demonstrate the utility of the proposed method.

中文翻译：

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半参数Copula模型下的多元生存数据分析

由于响应之间复杂的关联结构，多变量生存数据的建模变得复杂。为了平衡模型的灵活性和可解释性，我们提出了一种半参数 copula 模型来调节多元生存数据，并通过半参数线性变换模型描述响应分量的边缘分布。为了对模型参数进行推断，我们开发了两阶段最大似然法和三阶段伪似然估计程序。我们研究了模型错误指定对协变量效应估计的影响，并确定了一种场景，即使在 copula 模型指定错误的情况下，仍保留边缘参数的一致估计。所提出的方法在理论上和经验上都是合理的。