We propose a highly flexible distributional copula regression model for bivariate time-to-event data in the presence of right-censoring. The joint survival function of the response is constructed using parametric copulas, allowing for a separate specification of the dependence structure between the time-to-event outcome variables and their respective marginal survival distributions. The latter are specified using well-known parametric distributions such as the log-Normal, log-Logistic (proportional odds model), or Weibull (proportional hazards model) distributions. Hence, the marginal univariate event times can be specified as parametric (also known as Accelerated Failure Time, AFT) models. Embedding our model into the class of generalized additive models for location, scale and shape, possibly all distribution parameters of the joint survival function can depend on covariates. We develop a component-wise gradient-based boosting algorithm for estimation. This way, our approach is able to conduct data-driven variable selection. To the best of our knowledge, this is the first implementation of multivariate AFT models via distributional copula regression with automatic variable selection via statistical boosting. A special merit of our approach is that it works for high-dimensional (p>>n) settings. We illustrate the practical potential of our method on a high-dimensional application related to semi-competing risks responses in ovarian cancer. All of our methods are implemented in the open source statistical software R as add-on functions of the package gamboostLSS.

翻译：我们针对存在右删失的二元时间-事件数据，提出了一种高度灵活的分布Copula回归模型。该模型利用参数Copula构建响应变量的联合生存函数，从而允许对时间-事件结果变量之间的相依结构及其各自的边际生存分布进行独立设定。边际分布采用常见的参数分布进行设定，例如对数正态分布、对数Logistic分布（比例优势模型）或Weibull分布（比例风险模型）。因此，边际单变量事件时间可被设定为参数模型（亦称为加速失效时间模型）。通过将我们的模型嵌入位置、尺度与形状的广义可加模型框架，联合生存函数的所有分布参数均可依赖于协变量。我们开发了一种基于分量梯度提升的估计算法。通过这种方式，我们的方法能够执行数据驱动的变量选择。据我们所知，这是首次通过分布Copula回归结合统计提升实现自动变量选择的多变量加速失效时间模型实现。我们方法的一个突出优势是能够处理高维（p>>n）设定。我们在卵巢癌半竞争风险响应相关的高维应用中展示了本方法的实际潜力。所有方法均在开源统计软件R中实现，作为gamboostLSS软件包的附加函数。