The pseudo-observations approach has been gaining popularity as a method to estimate covariate effects on censored survival data. It is used regularly to estimate covariate effects on quantities such as survival probabilities, restricted mean life, cumulative incidence, and others. In this work, we propose to generalize the pseudo-observations approach to situations where a bivariate failure-time variable is observed, subject to right censoring. The idea is to first estimate the joint survival function of both failure times and then use it to define the relevant pseudo-observations. Once the pseudo-observations are calculated, they are used as the response in a generalized linear model. We consider two common nonparametric estimators of the joint survival function: the estimator of Lin and Ying (1993) and the Dabrowska estimator (Dabrowska, 1988). For both estimators, we show that our bivariate pseudo-observations approach produces regression estimates that are consistent and asymptotically normal. Our proposed method enables estimation of covariate effects on quantities such as the joint survival probability at a fixed bivariate time point, or simultaneously at several time points, and consequentially can estimate covariate-adjusted conditional survival probabilities. We demonstrate the method using simulations and an analysis of two real-world datasets.

翻译：伪观测方法作为一种估计协变量对删失生存数据影响的手段，正日益受到关注。该方法常用于估计协变量对生存概率、限制平均寿命、累积发生率等指标的影响。本研究提出将伪观测方法推广至存在右删失的双变量失效时间观测场景。其核心思想是先估计两个失效时间的联合生存函数，进而基于该函数定义相应的伪观测值。计算得到伪观测值后，将其作为广义线性模型的响应变量。我们采用两种常见的非参数联合生存函数估计量：Lin和Ying（1993）提出的估计量以及Dabrowska估计量（Dabrowska, 1988）。对于这两种估计量，我们证明所提出的双变量伪观测方法能够产生具有一致性和渐近正态性的回归估计。该方法可用于估计协变量对固定双变量时间点的联合生存概率、多个时间点的联合生存概率的影响，进而能够估计协变量调整后的条件生存概率。我们通过模拟实验和两个真实数据集的分析验证了该方法的有效性。