The Cox proportional hazards model is the most widely used regression model in univariate survival analysis, yet extensions to bivariate survival data remain scarce. We propose two novel extensions based on a Lehmann-type representation of the survival function. The first, the simple Lehmann model, is a direct extension that retains a straightforward structure. The second, the generalized Lehmann model, allows greater flexibility by incorporating three distinct regression parameters and includes the simple Lehmann model as a special case. The models admit a direct interpretation in terms of survival probabilities, providing a transparent, fully semiparametric framework for assessing covariate effects on both marginal survival probabilities and their dependence, without requiring specification of a copula or frailty distribution. To estimate the regression parameters, we build on a pseudo-observation-based approach for bivariate survival data and extend it to the generalized model via a two-step procedure. We establish consistency and asymptotic normality of the resulting estimators. The proposed approach is illustrated through simulation studies and an application to data from the Global Retinoblastoma Outcome Study.

翻译：Cox比例风险模型是单变量生存分析中最广泛使用的回归模型，但其在双变量生存数据中的扩展仍然稀缺。我们基于生存函数的Lehmann型表示提出了两种新的扩展。第一种是简单Lehmann模型，这是一种保持直接结构的直接扩展。第二种是广义Lehmann模型，通过引入三个不同的回归参数允许更大的灵活性，并将简单Lehmann模型作为特例包含在内。这些模型在生存概率方面具有直接解释，提供了一个透明、完全半参数化的框架，用于评估协变量对边际生存概率及其依赖关系的影响，而无需指定copula或脆弱性分布。为了估计回归参数，我们基于双变量生存数据的伪观测方法，并通过两步程序将其扩展到广义模型。我们建立了所得估计量的一致性和渐近正态性。通过模拟研究和全球视网膜母细胞瘤结局研究数据的应用展示了所提出方法的有效性。