Lymphovascular invasion (LVI) is an important prognostic marker for head and neck squamous cell carcinoma (HNSC), but the true effect of LVI on survival may be distorted by endogeneity arising from unmeasured confounding. Conventional one-stage conditional models and instrument-based two-stage estimators are prone to bias under endogeneity, and sufficiently strong instruments are often unavailable in practice. To address these challenges, we propose a semiparametric recursive copula framework that jointly specifies marginal models for both LVI, treated as an endogenous exposure, and a binary 2-year survival outcome, and links them through a flexible copula to account for latent confounding and accommodate censoring without requiring strong instruments. In two simulation studies, we systematically varied sample sizes, censoring rates from 0% to 60%, and endogeneity strengths, and assessed robustness under moderate model misspecification. The proposed copula framework exhibited reduced bias and improved interval coverage compared with both one-stage and two-stage approaches while maintaining robustness to moderate misspecification. We applied the method to HNSC cases with associated clinical and microRNA data from The Cancer Genome Atlas (n = 215), and found that LVI significantly reduced 2-year survival probability by approximately 47%, with a 95% confidence interval of -0.61 to -0.29 on the probability scale. The estimated positive dependence parameter indicates that the attenuation is driven by residual dependence between unobserved components of LVI and survival. Overall, the proposed copula framework yields more credible effect estimates for survival outcomes in the absence of strong instruments, mitigating biases due to endogeneity and censoring and strengthening quantitative evidence for HNSC research.

翻译：淋巴血管侵犯（LVI）是头颈部鳞状细胞癌（HNSC）的重要预后标志物，但LVI对生存的真实效应可能因未观测混杂导致的内生性而发生扭曲。传统的一阶段条件模型和基于工具变量的两阶段估计器在内生性下易产生偏误，且实践中常缺乏足够强的工具变量。为应对这些挑战，我们提出了一种半参数递归Copula框架，该框架联合指定了作为内生暴露的LVI与二元两年生存结局的边缘模型，并通过灵活的Copula函数将其连接，以刻画潜在混杂并适应删失数据，且无需强工具变量。在两项模拟研究中，我们系统改变了样本量、删失率（0%至60%）及内生性强弱，并评估了中等模型误设下的稳健性。与一阶段和两阶段方法相比，所提出的Copula框架展现出更低的偏误和更优的区间覆盖，同时对中等程度的模型误设保持稳健。我们将该方法应用于来自癌症基因组图谱（n = 215）的HNSC病例及其相关临床与微RNA数据，发现LVI使两年生存概率显著降低约47%，在概率尺度上的95%置信区间为-0.61至-0.29。估计的正相依参数表明，这种衰减是由LVI与生存中未观测成分之间的残差相依性驱动的。总体而言，所提出的Copula框架在缺乏强工具变量的情况下，为生存结局提供了更可信的效应估计，减轻了由内生性和删失导致的偏误，并为HNSC研究强化了定量证据。