For high dimensional gene expression data, one important goal is to identify a small number of genes that are associated with progression of the disease or survival of the patients. In this paper, we consider the problem of variable selection for multivariate survival data. We propose an estimation procedure for high dimensional accelerated failure time (AFT) models with bivariate censored data. The method extends the Buckley-James method by minimizing a penalized \(L_2\) loss function with a penalty function induced from a bivariate spike-and-slab prior specification. In the proposed algorithm, censored observations are imputed using the Kaplan-Meier estimator, which avoids a parametric assumption on the error terms. Our empirical studies demonstrate that the proposed method provides better performance compared to the alternative procedures designed for univariate survival data regardless of whether the true events are correlated or not, and conceptualizes a formal way of handling bivariate survival data for AFT models. Findings from the analysis of a myeloma clinical trial using the proposed method are also presented.

对于高维基因表达数据，一个重要目标是识别少数与疾病进展或患者生存相关的基因。在本文中，我们考虑了多变量生存数据的变量选择问题。我们提出了一种具有双变量删失数据的高维加速故障时间 (AFT) 模型的估计程序。该方法通过最小化惩罚\(L_2\)扩展了 Buckley-James 方法具有从双变量尖峰和平板先验规范诱导的惩罚函数的损失函数。在所提出的算法中，使用 Kaplan-Meier 估计器估算删失的观测值，这避免了对误差项的参数假设。我们的实证研究表明，无论真实事件是否相关，与为单变量生存数据设计的替代程序相比，所提出的方法都提供了更好的性能，并概念化了处理 AFT 模型的双变量生存数据的正式方法。还介绍了使用所提出的方法分析骨髓瘤临床试验的结果。