In this paper we use Cox's regression model to fit failure time data with continuous informative auxiliary variables in the presence of a validation subsample. We first estimate the induced relative risk function by kernel smoothing based on the validation subsample, and then improve the estimation by utilizing the information on the incomplete observations from non-validation subsample and the auxiliary observations from the primary sample. Asymptotic normality of the proposed estimator is derived. The proposed method allows one to robustly model the failure time data with an informative multivariate auxiliary covariate. Comparison of the proposed approach with several existing methods is made via simulations. Two real datasets are analyzed to illustrate the proposed method.

中文翻译：

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具有连续信息辅助协变量的故障时间回归。

在本文中，我们使用Cox回归模型在存在验证子样本的情况下使用连续的信息辅助变量拟合故障时间数据。我们首先基于核实子样本通过核平滑来估计诱发的相对风险函数，然后利用来自非核实子样本的不完整观测值和来自主样本的辅助观测值的信息来改进估计。推导了所提出估计量的渐近正态性。所提出的方法允许使用信息多变量辅助协变量对故障时间数据进行鲁棒建模。通过仿真将提出的方法与几种现有方法进行了比较。分析了两个真实的数据集以说明所提出的方法。