In survival analysis, estimating the failure time distribution is an important and difficult task, since usually the data is subject to censoring. Specifically, in this paper we consider current status data, a type of data where all of the observations are censored. The format of the data is such that the failure time is restricted to knowledge of whether or not the failure time exceeds a random monitoring time. We propose a flexible kernel machine approach for estimation of the failure time expectation as a function of the covariates, with current status data. In order to obtain the kernel machine decision function, we minimize a regularized version of the empirical risk with respect to a new loss function. Using finite sample bounds and novel oracle inequalities, we prove that the obtained estimator converges to the true conditional expectation for a large family of probability measures. Finally, we present a simulation study and an analysis of real-world data that compares the performance of the proposed approach to existing methods. We show empirically that our approach is comparable to current state of the art, and in some cases is even better.

中文翻译：

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用于当前状态数据的内核机器

在生存分析中，估计故障时间分布是一项重要且困难的任务，因为通常数据会受到审查。具体来说，在本文中，我们考虑当前状态数据，这是一种所有观察都被删失的数据。数据的格式使得故障时间仅限于了解故障时间是否超过随机监控时间。我们提出了一种灵活的内核机器方法，用于估计作为协变量函数的故障时间期望，以及当前状态数据。为了获得内核机器决策函数，我们最小化了关于新损失函数的经验风险的正则化版本。使用有限样本边界和新的预言机不等式，我们证明所获得的估计量收敛于大量概率测度的真实条件期望。最后，我们提出了一项模拟研究和对现实世界数据的分析，将所提出的方法与现有方法的性能进行了比较。我们凭经验表明，我们的方法可与当前最先进的技术相媲美，在某些情况下甚至更好。