Double-slicing assisted sufficient dimension reduction for high-dimensional censored data
Double-slicing assisted sufficient dimension reduction for high-dimensional censored data
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DOI：
10.1214/19-aos1880
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发表时间：
2020-08
影响因子：
4.5
通讯作者：
Shanshan Ding;W. Qian;Lan Wang
中科院分区：
文献类型：
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作者：
Shanshan Ding;W. Qian;Lan Wang
本文提供了一个统一的框架和一个有效的算法来分析高维生存数据在弱建模假设。特别是，它既不施加参数分布假设，也不施加线性回归假设。它仅假设生存时间T通过协变量ΓX的低维线性组合依赖于高维协变量向量X。在给定协变量的情况下，允许删失时间有条件地独立于生存时间。这个一般框架包括许多流行的参数和半参数生存回归模型作为特例。所提出的算法产生了一些实际有用的输出与理论保证，包括一致的估计的充分降维子空间的T| X，T的条件分布函数的一致相合Kaplan-Meier型估计和条件分位数生存时间的相合估计。我们的渐近结果显着地扩展了经典的删失数据的充分降维理论（特别是Li et al. 1999）和著名的非参数Kaplan-Meier估计的设置，其中协变量的数量p与样本大小n呈指数快速发散。我们通过模拟和一个真实的数据例子证明了所提出的新估计器的良好性能。
This paper provides a unified framework and an efficient algorithm for analyzing high-dimensional survival data under weak modeling assumptions. In particular, it imposes neither parametric distributional assumption nor linear regression assumption. It only assumes that the survival time T depends on a high-dimensional covariate vector X through low-dimensional linear combinations of covariates ΓX. The censoring time is allowed to be conditionally independent of the survival time given the covariates. This general framework includes many popular parametric and semiparametric survival regression models as special cases. The proposed algorithm produces a number of practically useful outputs with theoretical guarantees, including a consistent estimate of the sufficient dimension reduction subspace of T |X, a uniformly consistent Kaplan-Meier type estimator of the conditional distribution function of T and a consistent estimator of the conditional quantile survival time. Our asymptotic results significantly extend the classical theory of sufficient dimension reduction for censored data (particularly that of Li et al. 1999) and the celebrated nonparametric Kaplan-Meier estimator to the setting where the number of covariates p diverges exponentially fast with the sample size n. We demonstrate the promising performance of the proposed new estimators through simulations and a real data example.