We propose counting process-based dimension reduction methods for right-censored survival data. Semiparametric estimating equations are constructed to estimate the dimension reduction subspace for the failure time model. Our methods address two limitations of existing approaches. First, using the counting process formulation, they do not require estimation of the censoring distribution to compensate for the bias in estimating the dimension reduction subspace. Second, the nonparametric estimation involved adapts to the structural dimension, so our methods circumvent the curse of dimensionality. Asymptotic normality is established for the estimators. We propose a computationally efficient approach that requires only a singular value decomposition to estimate the dimension reduction subspace. Numerical studies suggest that our new approaches exhibit significantly improved performance. The methods are implemented in the [Formula: see text] package [Formula: see text].

中文翻译：

---

用于删失结果的基于计数过程的降维方法

我们提出了用于右删失生存数据的基于计数过程的降维方法。构造半参数估计方程来估计失效时间模型的降维子空间。我们的方法解决了现有方法的两个局限性。首先，使用计数过程公式，它们不需要估计删失分布来补偿估计降维子空间时的偏差。其次，所涉及的非参数估计适应结构维度，因此我们的方法规避了维度灾难。为估计量建立渐近正态性。我们提出了一种计算高效的方法，只需要奇异值分解来估计降维子空间。数值研究表明，我们的新方法表现出显着提高的性能。这些方法在 [Formula: see text] 包 [Formula: see text] 中实现。