Exponential regression models with censored data are most widely used in practice. In the modeling process, there exist situations where the covariates are not directly observed but are observed after being contaminated by unknown functions of an observable confounder in a multiplicative manner. The problem of outlier detection is a fundamental and important problem in applied statistics. In this paper, we use a nonparametric regression method to adjust the covariates and recast the outlier detection issue into a high-dimensional regularization regression issue in the covariate-adjusted exponential regression model with censored data. We propose a smoothly clipped absolute deviation (SCAD) penalized likelihood method to detect the possible outliers, which features that the proposed method can simultaneously deal with outlier detection and estimations for the regression coefficients. The coordinate descent algorithm is employed to facilitate computation. Simulation studies are conducted to evaluate the finite-sample performance of our proposed method. An application to a German breast cancer study demonstrates the utility of the proposed method in practice.

带有审查数据的指数回归模型在实践中使用最为广泛。在建模过程中，存在以下情况：协变量不是直接观察到的，而是在被可观察的混杂器的未知函数以乘法方式污染后才观察到的。离群检测问题是应用统计中的一个基本而重要的问题。在本文中，我们使用非参数回归方法来调整协变量，并在带有删失数据的协变量调整指数回归模型中将离群值检测问题重塑为高维正则化回归问题。我们提出了一种平滑修剪的绝对偏差（SCAD）惩罚似然方法，以检测可能的离群值，其特点是该方法可以同时处理离群值的检测和回归系数的估计。坐标下降算法用于简化计算。进行仿真研究以评估我们提出的方法的有限样本性能。在德国乳腺癌研究中的一项应用证明了该方法在实践中的实用性。