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arXiv 2104.01707stat.MEstat.CO
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高维半参数加速失效时间模型的可缩放算法

Scalable algorithms for semiparametric accelerated failure time models in high dimensions

Piotr M. Suder, Aaron J. Molstad

摘要:

半参数加速失效时间(AFT)模型是考克斯比例风险模型的一种有用的替代方法,特别是当常数风险比假设不成立时。然而,用于拟合AFT模型的基于秩的标准通常是不可微的,这在高维设置中构成了计算挑战。在这篇文章中,我们提出了一个新的交替方向方法的乘数算法拟合半参数AFT模型,通过最小化惩罚的基于秩的损失函数。我们的算法在受试者数量和预测因子数量方面都有很好的扩展性,并且可以轻松地适应各种流行的处罚。为了改善调整参数的选择,我们提出了一个新的标准,避免了一些常见的问题,交叉验证与删失响应。通过广泛的模拟研究,我们表明,我们的算法和软件比现有的方法(只能适用于特殊情况)要快得多,我们表明,估计最小化惩罚基于秩的标准往往优于替代估计最小化惩罚加权最小二乘标准。九个癌症数据集的应用程序进一步表明,基于秩的半参数AFT模型的估计量是有竞争力的估计,假设比例风险模型在高维设置,而加权最小二乘估计往往不是。实现该算法的软件包以及一组辅助函数可在github.com/ajmolstad/penAFT下载。

英文摘要:

Semiparametric accelerated failure time (AFT) models are a useful alternative to Cox proportional hazards models, especially when the assumption of constant hazard ratios is untenable. However, rank-based criteria for fitting AFT models are often non-differentiable, which poses a computational challenge in high-dimensional settings. In this article, we propose a new alternating direction method of multipliers algorithm for fitting semiparametric AFT models by minimizing a penalized rank-based loss function. Our algorithm scales well in both the number of subjects and number of predictors; and can easily accommodate a wide range of popular penalties. To improve the selection of tuning parameters, we propose a new criterion which avoids some common problems in cross-validation with censored responses. Through extensive simulation studies, we show that our algorithm and software is much faster than existing methods (which can only be applied to special cases), and we show that estimators which minimize a penalized rank-based criterion often outperform alternative estimators which minimize penalized weighted least squares criteria. Application to nine cancer datasets further demonstrates that rank-based estimators of semiparametric AFT models are competitive with estimators assuming proportional hazards model in high-dimensional settings, whereas weighted least squares estimators are often not. A software package implementing the algorithm, along with a set of auxiliary functions, is available for download at github.com/ajmolstad/penAFT.

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