Department of Biostatistics, Bloomberg School of Public Health, Johns Hopkins University, Baltimore, Maryland.
Department of Biostatistics, School of Public Health, University of Washington, Seattle, Washington.
Am J Epidemiol. 2018 Feb 1;187(2):358-365. doi: 10.1093/aje/kwx225.
We present a method for improving estimation in linear regression models in samples of moderate size, using shrinkage techniques. Our work connects the theory of causal inference, which describes how variable adjustment should be performed with large samples, with shrinkage estimators such as ridge regression and the least absolute shrinkage and selection operator (LASSO), which can perform better in sample sizes seen in epidemiologic practice. Shrinkage methods reduce mean squared error by trading off some amount of bias for a reduction in variance. However, when inference is the goal, there are no standard methods for choosing the penalty "tuning" parameters that govern these tradeoffs. We propose selecting the penalty parameters for these shrinkage estimators by minimizing bias and variance in future similar data sets drawn from the posterior predictive distribution. Our method provides both the point estimate of interest and corresponding standard error estimates. Through simulations, we demonstrate that it can achieve better mean squared error than using cross-validation for penalty parameter selection. We apply our method to a cross-sectional analysis of the association between smoking and carotid intima-media thickness in the Multi-Ethnic Study of Atherosclerosis (multiple US locations, 2000-2002) and compare it with similar analyses of these data.
我们提出了一种在中等大小样本中使用收缩技术改进线性回归模型估计的方法。我们的工作将因果推理理论（描述了如何在大样本中进行变量调整）与收缩估计器（如岭回归和最小绝对收缩和选择算子（LASSO））联系起来，这些估计器在流行病学实践中常见的样本大小下表现更好。收缩方法通过牺牲一定程度的偏差来减少方差，从而降低均方误差。然而，当推断是目标时，对于控制这些权衡的惩罚“调整”参数的选择，没有标准方法。我们建议通过最小化后验预测分布中抽取的未来类似数据集的偏差和方差来选择这些收缩估计器的惩罚参数。我们的方法提供了感兴趣的点估计值和相应的标准误差估计值。通过模拟，我们证明它可以比使用交叉验证选择惩罚参数获得更好的均方误差。我们将我们的方法应用于多民族动脉粥样硬化研究（多个美国地点，2000-2002 年）中吸烟与颈动脉内膜中层厚度之间关联的横断面分析，并将其与这些数据的类似分析进行比较。
