Application of shrinkage techniques in logistic regression analysis: a case study
Application of shrinkage techniques in logistic regression analysis: a case study
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DOI：
10.1111/1467-9574.00157
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发表时间：
2001-03-01
影响因子：
1.5
通讯作者：
Habbema, JDF
中科院分区：
文献类型：
--
作者：
Steyerberg, EW;Eijkemans, MJC;Habbema, JDF
逻辑回归分析很可能用于开发二分医疗结果的预测模型，例如短期死亡率。当数据集与所研究的协变量数量相比较小时，收缩技术可以改善预测。我们比较了收缩技术的三种变体的性能：1）线性收缩因子，它使用相同的因子收缩所有系数； 2）惩罚最大似然（或岭回归），其中将惩罚因子添加到似然函数中，以便根据每个协变量的方差单独缩小系数； 3）Lasso，通过对标准化协变量的系数绝对值之和设置约束，将一些系数缩小到零。构建Logistic回归模型来预测急性心肌梗死后30天的死亡率。小数据集是根据大型随机对照试验创建的，其中一半提供了独立的验证数据。我们发现，与标准最大似然估计相比，所有三种收缩技术都改进了预测的校准。这项研究表明，收缩是克服医疗数据中一些过度拟合问题的宝贵工具。
Logistic regression analysis may well be used to develop a predictive model for a dichotomous medical outcome, such as short-term mortality. When the data set is small compared to the number of covariables studied, shrinkage techniques may improve predictions. We compared the performance of three variants of shrinkage techniques: 1) a linear shrinkage factor, which shrinks all coefficients with the same factor; 2) penalized maximum likelihood (or ridge regression), where a penalty factor is added to the likelihood function such that coefficients are shrunk individually according to the variance of each covariable; 3) the Lasso, which shrinks some coefficients to zero by setting a constraint on the sum of the absolute values of the coefficients of standardized covariables.Logistic regression models were constructed to predict 30-day mortality after acute myocardial infarction. Small data sets were created from a large randomized controlled trial, half of which provided independent validation data. We found that all three shrinkage techniques improved the calibration of predictions compared to the standard maximum likelihood estimates. This study illustrates that shrinkage is a valuable tool to overcome some of the problems of overfitting in medical data.