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Application of Shrinkage Techniques in Logistic Regression Analysis: A Case Study

机译：收缩技术在Logistic回归分析中的应用

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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.
机译：逻辑回归分析可以很好地用于建立二分医疗结果（例如短期死亡率）的预测模型。当数据集与研究的协变量数量相比较小时，收缩技术可能会改善预测。我们比较了三种收缩技术的性能：1）线性收缩系数，它以相同的系数收缩所有系数； 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，以便根据每个协变量的方差分别缩小系数； 3）套索，通过设置标准化协变量系数的绝对值的总和来将一些系数缩小为零，构建Logistic回归模型来预测急性心肌梗塞后30天的死亡率。小数据集是从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善了预测的校准。这项研究表明，收缩是解决医学数据过拟合问题的宝贵工具。

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