罕见事件的Firth逻辑斯谛回归：精确的效应估计AND预测？
Firth's logistic regression with rare events: accurate effect estimates AND predictions?
摘要：
第五类逻辑斯谛回归已成为小样本二元结果分析的标准方法。虽然它减少了系数的最大似然估计中的偏差，但在预测概率中引入了朝向1/2的偏差。结果的不平衡性越强，预测概率的偏差就越严重。我们提出了两个简单的修改的第一型逻辑斯谛回归无偏的预测概率。第一个修正预测概率的事后调整的截距。另一种是基于替代配方的第一类型的估计作为一个迭代的数据增强过程。我们建议的修改包括引入一个指标变量，它区分原始和伪观测的扩增数据。在一个全面的模拟研究中，这些方法相比，其他尝试，以改善预测的基础上，第一型惩罚和其他已公布的惩罚策略，旨在为日常使用。例如，我们考虑最近建议的极大似然和第五类逻辑斯谛回归之间的妥协。模拟结果都与预测和回归系数方面仔细检查。最后，所考虑的方法进行了说明和比较的研究动脉闭合装置在微创心脏手术。
英文摘要：
Firth-type logistic regression has become a standard approach for the analysis of binary outcomes with small samples. Whereas it reduces the bias in maximum likelihood estimates of coefficients, bias towards 1/2 is introduced in the predicted probabilities. The stronger the imbalance of the outcome, the more severe is the bias in the predicted probabilities. We propose two simple modifications of Firth-type logistic regression resulting in unbiased predicted probabilities. The first corrects the predicted probabilities by a post-hoc adjustment of the intercept. The other is based on an alternative formulation of Firth-types estimation as an iterative data augmentation procedure. Our suggested modification consists in introducing an indicator variable which distinguishes between original and pseudo observations in the augmented data. In a comprehensive simulation study these approaches are compared to other attempts to improve predictions based on Firth-type penalization and to other published penalization strategies intended for routine use. For instance, we consider a recently suggested compromise between maximum likelihood and Firth-type logistic regression. Simulation results are scrutinized both with regard to prediction and regression coefficients. Finally, the methods considered are illustrated and compared for a study on arterial closure devices in minimally invasive cardiac surgery.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
