Logistic regression is a standard method in multivariate analysis for binary outcome data in epidemiological and clinical studies; however, the resultant odds-ratio estimates fail to provide directly interpretable effect measures. The modified Poisson and least-squares regressions are alternative standard methods that can provide risk-ratio and risk difference estimates without computational problems. However, the bias and invalid inference problems of these regression analyses under small or sparse data conditions (i.e.,the "separation" problem) have been insufficiently investigated. We show that the separation problem can adversely affect the inferences of the modified Poisson and least squares regressions, and to address these issues, we apply the ridge, lasso, and elastic-net estimating approaches to the two regression methods. As the methods are not founded on the maximum likelihood principle, we propose regularized quasi-likelihood approaches based on the estimating equations for these generalized linear models. The methods provide stable shrinkage estimates of risk ratios and risk differences even under separation conditions, and the lasso and elastic-net approaches enable simultaneous variable selection. We provide a bootstrap method to calculate the confidence intervals on the basis of the regularized quasi-likelihood estimation. The proposed methods are applied to a hematopoietic stem cell transplantation cohort study and the National Child Development Survey. We also provide an R package, regconfint, to implement these methods with simple commands.

翻译：逻辑回归是流行病学和临床研究中处理二分类结局数据的多变量分析标准方法；然而，其所得的比值比估计值无法提供可直接解释的效应度量。修正泊松回归与最小二乘回归是两种替代性标准方法，能够提供风险比与风险差值估计，且不存在计算问题。然而，这些回归分析在小样本或稀疏数据条件下（即“分离”问题）的偏倚与无效推断问题尚未得到充分研究。本文表明分离问题可能对修正泊松回归与最小二乘回归的推断产生不利影响，为应对这些问题，我们将岭回归、套索回归与弹性网络估计方法应用于这两种回归模型。由于这些方法并非基于最大似然原理，我们提出了基于广义线性模型估计方程的正则化拟似然方法。即使在分离条件下，这些方法也能提供风险比与风险差值的稳定收缩估计，且套索回归与弹性网络方法能够实现同步变量选择。我们提出了一种基于正则化拟似然估计的自举法来计算置信区间。所提出的方法已应用于一项造血干细胞移植队列研究和全国儿童发展调查。我们还开发了R软件包regconfint，可通过简单命令实现这些方法。