Lipsitz Stuart R, Fitzmaurice Garrett M, Regenbogen Scott E, Sinha Debajyoti, Ibrahim Joseph G, Gawande Atul A
Brigham and Women's Hospital, Boston, MA, U.S.A.
J R Stat Soc Ser C Appl Stat. 2013 Mar;62(2):233-250. doi: 10.1111/j.1467-9876.2012.01057.x.
The proportional odds logistic regression model is widely used for relating an ordinal outcome to a set of covariates. When the number of outcome categories is relatively large, the sample size is relatively small, and/or certain outcome categories are rare, maximum likelihood can yield biased estimates of the regression parameters. Firth (1993) and Kosmidis and Firth (2009) proposed a procedure to remove the leading term in the asymptotic bias of the maximum likelihood estimator. Their approach is most easily implemented for univariate outcomes. In this paper, we derive a bias correction that exploits the proportionality between Poisson and multinomial likelihoods for multinomial regression models. Specifically, we describe a bias correction for the proportional odds logistic regression model, based on the likelihood from a collection of independent Poisson random variables whose means are constrained to sum to 1, that is straightforward to implement. The proposed method is motivated by a study of predictors of post-operative complications in patients undergoing colon or rectal surgery (Gawande et al., 2007).
比例优势逻辑回归模型广泛用于将有序结果与一组协变量相关联。当结果类别数量相对较大、样本量相对较小和/或某些结果类别很罕见时，最大似然法可能会产生有偏的回归参数估计值。Firth（1993年）以及Kosmidis和Firth（2009年）提出了一种方法来消除最大似然估计量渐近偏差中的首项。他们的方法对于单变量结果最容易实现。在本文中，我们推导了一种偏差校正方法，该方法利用了多项回归模型中泊松似然和多项似然之间的比例关系。具体而言，我们基于来自一组独立泊松随机变量的似然，描述了比例优势逻辑回归模型的偏差校正方法，这些随机变量的均值被约束为总和为1，该方法易于实现。所提出的方法是受一项关于结肠或直肠手术患者术后并发症预测因素的研究（Gawande等人，2007年）的启发。
