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Lipsitz SR, Fitzmaurice GM, Regenbogen SE, et al. Bias correction for the proportional odds logistic regression model with application to a study of surgical complications. J R Stat Soc Ser C Appl Stat. 2013;62(2):233-250doi: 10.1111/j.1467-9876.2012.01057.x.
Lipsitz, S. R., Fitzmaurice, G. M., Regenbogen, S. E., Sinha, D., Ibrahim, J. G., & Gawande, A. A. (2013). Bias correction for the proportional odds logistic regression model with application to a study of surgical complications. Journal of the Royal Statistical Society. Series C, Applied statistics, 62(2), 233-250. https://doi.org/10.1111/j.1467-9876.2012.01057.x
Lipsitz, Stuart R, et al. "Bias correction for the proportional odds logistic regression model with application to a study of surgical complications." Journal of the Royal Statistical Society. Series C, Applied statistics vol. 62,2 (2013): 233-250. doi: https://doi.org/10.1111/j.1467-9876.2012.01057.x
Lipsitz SR, Fitzmaurice GM, Regenbogen SE, Sinha D, Ibrahim JG, Gawande AA. Bias correction for the proportional odds logistic regression model with application to a study of surgical complications. J R Stat Soc Ser C Appl Stat. 2013 Mar;62(2):233-250. doi: 10.1111/j.1467-9876.2012.01057.x. PMID: 23913986; PMCID: PMC3729470.
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J R Stat Soc Ser C Appl Stat. 2013 Mar;62(2):233-250. doi: 10.1111/j.1467-9876.2012.01057.x.

Bias correction for the proportional odds logistic regression model with application to a study of surgical complications.

Journal of the Royal Statistical Society. Series C, Applied statistics

Stuart R Lipsitz, Garrett M Fitzmaurice, Scott E Regenbogen, Debajyoti Sinha, Joseph G Ibrahim, Atul A Gawande

Affiliations

  1. Brigham and Women's Hospital, Boston, MA, U.S.A.

PMID: 23913986 PMCID: PMC3729470 DOI: 10.1111/j.1467-9876.2012.01057.x

Abstract

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).

Keywords: Discrete response; Poisson likelihood; multinomial likelihood; multinomial logistic regression; penalized likelihood

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