title: Bias correction for the proportional odds logistic regression model with application to a study of surgical complications.
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).
authors.affiliation: Brigham and Women's Hospital, Boston, MA, U.S.A.
authors.forename: Stuart R
authors.initials: SR
authors.lastname: Lipsitz
authors.forename: Garrett M
authors.initials: GM
authors.lastname: Fitzmaurice
authors.forename: Scott E
authors.initials: SE
authors.lastname: Regenbogen
authors.forename: Debajyoti
authors.initials: D
authors.lastname: Sinha
authors.forename: Joseph G
authors.initials: JG
authors.lastname: Ibrahim
authors.forename: Atul A
authors.initials: AA
authors.lastname: Gawande
keywords: Discrete response; Poisson likelihood; multinomial likelihood; multinomial logistic regression; penalized likelihood
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