Premium
Bias correction for the proportional odds logistic regression model with application to a study of surgical complications
Author(s) -
Lipsitz Stuart R.,
Fitzmaurice Garrett M.,
Regenbogen Scott E.,
Sinha Debajyoti,
Ibrahim Joseph G.,
Gawande Atul A.
Publication year - 2013
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.1111/j.1467-9876.2012.01057.x
Subject(s) - multinomial logistic regression , statistics , logistic regression , mathematics , univariate , covariate , estimator , outcome (game theory) , poisson distribution , econometrics , poisson regression , medicine , multivariate statistics , population , environmental health , mathematical economics
Summary. 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 and Kosmidis 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. 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 method proposed is motivated by a study of predictors of post‐operative complications in patients undergoing colon or rectal surgery.