title: Reducing Bias and Mean Squared Error Associated With Regression-Based Odds Ratio Estimators.
abstract: Ratio estimators of effect are ordinarily obtained by exponentiating maximum-likelihood estimators (MLEs) of log-linear or logistic regression coefficients. These estimators can display marked positive finite-sample bias, however. We propose a simple correction that removes a substantial portion of the bias due to exponentiation. By combining this correction with bias correction on the log scale, we demonstrate that one achieves complete removal of second-order bias in odds ratio estimators in important special cases. We show how this approach extends to address bias in odds or risk ratio estimators in many common regression settings. We also propose a class of estimators that provide reduced mean bias and squared error, while allowing the investigator to control the risk of underestimating the true ratio parameter. We present simulation studies in which the proposed estimators are shown to exhibit considerable reduction in bias, variance, and mean squared error compared to MLEs. Bootstrapping provides further improvement, including narrower confidence intervals without sacrificing coverage.
authors.affiliation: Department of Biostatistics and Bioinformatics, The Rollins School of Public Health of Emory University, 1518 Clifton Rd. N.E., Atlanta, GA 30322 phone: 404-727-1310; fax: 404-727-1370.
authors.forename: Robert H
authors.initials: RH
authors.lastname: Lyles
authors.forename: Ying
authors.initials: Y
authors.lastname: Guo
authors.forename: Sander
authors.initials: S
authors.lastname: Greenland