Reducing Bias and Mean Squared Error Associated With Regression-Based Odds Ratio Estimators

• Authors: Robert Lyles, Emory University; Ying Guo, Emory University; Sander Greenland, University of California
• Journal Title: Journal of Statistical Planning and Inference
• Volume: Volume 142, Number 12
• Publisher: Elsevier | 2012-12-01, Pages 3235-3241
• Type of Work: Article | Post-print: After Peer Review
• Publisher DOI: http://doi.org/10.1016/j.jspi.2012.05.005
• Subjects: Health Sciences, Epidemiology; Biology, Biostatistics; Health Sciences, Public Health
• Keywords: Absolute risk; Bias; Bootstrap; Logistic regression; Maximum likelihood; Odds ratio; Relative risk

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.