Sensitivity analysis for misclassification in logistic regression via likelihood methods and predictive value weighting

• Type of Material: Article
• Authors: Robert Lyles, Emory University; Ji Lin, Emory University
• Language: English
• Date: 2010-09-30
• Publisher: Wiley: 12 months
• Publication Version: Author Accepted Manuscript (After Peer Review)
• Copyright Statement: © 2010 John Wiley & Sons, Ltd.
• Final Published Version (URL): http://onlinelibrary.wiley.com/doi/10.1002/sim.3971/abstract
• Title of Journal or Parent Work: Statistics in Medicine
• ISSN: 0277-6715
• Volume: 29
• Issue: 22
• Start Page: 2297
• End Page: 2309
• Grant/Funding Information: Robert H. Lyles was partially supported by an R01 from the National Institute of Environmental Health Sciences (ES012458), and by a PHS grant (UL 1 RR025008) from the Clinical and Translational Science Award Program, National Institutes of Health, Center for Research Resources.
• Keywords: regression; bias; odds ratio; errors-in-variables
• Research Categories: Biology, Biostatistics

Abstract

The potential for bias due to misclassification error in regression analysis is well understood by statisticians and epidemiologists. Assuming little or no available data for estimating misclassification probabilities, investigators sometimes seek to gauge the sensitivity of an estimated effect to variations in the assumed values of those probabilities. We present an intuitive and flexible approach to such a sensitivity analysis, assuming an underlying logistic regression model. For outcome misclassification, we argue that a likelihood-based analysis is the cleanest and the most preferable approach. In the case of covariate misclassification, we combine observed data on the outcome, error-prone binary covariate of interest, and other covariates measured without error, together with investigator-supplied values for sensitivity and specificity parameters, to produce corresponding positive and negative predictive values. These values serve as estimated weights to be used in fitting the model of interest to an appropriately defined expanded data set using standard statistical software. Jackknifing provides a convenient tool for incorporating uncertainty in the estimated weights into valid standard errors to accompany log odds ratio estimates obtained from the sensitivity analysis. Examples illustrate the flexibility of this unified strategy, and simulations suggest that it performs well relative to a maximum likelihood approach carried out via numerical optimization.