title: Can efficiency be gained by correcting for misclassification?
abstract: This paper considers 2×2 tables arising from case-control studies in which the binary exposure may be misclassified. We found circumstances under which the inverse matrix method provides a more efficient odds ratio estimator than the naive estimator. We provide some intuition for the findings, and also provide a formula for obtaining the minimum size of a validation study such that the variance of the odds ratio estimator from the inverse matrix method is smaller than that of the naive estimator, thereby ensuring an advantage for the misclassification corrected result. As a corollary of this result, we show that correcting for misclassification does not necessarily lead to a widening of the confidence intervals, but, rather, in addition to producing a consistent estimate, can also produce one that is more efficient.
authors.affiliation: Channing Division of Network Medicine, Department of Medicine, Harvard Medical School, Boston, MA, 02115, USA ; Department of Biostatistics, Harvard School of Public Health, Boston, MA, 02115, USA ; Department of Epidemiology, Harvard School of Public Health, Boston, MA, 02115, USA.
authors.forename: Molin
authors.initials: M
authors.lastname: Wang
authors.forename: Xiaomei
authors.initials: X
authors.lastname: Liao
authors.forename: Donna
authors.initials: D
authors.lastname: Spiegelman
keywords: 2×2 table; Case control study; Misclassification; Odds ratio; Validation study design