Validation Study Methods for Estimating Odds Ratio in Tables When Exposure is Misclassified

Background. Misclassification of exposure variables in epidemiologic studies may lead to biased estimation of parameters and loss of power in statistical inferences. In this paper, the inverse matrix method, as an efficient method of the correction of odds ratio for the misclassification of a binary exposure, was generalized to nondifferential misclassification and tables. Methods. Simple estimates for predictive values when misclassification is nondifferential are presented. Using them, we estimated the corrected log odds ratio and its variance for tables, using the inverse matrix method. A two-step weighted likelihood method was also developed. Moreover, we compared the matrix and inverse matrix methods to the maximum likelihood (MLE) method using a simulation study. Results. In all situations, the inverse matrix method proved to be more efficient than the matrix method. Matrix and inverse matrix methods for nondifferential situations are more efficient than differential misclassification. Conclusions. Although MLE is optimal among all of the methods, it is computationally difficult and requires programming. On the other hand, the inverse matrix method with a simple closed-form presents acceptable efficiency. 1. Introduction In epidemiology studies, where the assessment of the relationship between exposure and outcome variables is the main goal, misclassification of exposure variable leads to biased estimate of odds ratio. In multicenter clinical trials with an increasing number of centers, the possibility of misclassification of the exposure variable and the biases induced by it will arise. Methods to correct a possibly misclassified exposure so that the strength of the association between exposure and outcome variables can be precisely assessed have been a focus of statistical and epidemiological research for over 30 years. Beginning with classic papers, the issue of misclassification on tabular data has long been recognized and their adjustment has been considered [1–5]. In 1977, the matrix method was presented by Barron in order to correct nondifferential misclassification in tables [6]. Greenland and Kleinbaum generalized it to differential misclassification and match paired data [7]. In addition, Greenland proposed a variance estimate for the matrix method under the assumptions of differential and nondifferential misclassifications [8]. Selen, in a simulation study, showed that both the matrix and the maximum likelihood methods performed equally well [9]. In 1990, Marshall presented a more direct inverse matrix approach for correcting