Use of two data sources to estimate odds ratios in case-control studies

Information bias is among the most serious and common problems in epidemiology. Approaches have been developed to reduce information bias by correcting for known amounts of misclassification. Unfortunately, in most studies, the extent of exposure misclassification cannot be easily estimated. We discuss the application to case-control studies of an approach originally proposed by Hui and Walter in 1980 to estimate the sensitivity and specificity of two independent classification schemes (Hui SL, Walter SD. Biometrics 1980;36:167-171). In this paper, we propose using the EM algorithm to provide a simple numeric technique for implementing their method that seems to converge for most real-world data. Our approach allows inclusion of a measure of non-independence of the two classification schemes, and we assess the influence of non-independence on the odds ratio. Finally, we provide a simple variance estimate for the odds ratio based on the delta method and maximum likelihood theory. We exemplify our results and method with data from a case-control study of sudden infant death syndrome in which data on some variables were obtained from both maternal interviews and medical records.