Case-Control Studies with Jointly Misclassified Exposure and Confounding Variables

The issue of 2 × 2 × 2 case-control studies is addressed when both exposure and confounding variables are jointly misclassified. Two scenarios are considered: the classification errors of exposure and confounding variables are independent or not independent. The bias-adjusted cell probability estimates which account for the misclassification bias are presented. The effect of misclassification on the measure of crude odds ratio either unstratified or stratified by the confounder, Mantel-Haenszel summary odds ratio, the confounding component in the crude odds ratio, the first and second order multiplicative interaction are assessed through the sensitivity analysis from using the data on the asthma deaths of 5-45 aged patients in New Zealand. Introduction Misclassification is a ubiquitous problem in epidemiologic studies. A 2 × 2 case-control study with a single exposure variable being misclassified has been thoroughly studied (Fleiss et al. the misclassification of a confounding factor has attracted less attention, although there are some important papers on this topic However, few papers address the issue when the study (or exposure) factor and the confounding factor are simultaneously misclassified. Most articles focused merely on the aspect that the confounding factor is misclassified. 192 Although Fung & Howe (1984) considered the joint misclassification of polytomous exposure and confounding variables, they do not provide the bias-adjusted estimator for the cell probability. Tzonou et al. (1986) investigates the effect of misclassification on the summary odds ratio in case-control studies in which both exposure and confounding variables are jointly misclassified. But they merely consider the scenario that the classification errors of the exposure and confounding factors are independent. Again, no bias-adjusted estimators are provided in their paper. The scenarios are addressed here in which the joint classification errors of the exposure and confounding factors are either independent or not independent. Below, necessary background materials are first reviewed. The misclassification probabilities are then defined. The formulas for all bias-adjusted measures of the effect caused by the joint misclassification of exposure and confounder are thus presented. A real-world data set is used as an example to illustrate how to calculate the misclassification probabilities by employing the counterfactual (or correctly classified) tables when the validation data are not available. A sensitivity analysis is then carried out for the admissible counterfactual tables. Let D, E, and C be three dichotomous variables, in which D denotes the subject's outcome (disease) variable (=1 if present, 0 otherwise), E the subject's exposure variable (= …