Recovering true risks when multilevel exposure and covariables are both misclassified

The authors extend previous results on nondifferential exposure misclassification to the situation in which multilevel exposure and covariables are both misclassified. They show that if misclassification is nondifferential and the predictive value matrices are independent of other predictor variables it is possible to recover the true relative risks as a function of the biased estimates and the misclassification matrices alone. If the covariable is a confounder, the true relative risks may be recovered from the apparent relative risks derived from misclassified data and the misclassification matrix for the exposure variable with respect to its surrogate. If the covariable is an effect modifier, the true relative risk matrix may be recovered from the apparent relative risk matrix and misclassification matrices for both the exposure variable with respect to its surrogate and the covariable with respect to its surrogate. By varying the misclassification matrices, the sensitivity of published relative risk estimates to different patterns of misclassification can be analyzed. If it is not possible to design a study protocol that is free of misclassification, choosing surrogate variables whose predictive value is constant with respect to other predictors appears to be a desirable design objective.