A Method to adjust for measurement error in multiple exposure variables measured with correlated errors in the absence of an internal validation study

Difficulty in obtaining the correct measurement for an individual’s longterm exposure is a major challenge in epidemiological studies that investigate the association between exposures and health outcomes. Measurement error in an exposure biases the association between the exposure and a disease outcome. Usually, an internal validation study is required to adjust for exposure measurement error; it is challenging if such a study is not available. We propose a general method for adjusting for measurement error where multiple exposures are measured with correlated errors (a multivariate method) and illustrate the method using real data. We compare the results from the multivariate method with those obtained using a method that ignores measurement error (the naive method) and a method that ignores correlations between the errors and true exposures (the univariate method). It is found that ignoring measurement error leads to bias and underestimates the standard error. A sensitivity analysis shows that the magnitude of adjustment in the multivariate method is sensitive to the magnitude of measurement error, sign, and the correlation between the errors. We conclude that the multivariate method can be used to adjust for bias in the outcome-exposure association in a case where multiple exposures are measured with correlated errors in the absence of an internal validation study. The method is also useful in conducting a sensitivity analysis on the magnitude of measurement error and the sign of the error correlation.