A Method to Adjust for Measurement Error in Three Exposures Measured with Correlated Errors in the Absence of Internal Validation Study

Abstract

Difficulty in obtaining the correct measurement for an individual's long-term 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 proposed a method (trivariate method) that adjusts for measurement error in three correlated exposures in the absence of internal validation study and illustrated the method using real data. We compared the results from the proposed method with those obtained using a method that ignores measurement error and a method that ignores correlations between the errors and true exposures (the univariate method). It was found that ignoring measurement error leads to bias and underestimates the standard error. It was also found that the magnitude of adjustment in the trivariate method is sensitive to the magnitude of measurement error, sign and correlation between the errors. We conclude that the proposed method can be used to adjust for bias in the outcome-exposure association in a case where three exposures are measured with correlated errors in the absence of an internal validation study. The method is useful in conducting a sensitivity analysis on the magnitude of measurement error and the sign of the error correlation.

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

“…The method combines external validation data from the literature with the observed self-reported data to adjust for bias in the association between the exposures and the outcome and conduct a sensitivity analysis on the measurement error and correlation between the errors. The advantages of the multivariate method presented in this work includes: (1) the method can be used to adjust for bias in the outcome-exposure association caused by measurement error reported in multiple exposures measured with correlated errors, (2) the method is useful in the absence of the costly internal validation data, provided that external information on the correlation between the observed and the true data or the error correlations of the observed data are plausible within the study context, (3) it can be used in the sensitivity analysis on the effect of uncertainty of the reported validity coefficients, (4) can be used for sensitivity analysis on the magnitude and the direction of correlated errors, (5) the method can adjust for confounding effect in the outcome regression model and (6) This method can be easily implemented on the readily available and free software R as shown in the extended data 28 . Often, fruit and vegetable intakes are considered as one food group.…”

“…MCMC convergence diagnostics of all the model parameters was done using trace plots and autocorrelation (ACF) plots from the coda package 33 . See extended data: Appendix C 28 for convergence diagnostics results. For each model, the burn-in iterations were set to 2,000 and 10,000 MCMC iterations were run after the burn-in iterations.…”

“…We compared the results obtained under naive, univariate, and trivariate methods. The R code used for analysis is presented in the extended data 28 .…”

“…With the trivariate method, the results further show that the estimates' uncertainty is slightly affected by the level of uncertainty assumed for the validity coefficients. Figure 4 to Figure 6 presents the mean coefficient estimates of fruit, vegetable and the average number of cigarettes smoked adjusted for measurement error using the trivariate method in the sensitivity analysis by varying the magnitude of error correlation between measurements for the exposures (see Tables D1 to D3 in the extended data for more details 28 ).…”