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

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.

Combining Ensemble Learning Techniques and G-Computation to Investigate Chemical Mixtures in Environmental Epidemiology Studies

ABSTRACTBackgroundAlthough biomonitoring studies demonstrate that the general population experiences exposure to multiple chemicals, most environmental epidemiology studies consider each chemical separately when assessing adverse effects of environmental exposures. Hence, the critical need for novel approaches to handle multiple correlated exposures.MethodsWe propose a novel approach using the G-formula, a maximum likelihood-based substitution estimator, combined with an ensemble learning technique (i.e. SuperLearner) to infer causal effect estimates for a multi-pollutant mixture. We simulated four continuous outcomes from real data on 5 correlated exposures under four exposure-response relationships with increasing complexity and 500 replications. The first simulated exposure-response was generated as a linear function depending on two exposures; the second was based on a univariate nonlinear exposure-response relationship; the third was generated as a linear exposure-response relationship depending on two exposures and their interaction; the fourth simulation was based on a non-linear exposure-response relationship with an effect modification by sex and a linear relationship with a second exposure. We assessed the method based on its predictive performance (Minimum Square error [MSE]), its ability to detect the true predictors and interactions (i.e. false discovery proportion, sensitivity), and its bias. We compared the method with generalized linear and additive models, elastic net, random forests, and Extreme gradient boosting. Finally, we reconstructed the exposure-response relationships and developed a toolbox for interactions visualization using individual conditional expectations.ResultsThe proposed method yielded the best average MSE across all the scenarios, and was therefore able to adapt to the true underlying structure of the data. The method succeeded to detect the true predictors and interactions, and was less biased in all the scenarios. Finally, we could correctly reconstruct the exposure-response relationships in all the simulations.ConclusionsThis is the first approach combining ensemble learning techniques and causal inference to unravel the effects of chemical mixtures and their interactions in epidemiological studies. Additional developments including high dimensional exposure data, and testing for detection of low to moderate associations will be carried out in future developments.