Statistical modelling for exposure measurement error with application to epidemiological data

Background Measurement error in exposure variables is an important issue in epidemiological studies that relate exposures to health outcomes. Such studies, however, usually pay limited attention to the quantitative effects of exposure measurement error on estimated exposure-outcome associations. Therefore, the estimators for exposure-outcome associations are prone to bias. Existing methods to adjust for the bias in the associations require a validation study with multiple replicates of a reference measurement. Validation studies with multiple replicates are quite costly and therefore, in some cases only a single–replicate validation study is conducted besides the main study. For a study that does not include an internal validation study, the challenge in dealing with exposure measurement error is even bigger. The challenge is how to use external data from other similar validation studies to adjust for the bias in the exposure-outcome association. In accelerometry research, various accelerometer models have currently been developed. However, some of these new accelerometer models have not been properly validated in field situations. Despite the widely recognized measurement error in the accelerometer, some accelerometers have been used to validate other instruments, such as physical activity questionnaires, in measuring physical activity. Consequently, if an instrument is validated against the accelerometer, and the accelerometer itself has considerable measurement error, the observed validity in the instrument being validated will misrepresent the true validity. Methodology In this thesis, we adapted regression calibration to adjust for exposure measurement error for a single-replicate validation study with zero-inflated reference measurements and assessed the adequacy of the adapted method in a simulation study. For the case where there is no internal validation study, we showed how to combine external data on validity for self-report instruments with the observed questionnaire data to adjust for the bias in the associations caused by measurement error in correlated exposures. In the last part, we applied a measurement error model to assess the measurement error in physical activity as measured by an accelerometer in free-living individuals in a recently concluded validation study. Results The performance of the proposed two-part model was sensitive to the form of continuous independent variables and was minimally influenced by the correlation between the probability of a non-zero response and the actual non-zero response values. Reducing the number of covariates in the model seemed beneficial, but was not critical in large-sample studies. We showed that if the confounder is strongly linked with the outcome, measurement error in the confounder can be more influential than measurement error in the exposure in causing the bias in the exposure-outcome association, and that the bias can be in any direction. We further showed that when accelerometers are used to monitor the level of physical activity in free-living individuals, the mean level of physical activity would be underestimated, the associations between physical activity and health outcomes would be biased, and there would be loss of statistical power to detect associations. Conclusion The following remarks were made from the work in this thesis. First, when only a single-replicate validation study with zero-inflated reference measurements is available, a correctly specified regression calibration can be used to adjust for the bias in the exposure-outcome associations. The performance of the proposed calibration model is influenced more by the assumption made on the form of the continuous covariates than the form of the response distribution. Second, in the absence of an internal validation study, carefully extracted validation data that is transportable to the main study can be used to adjust for the bias in the associations. The proposed method is also useful in conducting sensitivity analyses on the effect of measurement errors. Lastly, when “reference” instruments are themselves marred by substantial bias, the effect of measurement error in an instrument being validated can be seriously underestimated.