A linear mixed model approach for measurement error adjustment: applications to sedentary behavior assessment from wearable devices

In recent years, wearable devices have become more common to capture a wide range of health behaviors, especially for physical activity and sedentary behavior. These sensor-based measures are deemed to be objective and thus less prone to self-reported biases, inherent in questionnaire assessments. While this is undoubtedly a major advantage, there can still be measurement errors from the device recordings, which pose serious challenges for conducting statistical analysis and obtaining unbiased risk estimates. There is a vast literature proposing statistical methods for adjusting for measurement errors in self-reported behaviors, such as in dietary intake. However, there is much less research on error correction for sensor-based device measures, especially sedentary behavior. In this paper, we address this gap. Exploiting the excessive multiple-day assessments typically collected when sensor devices are deployed, we propose a two-stage linear mixed effect model (LME) based approach to correct bias caused by measurement errors. We provide theoretical proof of the debiasing process using the Best Linear Unbiased Predictors (BLUP), and use both simulation and real data from a cohort study to demonstrate the performance of the proposed approach while comparing to the na\"ive plug-in approach that directly uses device measures without appropriately adjusting measurement errors. Our results indicate that employing our easy-to-implement BLUP correction method can greatly reduce biases in disease risk estimates and thus enhance the validity of study findings.