A Function-Based Approach to Model the Measurement Error in Wearable Devices

TL;DR

This paper introduces a novel functional regression model that accounts for measurement error in wearable device data, improving the analysis of physical activity's impact on health outcomes.

Contribution

It develops a two-step estimation method for functional covariate models with measurement error, with proven consistency and significance testing capabilities.

Findings

Simulation studies show improved accuracy over existing methods.

Application to NHANES data reveals significant PA-BMI associations.

Method effectively handles high-dimensional, dependent, and noisy accelerometer data.

Abstract

Physical activity (PA) is an important risk factor for many health outcomes. Wearable-devices such as accelerometers are increasingly used in biomedical studies to understand the associations between PA and health outcomes. Statistical analyses involving accelerometer data are challenging due to the following three characteristics: (i) high-dimensionality, (ii) temporal dependence, and (iii) measurement error. To address these challenges we treat accelerometer-based measures of physical activity as a single function-valued covariate prone to measurement error. Specifically, in order to determine the relationship between PA and a health outcome of interest, we propose a regression model with a functional covariate that accounts for measurement error. Using regression calibration, we develop a two-step estimation method for the model parameters and establish their consistency. A test is also proposed to test the significance of the estimated model parameters. Simulation studies are conducted to compare the proposed methods with existing alternative approaches under varying scenarios. Finally, the developed methods are used to assess the relationship between PA intensity and BMI obtained from the National Health and Nutrition Examination Survey data.