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A Bayesian semi-parametric scalar-on-function regression with measurement error using instrumental variables.

Roger S Zoh1, Yuanyuan Luan1, Lan Xue2

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Summary
This summary is machine-generated.

This study introduces a new Bayesian method to accurately analyze physical activity data from wearable devices, improving our understanding of its link to health outcomes like obesity.

Keywords:
Bayesianenergy expenditureinstrumental variablesmeasurement errorphysical activityscalar‐on‐function

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Area of Science:

  • Biostatistics
  • Epidemiology
  • Wearable Technology

Background:

  • Wearable devices (e.g., ActiGraph) are crucial for monitoring physical activity in research.
  • Accurate assessment of physical activity's impact on health outcomes (e.g., obesity) is increasingly important.
  • Existing scalar-on-function regression (SoFR) methods often assume white noise measurement error, potentially underestimating parameters.

Purpose of the Study:

  • To develop a non-parametric Bayesian measurement error-corrected SoFR model.
  • To relax restrictive assumptions common in current SoFR models.
  • To provide a robust method for analyzing wearable device data and its association with health outcomes.

Main Methods:

  • Developed a non-parametric Bayesian SoFR model with measurement error correction.
  • Employed an instrumental variable approach with a time-varying biasing factor, departing from GMM.
  • Incorporated model-based grouping of the corrected functional covariate for enhanced interpretation.

Main Results:

  • The proposed method demonstrated strong finite sample properties in simulations.
  • The approach allows for flexible modeling without strict assumptions on measurement error.
  • Successfully applied to National Health and Examination Survey data.

Conclusions:

  • The novel Bayesian SoFR model effectively corrects for measurement error in functional covariates.
  • This method enhances the accuracy of assessing relationships between physical activity and health outcomes.
  • Facilitates easier interpretation of physical activity patterns and their health implications.