🤖 AI Summary
This study addresses attenuation bias in scalar-on-density regression when the number of repeated measurements per observational unit is limited, leading to insufficient effective sample size for accurate coefficient function estimation. The work systematically establishes, for the first time, a monotonic decreasing relationship between the number of measurements and the magnitude of attenuation bias. To correct this bias, the authors innovatively integrate the Simulation-Extrapolation (SIMEX) method with bootstrap resampling within a functional data analysis framework, simulating scenarios with fewer measurements and extrapolating estimates to the theoretical limit of infinite replicates. Combining techniques from functional data analysis and density estimation, the proposed approach substantially reduces estimation bias in simulations. Applied to NHANES data, it successfully identifies and corrects finite-measurement bias in the association between physical activity density and all-cause mortality.
📝 Abstract
In one extension of scalar-on-function regression modeling, the covariate is taken to be a density that is estimated from a finite number of measurements gathered for each observational unit. When this number of measurements is relatively small, the estimated coefficient function suffers from attenuation bias. This paper studies how the bias depends on the number of measurements per unit and proposes a bias-correction method based on simulation extrapolation (SIMEX). We establish that the bias decreases monotonically as the number of measurements per unit increases. The proposed SIMEX procedure applies bootstrap resampling to simulate smaller measurement counts and then extrapolates to infinitely many measurements, thereby correcting finite-measurement bias. A comprehensive simulation study, conducted over a range of sample sizes and noise levels, shows that the mean integrated squared error of the coefficient function decreases with more measurements per unit and that the SIMEX-extrapolated estimates achieve lower bias than the naive estimates based on the full set of measurements. The practical utility of the method is further illustrated through an application to the National Health and Nutrition Examination Survey, for which we relate 24-hour physical activity profiles to all-cause mortality. This example supports the validity of the method and demonstrates its ability to detect and correct for finite-measurement bias.