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Scalar-on-function regression: Estimation and inference under complex survey designs.

Ekaterina Smirnova1, Erjia Cui2, Lucia Tabacu3

  • 1Department of Biostatistics, Virginia Commonwealth University, Richmond, Virginia, USA.

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Summary
This summary is machine-generated.

This study introduces new methods for analyzing complex survey data, linking functional data like activity profiles to health outcomes such as mortality. The approach enhances statistical inference for large-scale health research.

Keywords:
NHANESaccelerometrycomplex survey designfunctional regression

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Area of Science:

  • Statistics
  • Biostatistics
  • Functional Data Analysis

Background:

  • Large health surveys collect high-dimensional, correlated data (e.g., sensor, imaging).
  • Analyzing complex survey data requires advanced methods at the intersection of survey statistics and functional data analysis.
  • Existing methods are insufficient for generalizable scalar-on-function regression in complex survey designs.

Purpose of the Study:

  • To propose a novel estimation and inferential framework for generalizable scalar-on-function regression models tailored for complex survey data.
  • To address the gap in statistical methodology for analyzing high-dimensional functional data from national health surveys.
  • To provide a robust framework for associating complex functional data with health outcomes.

Main Methods:

  • Developed a framework using weighted score equations for estimating functional regression coefficients.
  • Proposed novel functional balanced repeated replication and survey-weighted bootstrap methods for inference in multistage survey designs.
  • Implemented methods using R package surveySoFR for computational efficiency.

Main Results:

  • The study is the first frequentist approach to estimate scalar-on-function regression models within complex survey contexts.
  • Assessed the validity of resampling-based inferential techniques through a comprehensive simulation study.
  • Successfully applied the methods to predict mortality using National Health and Nutrition Examination Survey (NHANES) accelerometer data.

Conclusions:

  • The proposed methods offer a statistically rigorous approach for analyzing functional data from complex surveys.
  • The framework enables reliable association of complex health-related data (e.g., diurnal activity) with health outcomes.
  • The R package surveySoFR provides an accessible tool for researchers in public health and biostatistics.