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Threshold regression to accommodate a censored covariate.

Jing Qian1, Sy Han Chiou2, Jacqueline E Maye3,4

  • 1Department of Biostatistics and Epidemiology, University of Massachusetts, Amherst, Massachusetts, U.S.A.

Biometrics
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Summary

This study introduces threshold regression for handling censored covariates in regression modeling, improving unbiased estimation and significance testing for complex datasets. The method demonstrates strong performance and efficiency in simulations and real-world Alzheimer's disease research.

Keywords:
Alzheimer's diseaseBias correctionCensored predictorCox proportional hazards modelKaplan-Meier estimatorLimit of detection

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Area of Science:

  • Biostatistics
  • Statistical Modeling
  • Epidemiology

Background:

  • Regression modeling is often complicated by censored covariates, common in medical research (e.g., Alzheimer's disease, cardiovascular disease).
  • Existing methods struggle with accurate significance testing and unbiased estimation when covariates are subject to censoring (e.g., limit of detection, right censoring).

Purpose of the Study:

  • To propose novel threshold regression approaches for linear regression models with randomly censored covariates.
  • To enable immediate significance testing and provide unbiased estimation of regression coefficients for censored covariates.
  • To develop a principled method for threshold selection in these models.

Main Methods:

  • Development of threshold regression techniques for linear models incorporating censored covariates.
  • Derivation of asymptotic properties for the proposed estimators under mild regularity conditions.
  • Application to an Alzheimer's disease study examining brain amyloid levels and maternal age of dementia onset.

Main Results:

  • Simulations show the proposed estimators possess good finite-sample performance.
  • The threshold regression method offers improved efficiency compared to existing approaches.
  • The method was successfully illustrated in an Alzheimer's disease dataset.

Conclusions:

  • Threshold regression provides a robust framework for analyzing data with censored covariates.
  • The proposed method enhances accuracy in significance testing and coefficient estimation.
  • An R package, censCov, is available for implementing this statistical approach.