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Estimating and testing interactions when explanatory variables are subject to non-classical measurement error.

Havi Murad1, Victor Kipnis2, Laurence S Freedman3

  • 1Biostatistics Unit, Gertner Institute for Epidemiology and Health Policy Research, Tel-Hashomer, Israel HaviM@gertner.health.gov.il.

Statistical Methods in Medical Research
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Summary

Regression calibration methods effectively assess interactions in linear models with measurement error. Efficient normal-based regression calibration (NBRC) is preferred for normal covariates, while efficient linear regression calibration (LRC) is better for non-normal covariates.

Keywords:
efficient regression calibrationerrors in variablesinteractionlinear regression calibrationmeasurement error (ME)powerregression calibration (RC)type I error probability

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Area of Science:

  • Statistics
  • Biostatistics
  • Epidemiology

Background:

  • Assessing interactions in linear regression models with measurement error (ME) presents significant challenges.
  • Previous work established regression calibration (RC) methods for normally distributed covariates with classical ME.

Purpose of the Study:

  • To extend normal-based RC (NBRC) and linear RC (LRC) methods to non-classical ME models.
  • To develop and evaluate more efficient versions of NBRC and LRC by combining data from main studies and internal sub-studies.
  • To assess the performance of these methods in the Observing Protein and Energy Nutrition (OPEN) study.

Main Methods:

  • Extension of NBRC and LRC to non-classical ME models.
  • Development of efficient methods combining main study and sub-study data.
  • Application to the OPEN study data and extensive simulations.

Main Results:

  • Efficient NBRC and LRC showed near unbiasedness and good performance for normal covariates with sub-study size ≥200.
  • Efficient NBRC demonstrated lower mean squared error (MSE) than efficient LRC for normal covariates.
  • For non-normal covariates, efficient LRC provided less biased estimators with smaller variance compared to efficient NBRC.
  • Naïve interaction tests maintained nominal Type I error, but efficient NBRC and LRC were more powerful despite slight anti-conservatism.

Conclusions:

  • Efficient NBRC is recommended for estimating and testing interaction effects with normally distributed covariates.
  • Efficient LRC is recommended for estimating and testing interaction effects with markedly non-normal covariates.