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Hypothesis testing in an errors-in-variables model with heteroscedastic measurement errors.

Mário de Castro1, Manuel Galea, Heleno Bolfarine

  • 1Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Caixa Postal 668, 13560-970 São Carlos-SP, Brazil. mcastro@icmc.usp.br

Statistics in Medicine
|June 19, 2008
PubMed
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This study addresses statistical models for disease incidence and risk factors with measurement errors. It introduces methods for accurate inference and model assessment, crucial for epidemiological research.

Area of Science:

  • Epidemiology
  • Biostatistics
  • Statistical Modeling

Background:

  • Regression models are vital in epidemiology for disease incidence and risk factor analysis.
  • Handling error-prone observations and varying measurement error variances presents significant statistical challenges.

Purpose of the Study:

  • To develop robust inference methods for regression models with measurement errors in epidemiological studies.
  • To address situations where measurement error variances change across observations.

Main Methods:

  • Utilizing bivariate normal distribution for observations and normal distribution for measurement errors.
  • Employing the Expectation-Maximization (EM) algorithm for numerical computation of maximum likelihood estimates.
  • Estimating error variances using aggregate data.

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Main Results:

  • Developing consistent estimation for the asymptotic variance of maximum likelihood estimators.
  • Proposing test statistics for hypothesis testing and a graphical device for model goodness-of-fit assessment.
  • Demonstrating the approach with data from the WHO MONICA Project on cardiovascular disease.

Conclusions:

  • The proposed methods provide a framework for reliable statistical inference in epidemiological studies with complex measurement error structures.
  • The EM algorithm and associated statistical tests offer practical tools for analyzing disease incidence data.
  • The graphical assessment aids in evaluating the suitability of the model for real-world epidemiological data.