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Multiple Regression01:25

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Multiple regression assesses a linear relationship between one response or dependent variable and two or more independent variables. It has many practical applications.
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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Maximum likelihood, multiple imputation and regression calibration for measurement error adjustment.

Karen Messer1, Loki Natarajan

  • 1Division of Biostatistics, Moores UCSD Cancer Center, University of California, La Jolla, CA 92093-0901, USA.

Statistics in Medicine
|October 22, 2008
PubMed
Summary
This summary is machine-generated.

This study compares maximum likelihood (ML), multiple imputation (MI), and regression calibration (RC) for estimating exposure-disease associations using surrogate measures. ML performs best with large measurement error or sample sizes, while ML or RC are advantageous for smaller errors and samples.

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Area of Science:

  • Epidemiology
  • Biostatistics
  • Statistical Modeling

Background:

  • Epidemiologic studies often rely on surrogate exposure measures due to practical limitations.
  • Validation sub-studies are crucial for assessing the relationship between surrogate and true exposure.
  • Accurate exposure measurement is vital for reliable exposure-disease association studies.

Purpose of the Study:

  • To evaluate three estimation methods: maximum likelihood (ML), multiple imputation (MI), and regression calibration (RC) in main study/validation study designs.
  • To compare the performance of ML, MI, and RC under various conditions of measurement error and sample size.
  • To provide insights into the selection of appropriate statistical methods for handling surrogate exposure data in epidemiology.

Main Methods:

  • The study discusses and adapts standard software for computing ML and MI estimates for logistic regression.
  • Numerical approximations to the likelihood function are explored for each method.
  • Simulations are conducted to compare estimator performance in realistic and extreme settings, including internal and external validation designs.

Main Results:

  • Maximum likelihood (ML) demonstrated comparable or superior performance to multiple imputation (MI) and regression calibration (RC) when measurement error was large or sample sizes were sufficient.
  • For smaller measurement error and limited sample sizes, ML or RC showed an advantage.
  • The relative variance, rather than bias, primarily determined the performance advantage of RC over ML in most scenarios.

Conclusions:

  • The choice between ML, MI, and RC depends on the interplay between measurement error magnitude and sample size.
  • ML is robust in high measurement error or large sample settings.
  • SAS software code for implementing all three methods is provided to facilitate their application in research.