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Segmented regression with errors in predictors: semi-parametric and parametric methods

H Küchenhoff1, R J Carroll

  • 1Department of Statistics, Texas A&M University, College Station 77843-3143, USA.

Statistics in Medicine
|January 15, 1997
PubMed
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Measurement error in predictor variables significantly biases threshold estimates in segmented regression models. Functional methods like regression calibration and simulation extrapolation (simex) perform differently than structural methods, with structural models showing better performance in threshold regression.

Area of Science:

  • Statistics
  • Epidemiology
  • Biostatistics

Background:

  • Segmented regression models, particularly threshold models, are common in epidemiology.
  • Exposure variables in occupational and environmental studies often have measurement error.
  • Ignoring measurement error in threshold models leads to biased parameter estimation.

Purpose of the Study:

  • To investigate the impact of additive measurement error on parameter estimation in segmented generalized linear models.
  • To compare the performance of functional (regression calibration, simex) and structural (maximum likelihood) methods in threshold regression with measurement error.

Main Methods:

  • Focus on linear and logistic segmented regression models with additive measurement error.
  • Evaluation of regression calibration and simulation extrapolation (simex) for bias correction.

Related Experiment Videos

  • Comparison with structural, parametric maximum likelihood estimation.

    • Main Results:

    • Measurement error introduces larger and directionally different asymptotic bias in threshold estimation compared to standard generalized linear models.
    • Regression calibration and simex exhibit distinct behaviors in threshold models, with regression calibration often having higher bias and lower variance.
    • Functional and structural methods show substantial performance differences in threshold regression, contrary to findings in standard linear regression.

    Conclusions:

    • Structural (parametric) modeling is a valuable, often neglected, tool for measurement error models, especially in threshold regression.
    • Functional methods can yield estimates significantly more variable than structural methods in threshold regression.
    • Accurate parameter estimation in threshold models requires careful consideration of measurement error and appropriate modeling strategies.