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Flexible parametric approach to classical measurement error variance estimation without auxiliary data.

Aurélie Bertrand1, Ingrid Van Keilegom1,2, Catherine Legrand1

  • 1Institute of Statistics, Biostatistics and Actuarial Sciences, Université catholique de Louvain, Louvain-la-Neuve, Belgium.

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Summary
This summary is machine-generated.

This study introduces a new statistical method to estimate measurement error variance without extra data. This approach corrects bias in models, particularly useful for the Cox proportional hazards model.

Keywords:
Error varianceMeasurement errorProportional hazards modelSurvival analysis

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Area of Science:

  • Statistics
  • Biostatistics
  • Statistical Modeling

Background:

  • Measurement error in continuous covariates causes biased model estimators.
  • Existing correction methods often require information on measurement error distribution, which is frequently unavailable.
  • Validation or auxiliary data, like replicated measurements, are often lacking in practical scenarios.

Purpose of the Study:

  • To develop a flexible, likelihood-based procedure for estimating classical additive error variance.
  • To address scenarios where covariate measurement error distribution is unknown and no auxiliary data is available.
  • To estimate error variance for covariates with compact support.

Main Methods:

  • Developed a likelihood-based estimation procedure for classical additive error variance.
  • Assumed Gaussian distribution for the error and compact support for the covariate.
  • Investigated estimator performance via asymptotic analysis and finite sample simulations.
  • Applied the estimator within the simulation extrapolation (SIMEX) algorithm for the Cox proportional hazards model.

Main Results:

  • The proposed method effectively estimates measurement error variance without requiring additional information.
  • Asymptotic and simulation studies demonstrate the estimator's performance.
  • The method shows utility when integrated with the simulation extrapolation (SIMEX) algorithm.
  • The procedure was successfully illustrated using real-world data.

Conclusions:

  • A novel statistical method is presented for estimating measurement error variance under specific conditions (Gaussian error, compact support).
  • This technique offers a valuable tool for bias correction in statistical models when data is limited.
  • The approach enhances the application of methods like SIMEX in survival analysis, particularly with the Cox proportional hazards model.