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A joint Bayesian framework for missing data and measurement error using integrated nested Laplace approximations.

Emma Skarstein1, Sara Martino1, Stefanie Muff1,2

  • 1Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway.

Biometrical Journal. Biometrische Zeitschrift
|September 22, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces a unified Bayesian framework to simultaneously address measurement error (ME) and missing data in regression covariates. The method leverages integrated nested Laplace approximations (INLA) for robust data analysis.

Keywords:
Bayesian joint modelBerkson measurement errorclassical measurement errorintegrated nested Laplace approximationmissing data

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Area of Science:

  • Statistical modeling
  • Data analysis methodologies

Background:

  • Measurement error (ME) and missing data are common challenges in statistical analysis.
  • Existing methods often treat ME and missing data as separate issues, despite their theoretical links.
  • Accounting for ME in regression covariates is less common than handling missing data.

Purpose of the Study:

  • To develop a unified Bayesian framework for simultaneously handling ME and missing data in continuous covariates.
  • To extend existing ME methodology to incorporate missing data as an extreme case of ME.
  • To provide a flexible approach applicable to various ME types (classical, Berkson) and missing data scenarios within regression models.

Main Methods:

  • Utilizing a Bayesian framework with integrated nested Laplace approximations (INLA).
  • Exploiting the relationship between missing data and classical ME.
  • Developing an approach for handling missing data within INLA, applicable when no ME is present.
  • Incorporating Berkson ME into the same Bayesian framework.

Main Results:

  • Demonstrated simultaneous accounting for ME and missing data in the same covariate.
  • Showcased an approach for handling missing data in INLA as a special case of ME.
  • Extended the framework to include Berkson ME.
  • The joint Bayesian framework accommodates combinations of ME and missing data in continuous covariates.

Conclusions:

  • The proposed joint Bayesian framework offers a unified solution for ME and missing data in regression models.
  • The approach is versatile, handling classical ME, Berkson ME, and missing data, individually or in combination.
  • The methodology is exemplified with simulated and real data, supported by reproducible R-INLA and inlabru examples.