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Bayesian second-order sensitivity of longitudinal inferences to non-ignorability: an application to antidepressant clinical trial data.

The international journal of biostatistics·2023
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Second-order local sensitivity to non-ignorability in Bayesian inferences.

Samaneh Eftekhari Mahabadi1

  • 1School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, 14155-6455, Iran.

Statistics in Medicine
|June 7, 2018
PubMed
Summary
This summary is machine-generated.

This study introduces a second-order sensitivity analysis for Bayesian inferences in generalized linear models (GLMs) with incomplete data. This method accurately assesses non-ignorability, even with curved posterior expectations, unlike simpler first-order methods.

Keywords:
Bayesian approachgeneralized linear modelignorabilityincomplete datasecond-order sensitivity analysis

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Area of Science:

  • Statistics
  • Biostatistics
  • Computational Statistics

Background:

  • Bayesian inference for incomplete data requires careful handling of non-ignorability.
  • Current first-order sensitivity analyses may inadequately capture potential sensitivity when posterior expectations exhibit significant curvature.

Purpose of the Study:

  • To develop and present a second-order sensitivity analysis method for Bayesian inferences in generalized linear models (GLMs).
  • To provide a more precise tool for assessing the impact of non-ignorability, especially when first-order methods are insufficient.

Main Methods:

  • The proposed method calculates a second-order sensitivity index locally around the ignorable model in GLMs.
  • This calculation relies on posterior covariances from the standard ignorable model, ensuring computational efficiency.
  • The approach is validated through simulation studies and applied to a real-world dataset with incomplete CD4 cell counts.

Main Results:

  • The second-order sensitivity index effectively identifies potential sensitivity to non-ignorability, particularly in cases with curved posterior expectations where first-order methods fail.
  • The proposed method demonstrates comparable or superior performance to first-order methods, especially in non-linear scenarios.
  • The computational overhead for the second-order index is minimal.

Conclusions:

  • Second-order sensitivity analysis offers a more robust and precise approach to evaluating the impact of non-ignorability in Bayesian analyses of incomplete data.
  • The developed method is efficient and applicable to GLMs, providing valuable insights for statistical modeling and data analysis.
  • The approach is particularly useful for screening and understanding the influence of missing data assumptions.