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Identification and Quantification of Deranged Metabolites in Critically Ill Patients Using NMR-Based Metabolomics
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Sensitivity and identification quantification by a relative latent model complexity perturbation in Bayesian

Małgorzata Roos1, Sona Hunanyan1, Haakon Bakka2

  • 1Department of Biostatistics, EBPI, University of Zurich, Zurich, Switzerland.

Biometrical Journal. Biometrische Zeitschrift
|August 11, 2021
PubMed
Summary

This study introduces a new method to assess how prior beliefs and data uncertainty affect Bayesian meta-analysis results. The developed quantification (S-I) helps identify sensitive model parameters for more reliable evidence synthesis.

Keywords:
Bayesian meta-analysisformal sensitivity and identification diagnosticsnormal-normal hierarchical modelnormal-t hierarchical modelrelative latent model complexity

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Area of Science:

  • Statistics
  • Biostatistics
  • Evidence Synthesis

Background:

  • Bayesian meta-analysis using normal-normal hierarchical models (NNHM) is common but sensitive to prior choices and data uncertainty.
  • Existing methods lack a unified approach to quantify the impact of heterogeneity priors (sensitivity) and within-study standard deviation uncertainty (identification) on NNHM posterior inference.

Purpose of the Study:

  • To develop and present a unified method for simultaneously quantifying sensitivity (S) and identification (I) for all parameters in Bayesian NNHM.
  • To assess the impact of heterogeneity priors and within-study standard deviation uncertainty on Bayesian meta-analysis.
  • To extend the applicability of the S-I quantification to Bayesian non-normal hierarchical models (NtHM).

Main Methods:

  • Developed a unified method based on derivatives of the Bhattacharyya coefficient with respect to relative latent model complexity (RLMC) perturbations.
  • Applied the method to quantify S-I for model parameters in Bayesian NNHM.
  • Investigated six scenarios crossing three RLMC targets with two heterogeneity priors (half-normal, half-Cauchy).
  • Extended the S-I quantification to Bayesian NtHM.

Main Results:

  • The S-I quantification explicitly identifies model parameters influenced by heterogeneity priors and uncertainty in within-study standard deviations.
  • Compared the impact of different heterogeneity priors and quantified the effect of omitting a large study and randomization status on S-I values.
  • Demonstrated the method's applicability through three case studies involving historical data, study exclusion, and subgroup meta-analyses.

Conclusions:

  • The developed S-I method provides crucial insights into parameter sensitivity and data identification in Bayesian meta-analysis.
  • This quantification aids researchers in understanding the robustness of their findings to prior assumptions and data limitations.
  • An R package is available to facilitate automatic S-I quantification in applied Bayesian meta-analyses, enhancing reproducibility and reliability.