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Mediation analysis for count and zero-inflated count data without sequential ignorability and its application in

Zijian Guo1, Dylan S Small2, Stuart A Gansky3

  • 1Rutgers University, Piscataway, USA.

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Summary

This study introduces new causal mediation analysis methods for count data, addressing zero-inflation and avoiding unmeasured confounding. The approach uses instrumental variables to accurately estimate direct and indirect effects in complex scenarios.

Keywords:
Estimating equationInstrumental variableNegative binomial modelNeyman type A distributionPoisson modelSensitivity analysis

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Area of Science:

  • Causal inference
  • Biostatistics
  • Epidemiology

Background:

  • Mediation analysis investigates treatment-outcome mechanisms.
  • Count and zero-inflated count outcomes are prevalent in research.
  • Standard mediation methods often assume sequential ignorability, which is frequently violated due to unmeasured confounding.

Purpose of the Study:

  • To develop causal mediation analysis methods for count data with potential zero-inflation.
  • To overcome the limitation of sequential ignorability assumption using instrumental variable approaches.
  • To consistently estimate direct and indirect effects in the presence of unmeasured confounding.

Main Methods:

  • Development of causal methods based on instrumental variable approaches for count data.
  • Definition of direct and indirect effect ratios for zero-inflated count outcomes.
  • Proposal of estimating equations and use of empirical likelihood for consistent estimation.
  • Inclusion of a sensitivity analysis for instrumental variable exclusion restriction violations.

Main Results:

  • Simulation studies confirm the method's efficacy across various outcome types and settings.
  • The proposed method effectively handles count data with high proportions of zeros.
  • Demonstrated robustness against violations of the sequential ignorability assumption.

Conclusions:

  • The novel instrumental variable-based mediation analysis provides a robust framework for count data.
  • This method is applicable to diverse fields, including dental research and public health studies on child diarrhea.
  • Offers a significant advancement for causal mediation analysis when dealing with complex count outcomes and unmeasured confounding.