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Direct effect and indirect effect on an outcome under nonlinear modeling.

Kai Wang1

  • 1Department of Biostatistics, University of Iowa, Iowa City, 52242-1002, IA, USA.

The International Journal of Biostatistics
|May 23, 2020
PubMed
Summary

This study introduces exact formulas for generalized linear models, revealing that counterfactual and difference/product methods yield different effect estimates. These methods are only equivalent under specific conditions, particularly for accelerated failure time and proportional hazards models.

Keywords:
causal inferencedifference methodlikelihoodmediationnatural effectsproduct method

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Area of Science:

  • Statistics
  • Epidemiology
  • Biostatistics

Background:

  • Generalized linear models (GLMs) are widely used in statistical analysis.
  • Understanding mediation and effect decomposition is crucial for causal inference.
  • Existing methods for estimating direct and indirect effects have varying assumptions and properties.

Purpose of the Study:

  • To derive exact formulas relating parameters in conditional and reduced GLMs.
  • To compare the counterfactual, difference, and product methods for effect estimation.
  • To investigate the conditions under which these methods yield equivalent results.

Main Methods:

  • Development of exact formulas for parameter relationships in GLMs.
  • Mathematical comparison of effect decomposition methods (counterfactual, difference, product).
  • Analysis of specific link functions (logit) and survival models (accelerated failure time, proportional hazards).

Main Results:

  • Counterfactual direct and indirect effects are generally smaller in magnitude than difference and product method estimates, respectively.
  • Total effects from counterfactual and difference methods are not always equivalent, contrary to prior assumptions.
  • Equivalence between difference and product methods is demonstrated for accelerated failure time models and under specific conditions for proportional hazards models.

Conclusions:

  • The choice of method for effect decomposition in GLMs impacts results.
  • Careful consideration of model specifications and link functions is necessary for accurate causal effect estimation.
  • The study provides a framework for understanding discrepancies and achieving equivalence between different mediation analysis approaches.