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Table 1 Main characteristics of each of four approaches

From: Applied causal inference methods for sequential mediators

Decomposition of total effect

IORW\(^{*}\)

IPW\(^{**}\)

Imputation

Extended imputation

     Two-way

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     Three-way

   

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Type of estimated effects

    

     Marginal

 

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     Conditional

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Models for

    

     Outcome

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     Mediators\(^{\#}\)

   

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     Exposure

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     Nested counterfactual

  

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Exposure type

    

     Binary

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     Categorical

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     Count

    

     Continuous

\(\surd ^{++}\)

\(\surd ^{++}\)

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Outcome type

    

     Binary

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     Categorical

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     Count

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     Continuous

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Mediator type

    

     Binary

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     Categorical

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     Count

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     Continuous

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Interactions

    

     Exposure-mediators

\(^{\#\#}\)

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     Exposure-covariates

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     Mediator-mediator

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     Mediators-covariates

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  1. *Inverse odds ratio weighting.
  2. ** Inverse probability weighting.
  3. # The presented methods circumvent the difficulty of specifying a regression model for the joint density of multiple mediators, with the exception of the extended imputation approach, which requires the specification of a model for the first or the second mediator in presence of two mediators.
  4. ++ The performance improves as the exposure is binary or categorical with few levels.
  5. ## IOR is equally valid regardless of whether such interactions are present, without having to specify them, since the mediators are never entered into the regression model for the outcome and are only used to calculate the weights which are obtained by a regression model of the exposure on the mediators and the covariates