On marginal and conditional parameters in logistic regression models

We derive the exact formula linking the parameters of marginal and conditional logistic regression models with binary mediators when no conditional independence assumptions can be made. The formula has the appealing property of being the sum of terms that vanish whenever parameters of the conditiona...

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Bibliographic Details
Published in:Biometrika 2019-09, Vol.106 (3), p.732-739
Main Authors: Stanghellini, Elena, Doretti, Marco
Format: Article
Language:English
Subjects:
Graphical representations
Parameter sensitivity
Random variables
Regression analysis
Regression models
Sensitivity analysis
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Summary:We derive the exact formula linking the parameters of marginal and conditional logistic regression models with binary mediators when no conditional independence assumptions can be made. The formula has the appealing property of being the sum of terms that vanish whenever parameters of the conditional models vanish, thereby recovering well-known results as particular cases. It also permits the disentangling of direct and indirect effects as well as quantifying the distortion induced by the omission of relevant covariates, opening the way to sensitivity analysis. As the parameters of the conditional models are multiplied by terms that are always bounded, the derivations may also be used to construct reasonable bounds on the parameters of interest when relevant intermediate variables are unobserved. We assume that, conditionally on a set of covariates, the data-generating process can be represented by a directed acyclic graph. We also show how the results presented here lead to the extension of path analysis to a system of binary random variables.
ISSN:0006-3444
1464-3510
DOI:10.1093/biomet/asz019