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.

On marginal and conditional parameters in logistic regression models / Stanghellini Elena; Doretti Marco. - In: BIOMETRIKA. - ISSN 0006-3444. - STAMPA. - Volume 106,:(2019), pp. 732-739. [10.1093/biomet/asz019]

### On marginal and conditional parameters in logistic regression models

#### Abstract

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.
##### Scheda breve Scheda completa Scheda completa (DC)
2019
Volume 106,
732
739
Stanghellini Elena; Doretti Marco
File in questo prodotto:
File
1804.03062.pdf

Accesso chiuso

Licenza: Tutti i diritti riservati
Dimensione 135.97 kB
Stanghellini&Doretti.pdf

Accesso chiuso

Licenza: Tutti i diritti riservati
Dimensione 169.86 kB
Utilizza questo identificatore per citare o creare un link a questa risorsa: `https://hdl.handle.net/2158/1344357`