Stanghellini, Elena; Doretti, Marco On marginal and conditional parameters in logistic regression models. (English) Zbl 1464.62353 Biometrika 106, No. 3, 732-739 (2019). 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. Cited in 1 ReviewCited in 2 Documents MSC: 62J12 Generalized linear models (logistic models) 05C90 Applications of graph theory Keywords:collapsibility; distortion; marginal odds ratio; mediation; path analysis; sensitivity analysis; directed acyclic graph PDFBibTeX XMLCite \textit{E. Stanghellini} and \textit{M. Doretti}, Biometrika 106, No. 3, 732--739 (2019; Zbl 1464.62353) Full Text: DOI arXiv