Browsing by Subject "Path analysis"

Now showing 1 - 2 of 2
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    Identifying brain hierarchical structures associated with Alzheimer’s disease using a regularized regression method with tree predictors
    (Oxford University Press, 2023) Zhao, Yi; Wang, Bingkai; Liu, Chin-Fu; Faria, Andreia V.; Miller, Michael I.; Caffo, Brian S.; Luo, Xi; Biostatistics and Health Data Science, School of Medicine
    Brain segmentation at different levels is generally represented as hierarchical trees. Brain regional atrophy at specific levels was found to be marginally associated with Alzheimer’s disease outcomes. In this study, we propose an ℓ1-type regularization for predictors that follow a hierarchical tree structure. Considering a tree as a directed acyclic graph, we interpret the model parameters from a path analysis perspective. Under this concept, the proposed penalty regulates the total effect of each predictor on the outcome. With regularity conditions, it is shown that under the proposed regularization, the estimator of the model coefficient is consistent in ℓ2-norm and the model selection is also consistent. When applied to a brain sMRI dataset acquired from the Alzheimer’s Disease Neuroimaging Initiative (ADNI), the proposed approach identifies brain regions where atrophy in these regions demonstrates the declination in memory. With regularization on the total effects, the findings suggest that the impact of atrophy on memory deficits is localized from small brain regions, but at various levels of brain segmentation. Data used in preparation of this paper were obtained from the ADNI database.
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    Pathway Lasso: Pathway Estimation and Selection with High-Dimensional Mediators
    (International Press, 2022) Zhao, Yi; Luo, Xi; Biostatistics, School of Public Health
    In many scientific studies, it becomes increasingly important to delineate the pathways through a large number of mediators, such as genetic and brain mediators. Structural equation modeling (SEM) is a popular technique to estimate the pathway effects, commonly expressed as the product of coefficients. However, it becomes unstable and computationally challenging to fit such models with high-dimensional mediators. This paper proposes a sparse mediation model using a regularized SEM approach, where sparsity means that a small number of mediators have a nonzero mediation effect between a treatment and an outcome. To address the model selection challenge, we innovate by introducing a new penalty called Pathway Lasso. This penalty function is a convex relaxation of the non-convex product function for the mediation effects, and it enables a computationally tractable optimization criterion to estimate and select pathway effects simultaneously. We develop a fast ADMM-type algorithm to compute the model parameters, and we show that the iterative updates can be expressed in closed form. We also prove the asymptotic consistency of our Pathway Lasso estimator for the mediation effect. On both simulated data and an fMRI data set, the proposed approach yields higher pathway selection accuracy and lower estimation bias than competing methods.