Speaker: Qi Zheng, Ph.D, Department of Bioinformatics and Biostatistics, University of Louisville

Title: "Globally Adaptive Longitudinal Quantile Regression with High Dimensional Compositional Covariates"

The human microbiome is associated with many diseases and is often characterized by high dimensional compositional structure. In many microbiome studies, measurements are taken longitudinally and the outcome of interest is subject to left censoring due to detection limit or other reasons. In this paper, we propose a cross-sectional longitudinal quantile regression framework that investigates the association between the continuous outcome of interest and human microbiome composition along with other usual covariates. Log-contrast of compositions is used and then be reformulated as asymmetric form with zero-sum coefficients. To minimize the objective function with non-differentiable terms and linear constraint, we smooth quantie loss function to use the maximization-minimization trick that yield closed-form updates in each step of coordinate descent algorithm. The oracle properties of the regularized globally concerned quantile estimator are obtained. No matter which active variable is chosen as a reference, the asymptotic behaviors are equivalent. We conduct several setups of simulation studies to assess the finite sample performance of the proposed estimator. The human microbiome data is used to illustrate the practicality of the proposed method.

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