Qi Zheng, Ph.D., University of Louisville

"Censored quantile regression in high dimensional data"

Quantile regression has emerged as a flexible tool to investigate varying covariate effects on respons-es, and thus attracts increasing interests in applications. While most of current quantile regression in high dimensional analysis primary focuses on complete data, the related development in dealing with censored survival (i.e. time-to-event) responses has been relatively sparse. We propose a new penalized censored quantile regression (CQR) in high dimensional survival data. Our two-step procedure sequentially investigates conditional quantiles over a continuum of quantile indices. In the first step, we incorporate Lasso type L1 penalty functions into the stochastic integral based estimating equation for CQR to obtain a uniformly consistent estimator over the quantile region of interest. In the second step, we employ the Adaptive Lasso type penalties and uniform tuning parameter selectors to further reduce the bias induced by L1 penalties. We show that the resulting estimator achieves improved estimation efficiency and model selection consistency. Our theoretical results also include the oracle rate of uniform convergence and weak convergence of the parameter estimators. Moreover, we use numerical studies to confirm our theoretical findings and illustrate the practical utility of our proposal.

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