Session title: Survival analysis with high-dimensional data
Organizer: Ingrid Van Keilegom (KU Leuven)
Chair: Ricardo Cao (Universidade da Coruña)
Time: June 4th, 11:00am-12:30am
Location: VEC 903
Speech 1: Robust optimal treatment regime estimation with survival outcome
Speaker: Lan Wang (U Minnesota)
Abstract: We consider estimating the single-stage quantile-optimal treatment regime from data with right-censored outcome. The proposed method is directly applicable to individualized treatment decision making in medicine when survival time or time to event is used as the primary end point, and the produced estimated rule is easy to interpret since the quantile-type statistics is widely used in such context. We proposed a nonparametric estimator belonging to value search category in literature, which directly estimates the optimal rule from a class of practically useful treatment regimes without posing constraints on the way treatment interact with covariates. We studied the nonstandard asymptotics for the estimated parameter of the optimal rule using semiparametric
M-estimation theories, which reveals how censoring is influencing the uncertainty in the learned rule. (Joint work with Yu Zhou and Rui Song).
Speech 2: Fine-Gray Competing Risks Model with High-Dimensional Covariates: Estimation and Inference
Speaker: Jelena Bradic (University of California, San Diego)
Abstract: The purpose of this paper is to construct confidence intervals for the regression coefficients in the Fine-Gray model for competing risks data with random censoring, where the number of covariates can be larger than the sample size. Despite strong motivation from biostatistics applications, highdimensional Fine-Gray model has attracted relatively little attention among the methodological or theoretical literatures. We fill in this blank by proposing first a consistent regularized estimator and then the confidence intervals based on the one-step bias-correcting estimator. We are able to generalize the partial likelihood approach for the Fine-Gray model under random censoring despite many technical difficulties. We lay down a methodological and theoretical framework for the one-step bias-correcting estimator with the partial likelihood, which does not have independent and identically distributed entries. We also handle for our theory the approximation error from the inverse probability weighting (IPW), proposing novel concentration results for time dependent processes. In addition to the theoretical results and algorithms, we present extensive numerical experiments and an application to a study of non-cancer mortality among prostate cancer patients using the linked Medicare-SEER data.
Speech 3: Envelopes for censored quantile regression
Speaker: Yue Zhao (KU Leuven)
Abstract: Quantile regression has emerged as a powerful tool for survival analysis with censored data. We propose an efficient estimator for the coefficients in quantile regression with censored data using the envelope model. The envelope model uses dimension reduction techniques to identify material and immaterial components in the data, and forms the estimator of the regression coefficient based only on the material component, thus reducing the variability of the estimation. We will derive asymptotic properties of the proposed estimator and demonstrate its efficiency gains compared to the traditional estimator for the quantile regression with censored data. The starting point of our technical analysis is the Z-estimation approach with local weighing (e.g., Wang & Wang 2009) that in particular involves the conditional Kaplan-Meier estimator. Traditionally, the Kaplan-Meier estimator is treated as an infinite dimensional nuisance parameter. We will instead invoke the i.i.d. representation of the Kaplan-Meier estimator, which leads to a re-writing of our objective function as a U-process indexed by only the Euclidean parameter in the envelope model. The modified Z-estimation problem then becomes much more amenable to analysis.