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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 biomedical applications, a high-dimensional Fine-Gray model has attracted relatively little attention among the methodological or theoretical literature. We fill in this gap by developing confidence intervals based on a one-step bias-correction for a regularized estimation. We develop a theoretical framework for the partial likelihood, which does not have independent and identically distributed entries and therefore presents many technical challenges. We also study the approximation error from the weighting scheme under random censoring for competing risks and establish new 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.
Causal inference has been increasingly reliant on observational studies with rich covariate information. To build tractable causal models, including the propensity score models, it is imperative to first extract important features from high dimension
Though Gaussian graphical models have been widely used in many scientific fields, limited progress has been made to link graph structures to external covariates because of substantial challenges in theory and computation. We propose a Gaussian graphi
There are many scenarios such as the electronic health records where the outcome is much more difficult to collect than the covariates. In this paper, we consider the linear regression problem with such a data structure under the high dimensionality.
Estimating causal effects for survival outcomes in the high-dimensional setting is an extremely important topic for many biomedical applications as well as areas of social sciences. We propose a new orthogonal score method for treatment effect estima
Consider the problem of estimating the local average treatment effect with an instrument variable, where the instrument unconfoundedness holds after adjusting for a set of measured covariates. Several unknown functions of the covariates need to be es