Yanyan Liu, Ke Tian, Danlu Wang, Jing Zhang
The case-cohort design has been widely used to reduce the cost of covariate measurements in large cohort studies. In this paper, we study the high-dimensional accelerated failure time (AFT) model under the case-cohort design. Based on $\ell_0$-regularization and a newly defined weight function, we propose a weighted least squares procedure for variable selection and parameter estimation. Computationally, we develop a support detection and root finding (SDAR) algorithm, where the support is first determined based on the primal and dual information, then the estimator is obtained by solving the weighted least squares problem restricted to the estimated support. We show the proposed algorithm is essentially one Newton-type algorithm, thus it is more efficient and stable compared with other regularized methods. Theoretically, we establish a sharp error bound for the solution sequences generated from the proposed method. Furthermore, we propose an adaptive version of the proposed SDAR algorithm, which determines the support size of the estimated coefficient in a data-driven manner. Extensive simulation studies demonstrate the superior performance of the proposed procedures, especially for the computational efficiency. As an illustration, we apply the proposed method to a malignant breast tumor gene expression data.
