Sparse estimation of Cox proportional hazards models via approximated information criteria
Summary
We propose a new sparse estimation method for Cox (1972) proportional hazards models by optimizing an approximated information criterion. The main idea involves approximation of the 
norm with a continuous or smooth unit dent function. The proposed method bridges the best subset selection and regularization by borrowing strength from both. It mimics the best subset selection using a penalized likelihood approach yet with no need of a tuning parameter. We further reformulate the problem with a reparameterization step so that it reduces to one unconstrained nonconvex yet smooth programming problem, which can be solved efficiently as in computing the maximum partial likelihood estimator (MPLE). Furthermore, the reparameterization tactic yields an additional advantage in terms of circumventing postselection inference. The oracle property of the proposed method is established. Both simulated experiments and empirical examples are provided for assessment and illustration.
Citing Literature
Number of times cited according to CrossRef: 9
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- Shuwei Li, Qiwei Wu, Jianguo Sun, Penalized estimation of semiparametric transformation models with interval-censored data and application to Alzheimer’s disease, Statistical Methods in Medical Research, 10.1177/0962280219884720, (096228021988472), (2019).
- Ai Ni, Jianwen Cai, Tuning Parameter Selection in Cox Proportional Hazards Model with a Diverging Number of Parameters, Scandinavian Journal of Statistics, 10.1111/sjos.12313, 45, 3, (557-570), (2018).
- Dongxiao Han, Lei Liu, Xiaogang Su, Bankole Johnson, Liuquan Sun, Variable selection for random effects two-part models, Statistical Methods in Medical Research, 10.1177/0962280218784712, (096228021878471), (2018).
- Clara Rodriguez-Sabate, Ingrid Morales, Alberto Sanchez, Manuel Rodriguez, The Multiple Correspondence Analysis Method and Brain Functional Connectivity: Its Application to the Study of the Non-linear Relationships of Motor Cortex and Basal Ganglia, Frontiers in Neuroscience, 10.3389/fnins.2017.00345, 11, (2017).
