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 ℓ0 norm with a continuous or smooth unit dent function. The proposed method bridges the best subset selection and regularisation by borrowing strength from both. It mimics the best subset selection using a penalised likelihood approach yet with no need of a tuning parameter. We further reformulate the problem with a reparameterisation 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 reparameterisation tactic yields an additional advantage in terms of circumventing post-selection inference. The oracle property of the proposed method is established. Both simulated experiments and empirical examples are provided for assessment and illustration.