Rank-based variable selection with censored data

A rank-based variable selection procedure is developed for the semiparametric accelerated failure time model with censored observations where the penalized likelihood (partial likelihood) method is not directly applicable. The new method penalizes the rank-based Gehan-type loss function with the ℓ₁ penalty. To correctly choose the tuning parameters, a novel likelihood-based χ²-type criterion is proposed. Desirable properties of the estimator such as the oracle properties are established through the local quadratic expansion of the Gehan loss function. In particular, our method can be easily implemented by the standard linear programming packages and hence numerically convenient. Extensions to marginal models for multivariate failure time are also considered. The performance of the new procedure is assessed through extensive simulation studies and illustrated with two real examples.