Sure joint feature screening in nonparametric transformation model for right censored data

Existing screening procedures for right censored data either posit a specific model or adopt a marginal approach; hence, they are prone to model misspecification or erroneous screening. To address these problems, we develop a joint feature screening method in nonparametric transformation models for censored survival data. A sparsity‐restricted estimator is proposed using a smoothed partial rank objective function and an iterative hard thresholding algorithm. We rigorously show that with probability tending to 1, the proposed method is capable of retaining all relevant features in the model and is more desirable than marginal screening. Furthermore, because the transformation model encompasses many popular models, such as the Cox model, as special cases, the developed joint screening method is more robust than its competitors. Its finite sample performance is illustrated using both simulation studies and a real data example. We have implemented our method using Matlab and made it available through Github https://github.com/yiucla/SPR-SJS .