  Variable selection problem for the nonlinear Cox regression model is
considered. In survival analysis, one main objective is to identify the
covariates that are associated with the risk of experiencing the event of
interest. The Cox proportional hazard model is being used extensively in
survival analysis in studying the relationship between survival times and
covariates, where the model assumes that the covariate has a log-linear effect
on the hazard function. However, this linearity assumption may not be satisfied
in practice. In order to extract a representative subset of features, various
variable selection approaches have been proposed for survival data under the
linear Cox model. However, there exists little literature on variable selection
for the nonlinear Cox model. To break this gap, we extend the recently
developed deep learning-based variable selection model LassoNet to survival
data. Simulations are provided to demonstrate the validity and effectiveness of
the proposed method. Finally, we apply the proposed methodology to analyze a
real data set on diffuse large B-cell lymphoma.
