  IMPORTANCE: Feature selection with respect to time-to-event outcomes is one
of the fundamental problems in clinical trials and biomarker discovery studies.
But it's unclear which statistical methods should be used when sample size is
small or some of the key covariates are not measured. DESIGN: In this
simulation study, the true models are multivariate Cox proportional hazards
models with 10 covariates. It's assumed that only 5 out the 10 true features
are observed/measured for all model fitting, along with 5 random noise
features. Each sample size scenario is explored using 10,000 simulation
datasets. Eight regression models are applied to each dataset to estimate
feature effects, including both regularized Gaussian regression (elastic net
penalty) and regularized Cox regression (glmnet Cox). RESULTS: If the
covariates are highly correlated Gaussian, the Gaussian regression of
log-transformed survival time with only two covariates outperforms all tested
Cox regression models when total number of events <500.
