When to encourage using Gaussian regression for feature selection tasks with time-to-event outcome

TL;DR

This study compares Gaussian regression and Cox regression for feature selection in time-to-event data, finding Gaussian regression effective with small samples and highly correlated covariates.

Contribution

It demonstrates that Gaussian regression can outperform Cox regression in small-sample, high-correlation scenarios for feature selection in survival analysis.

Findings

Gaussian regression outperforms Cox regression with fewer than 500 events.

Highly correlated covariates favor Gaussian regression.

Gaussian regression is effective with small sample sizes and unmeasured covariates.

Abstract

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.