Should univariate Cox regression be used for feature selection with respect to time-to-event outcomes?

TL;DR

This study compares Cox regression and Gaussian regression of log-transformed survival time for feature selection in time-to-event data, finding Gaussian regression often outperforms Cox models in simulation scenarios.

Contribution

It introduces the use of Gaussian regression of log-transformed survival time as a superior alternative for feature selection over traditional Cox models.

Findings

Gaussian regression outperforms Cox in sensitivity and effect size ranking

Log-transformed Gaussian regression maintains high accuracy across scenarios

Cox models are less effective for feature selection in simulated time-to-event data

Abstract

IMPORTANCE: Time-to-event outcomes are commonly used in clinical trials and biomarker discovery studies and have been primarily analyzed using Cox proportional hazards models. But it's unclear which statistical models should be recommended for feature selection tasks when time-to-event outcomes are of the primary interest. OBJECTIVE: To explore if Gaussian regression of log-transformed survival time could outperform Cox proportional hazards models in feature selection. DESIGN: In this simulation study, the true models are multivariate Cox proportional hazards models with 10 covariates. For all feature selection comparisons, 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 and censoring rate scenario is explored using 10,000 simulation datasets. Different statistical models are applied to the same dataset to estimate feature effects. Model performance is compared using sensitivity, specificity, and accuracy of effect size ranking. RESULTS: When features are independent and the true models are multivariate Cox proportional hazards models, Gaussian regression of log-transformed survival time (response variable) with only two covariates outperformed both the univariate Cox proportional hazards model and logistic regression in feature selection, in terms of not only higher sensitivity, comparable specificity, but also higher accuracy of effect size ranking, regardless of the sample size and censoring rate values. CONCLUSIONS AND RELEVANCE: This study demonstrates the importance of including Gaussian regression of log-transformed survival time in feature selection practice for time-to-event outcomes.