Square root Cox's survival analysis by the fittest linear and neural networks model

TL;DR

This paper introduces a novel survival analysis method that directly tunes the penalty parameter for feature selection using a square root transformation of Cox's partial likelihood, applicable to both linear models and neural networks.

Contribution

It presents a new approach to feature selection in survival analysis that improves over traditional methods by using an asymptotically pivotal penalty parameter based on the square root of Cox's likelihood.

Findings

Outperforms cross-validation LASSO and BIC in feature selection accuracy.

Exhibits a phase transition in feature recovery probability similar to compressed sensing.

Applicable to both linear models and neural networks.

Abstract

We revisit Cox's proportional hazard models and LASSO in the aim of improving feature selection in survival analysis. Unlike traditional methods relying on cross-validation or BIC, the penalty parameter $\lambda$ is directly tuned for feature selection and is asymptotically pivotal thanks to taking the square root of Cox's partial likelihood. Substantially improving over both cross-validation LASSO and BIC subset selection, our approach has a phase transition on the probability of retrieving all and only the good features, like in compressed sensing. The method can be employed by linear models but also by artificial neural networks.