Variable selection with time-to-event data: Cox or Weibull regression?

Abstract

The Cox proportional hazards and Weibull accelerated failure time regression models are compared in the context of variable selection, focusing on their characteristics from the practitioner’s perspective and their practical uses, with less focus on a comparison of their theoretical properties. The question of whether there is a practical difference between the two models that could be beneficial, mainly for practitioners in the field of variable selection, is addressed. The two regression models are assessed through comparative evaluation studies, using real, high dimensional, gene expression data, followed by Monte Carlo simulation studies. Both the empirical evaluation and simulation studies provide strong evidence that Weibull regression outperforms that of Cox in terms of predictive performance, the number of selected variables, and the number of falsely-selected ones. Despite the popularity of the Cox regression model, the results show that in terms of predictability, the Weibull model outperforms it.