Statistical approaches to identifying significant differences in predictive performance between machine learning and classical statistical models for survival data

Abstract

Research that seeks to compare two predictive models requires a thorough statistical approach to draw valid inferences about comparisons between the performance of the two models. Researchers present estimates of model performance with little evidence on whether they reflect true differences in model performance. In this study, we apply two statistical tests, that is, the 5 × 2-fold cv paired t-test, and the combined 5 × 2-fold cv F-test to provide statistical evidence on differences in predictive performance between the Fine-Gray (FG) and random survival forest (RSF) models for competing risks. These models are trained on different scenarios of low-dimensional simulated survival data to determine whether the differences in their predictive performance that exist are indeed significant. Each simulation was repeated one hundred times on ten different seeds. The results indicate that the RSF model is superior in predictive performance in the presence of complex relationships (quadratic and interactions) between the outcome and its predictors. The two statistical tests show that the differences in performance are significant in quadratic simulation but not significant in interaction simulations. The study has also revealed that the FG model is superior in predictive performance in linear simulations and its differences in predictive performance compared to the RSF model are significant. The combined 5 × 2-fold cv F-test has lower type I error rates compared to the 5 × 2-fold cv paired t-test.