Support vector machine for dynamic survival prediction with time-dependent covariates

Abstract

Predicting time-to-event outcomes using time-dependent covariates is a challenging problem. Many machine learning approaches, such as tree-based methods and support vector regression, predominantly utilize only baseline covariates. Only a few methods can incorporate time-dependent covariates, but they often lack theoretical justification. In this paper we present a new framework for event time prediction, leveraging the support vector machines to forecast the associated counting processes. Utilizing the kernel trick, we accommodate nonlinear functions in both time and covariate spaces. Subsequently, we use a chain algorithm to predict future events. Theoretical analysis proves that our method is equivalent to comparing time-varying hazard rates among at-risk subjects, and we obtain the convergence rate of the resulting prediction loss. Through simulation studies and a case study on Huntington’s disease, we demonstrate the superior performance of our approach compared to alternative methods based on machine learning, deep learning, and statistical models.