Joint Models for Event Prediction From Time Series and Survival Data

We present a nonparametric prognostic framework for individualized event prediction based on joint modeling of both time series and time-to-event data. Our approach exploits a multivariate Gaussian convolution process (MGCP) to model the evolution of time series signals and a Cox model to map time-to-event data with time series data modeled through the MGCP. Taking advantage of the unique structure imposed by convolved processes, we provide a variational inference framework to simultaneously estimate parameters in the joint MGCP-Cox model. This significantly reduces computational complexity and safeguards against model overfitting. Experiments on synthetic and real world data show that the proposed framework outperforms state-of-the art approaches built on two-stage inference and strong parametric assumptions. Technical details are available in the supplementary materials.