The Multivariate Bernoulli detector: Change point estimation in discrete survival analysis

TL;DR

This paper introduces the Multivariate Bernoulli detector, a novel Bayesian change point model for discrete survival data with competing risks, enabling accurate detection of risk-specific hazard changes and their dependencies over time.

Contribution

It proposes a new Bayesian multivariate change point model with data-driven learning of change points and risk involvement, tailored for discrete survival analysis with competing risks.

Findings

Effective in simulations for detecting change points and risk dependencies.

Outperforms existing methods on ICU survival data.

Provides detailed posterior inference on cause-specific hazards.

Abstract

Time-to-event data are often recorded on a discrete scale with multiple, competing risks as potential causes for the event. In this context, application of continuous survival analysis methods with a single risk suffer from biased estimation. Therefore, we propose the Multivariate Bernoulli detector for competing risks with discrete times involving a multivariate change point model on the cause-specific baseline hazards. Through the prior on the number of change points and their location, we impose dependence between change points across risks, as well as allowing for data-driven learning of their number. Then, conditionally on these change points, a Multivariate Bernoulli prior is used to infer which risks are involved. Focus of posterior inference is cause-specific hazard rates and dependence across risks. Such dependence is often present due to subject-specific changes across time that affect all risks. Full posterior inference is performed through a tailored local-global Markov chain Monte Carlo (MCMC) algorithm, which exploits a data augmentation trick and MCMC updates from non-conjugate Bayesian nonparametric methods. We illustrate our model in simulations and on ICU data, comparing its performance with existing approaches.