Joint Models with Multiple Markers and Multiple Time-to-event Outcomes Using Variational Approximations

TL;DR

This paper introduces a scalable, flexible joint modeling approach using variational approximations to handle multiple markers and survival outcomes, including complex event types, with demonstrated efficiency and accuracy.

Contribution

It proposes a full likelihood joint model with variational approximation for multiple markers and survival outcomes, enhancing scalability and flexibility.

Findings

Variational lower bound closely approximates full likelihood.

Approach is fast and scalable for complex joint models.

Application to breast tissue measurements and cancer diagnosis.

Abstract

Joint models are well suited to modelling linked data from laboratories and health registers. However, there are few examples of joint models that allow for (a) multiple markers, (b) multiple survival outcomes (including terminal events, competing events, and recurrent events), (c) delayed entry and (d) scalability. We propose a full likelihood approach for joint models based on a Gaussian variational approximation to satisfy criteria (a)-(d). We provide an open-source implementation for this approach, allowing for flexible sets of models for the longitudinal markers and survival outcomes. Through simulations, we find that the lower bound for the variational approximation is close to the full likelihood. We also find that our approach and implementation are fast and scalable. We provide an application with a joint model for longitudinal measurements of dense and fatty breast tissue and time to first breast cancer diagnosis. The use of variational approximations provides a promising approach for extending current joint models.