TransformerLSR: Attentive Joint Model of Longitudinal Data, Survival,
  and Recurrent Events with Concurrent Latent Structure
Zhiyue Zhang Yao Zhao Yanxun Xu
In applications such as biomedical studies, epidemiology, and social
sciences, recurrent events often co-occur with longitudinal measurements and a
terminal event, such as death. Therefore, jointly modeling longitudinal
measurements, recurrent events, and survival data while accounting for their
dependencies is critical. While joint models for the three components exist in
statistical literature, many of these approaches are limited by heavy
parametric assumptions and scalability issues. Recently, incorporating deep
learning techniques into joint modeling has shown promising results. However,
current methods only address joint modeling of longitudinal measurements at
regularly-spaced observation times and survival events, neglecting recurrent
events. In this paper, we develop TransformerLSR, a flexible transformer-based
deep modeling and inference framework to jointly model all three components
simultaneously. TransformerLSR integrates deep temporal point processes into
the joint modeling framework, treating recurrent and terminal events as two
competing processes dependent on past longitudinal measurements and recurrent
event times. Additionally, TransformerLSR introduces a novel trajectory
representation and model architecture to potentially incorporate a priori
knowledge of known latent structures among concurrent longitudinal variables.
We demonstrate the effectiveness and necessity of TransformerLSR through
simulation studies and analyzing a real-world medical dataset on patients after
kidney transplantation.