TransformerLSR: Attentive Joint Model of Longitudinal Data, Survival, and Recurrent Events with Concurrent Latent Structure (2404.03804v1)

Abstract: 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.

• The paper introduces TransformerLSR, a novel joint modeling framework that integrates longitudinal data, survival outcomes, and recurrent events.
• It employs an encoder-decoder transformer architecture with causal masking and trajectory representation to enhance interpretability and dynamic forecasting.
• Empirical tests, including a kidney transplantation dataset, show superior performance over traditional methods, offering potential in personalized medicine.

TransformerLSR: A Novel Approach for Joint Modeling of Longitudinal Data, Survival, and Recurrent Events

Introduction to TransformerLSR

The need for joint modeling of longitudinal data, survival data, and recurrent events has become increasingly essential in various fields including biomedical studies, epidemiology, and social sciences. While significant advancements have been made in statistical methodologies to handle these components, existing methods often fall short due to heavy parametric assumptions and lack of scalability. In response to these limitations, a novel approach, TransformerLSR, is proposed. This method leverages the flexibility of deep learning models, specifically transformer-based architecture, to overcome the challenges presented by the conventional joint modeling techniques.

TransformerLSR innovatively integrates deep temporal point processes for modeling recurrent events alongside longitudinal variables and survival data. This model distinguishes itself by treating recurrent and terminal events as two competing processes, which depend on past longitudinal measurements and event times, thus capturing the inherent complexities of the data structures. Furthermore, TransformerLSR introduces a unique trajectory representation, allowing for the incorporation of known latent structures among concurrent longitudinal variables. This aspect is particularly crucial for improving model interpretability and harnessing clinical knowledge in the modeling process.

Methodological Foundations of TransformerLSR

The proposed TransformerLSR framework centers around an encoder-decoder transformer architecture, conducive for modeling time-dependent data. Key components of this model include:

• Trajectory Representation and Causal Masking: It adopts an autoregressive modeling approach for longitudinal variables, which is refined by clinical insights into the causal relationships among these variables. Such representation enhances model interpretability and utilization of clinical knowledge.
• Encoder Architecture: The encoder processes patient histories by embedding baseline covariates, longitudinal measurements, and temporal information. This design ensures the comprehensive representation of patient data.
• Decoder Design: It outputs predictions for future longitudinal measurements, event intensities, and hazard rates. The decoder architecture facilitates dynamic forecasting, offering insights into both immediate and long-term patient outcomes.
• Training: Incorporates losses from longitudinal variable predictions, recurrent event modeling, and survival analysis, ensuring comprehensive learning of the data dynamics.

Comparative Analysis and Practical Implications

TransformerLSR was rigorously tested through simulation studies against several alternative approaches, demonstrating superior performance in modeling longitudinal measurements and survival data, as well as accurately capturing recurrent event intensities. Furthermore, the application of TransformerLSR to a real-world medical dataset on patients post-kidney transplantation illustrated its capability to make meaningful inferences and predictions.

This framework opens up new avenues for the dynamic prediction of individual patient outcomes, holding significant potential for personalized medicine. By providing detailed insights into the relationships between patient visits, health measurements, and survival chances, TransformerLSR enables healthcare providers to make informed decisions tailored to individual patient needs.

Future Directions

Looking ahead, there are several promising directions for further research based on the TransformerLSR framework. Exploring techniques for enhancing model interpretability, integrating causal modeling for counterfactual outcome estimation, and extending the model's application to other domains are among the key areas for future development.

TransformerLSR stands as a pioneering model in the landscape of joint modeling, paving the way for more accurate, scalable, and clinically informed approaches to understanding complex health data.