Physics

Trajectory

Mathematical economics

Mathematics

Statistics

Astronomy

Machine learning

Outcome (game theory)

Mathematical analysis

Artificial intelligence

Multivariate statistics

Generalization

Computer science

Statistical Methods in Medical Research

Identifying and monitoring multiple disease biomarkers and other clinically important factors affecting the course of a disease, behavior or health status is of great clinical relevance. Yet conventional statistical practice generally falls far short of taking full advantage of the information available in multivariate longitudinal data for tracking the course of the outcome of interest. We demonstrate a method called multi-trajectory modeling that is designed to overcome this limitation. The method is a generalization of group-based trajectory modeling. Group-based trajectory modeling is designed to identify clusters of individuals who are following similar trajectories of a single indicator of interest such as post-operative fever or body mass index. Multi-trajectory modeling identifies latent clusters of individuals following similar trajectories across multiple indicators of an outcome of interest (e.g., the health status of chronic kidney disease patients as measured by their eGFR, hemoglobin, blood CO2 levels). Multi-trajectory modeling is an application of finite mixture modeling. We lay out the underlying likelihood function of the multi-trajectory model and demonstrate its use with two examples.

Group-based multi-trajectory modeling