Incorporating latent survival trajectories and covariate heterogeneity in time-to-event data analysis: a joint mixture model approach

Abstract

Background

Finite mixture models have been recently applied in time-to-event data to identify subgroups with distinct hazard functions, yet they often assume differing covariate effects on failure times across latent classes but homogeneous covariate distributions. This study aimed to develop a method for analyzing time-to-event data while accounting for unobserved heterogeneity within a mixture modeling framework.

Methods

A joint model was developed to incorporate latent survival trajectories and observed information for the joint analysis of time-to-event outcomes, correlated discrete and continuous covariates, and a latent class variable. It assumed covariate effects on survival times and covariate distributions vary across latent classes. Unobservable trajectories were identified by estimating the probability of belonging to a particular class based on observed information. This method was applied to a Hodgkin lymphoma study, identifying four distinct classes in terms of long-term survival and distributions of prognostic factors.

Results

Results from simulation studies and the Hodgkin lymphoma study demonstrated the superiority of our joint model compared with the conventional survival model. Four unobserved subgroups were identified, each characterized by distinct survival parameters and varying distributions of prognostic factors. A notable decreasing trend in the incidence of second malignancy over time was noted, along with different effects of second malignancy and relapse on survival across subgroups, providing deeper insights into disease progression over time.

Conclusions

The proposed joint model effectively identifies latent subgroups, revealing unobserved heterogeneity in survival outcomes and prognostic factors. Its flexibility enables more precise estimation of survival trajectories, with broad applicability in survival analysis.