Joint latent class trees: A Tree-Based Approach to Joint Modeling of Time-to-event and Longitudinal Data
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Joint modeling of longitudinal and time-to-event data provides insights into the association between the two quantities. The joint latent class modeling approach assumes that conditioning on latent class membership, the trajectories of longitudinal data such as biomarkers are independent of survival risks. Furthermore, the resulting latent classes provide a data-dependent clustering of the population, which is also of interest in clinical studies. Existing joint latent modeling approaches are parametric and suffer from high computational cost. The most common parametric approach, the joint latent class model (JLCM), further restricts analysis to using time-invariant covariates in modeling survival risks and latent class memberships. We propose a nonparametric joint latent class modeling approach based on trees (JLCT). JLCT is fast to fit, and can use time-varying covariates in all of its modeling components. We compare JLCT with JLCM on simulated data, where we show that JLCT and JLCM have similar performance when using only time-invariant covariates. Further, we demonstrate the prognostic value of using time-varying covariates in each of the modeling components, and thus display the advantage of JLCT when making predictions. We further apply JLCT to a real application, the PAQUID dataset, and demonstrate again that JLCT admits competitive prediction performance, while being orders of magnitude faster than the parametric approach JLCM.
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