Joint latent class trees: A tree-based approach to modeling time-to-event and longitudinal data

In this paper, we propose a semiparametric, tree-based joint latent class model for the joint behavior of longitudinal and time-to-event data. Existing joint latent class approaches are parametric and can suffer from high computational cost. The most common parametric approach, the joint latent class model, further restricts analysis to using time-invariant covariates in modeling survival risks and latent class memberships. The proposed tree method (joint latent class tree) is fast to fit, and permits time-varying covariates in all of its modeling components. We demonstrate the prognostic value of using time-varying covariates, and therefore the advantage of joint latent class tree over joint latent class model on simulated data. We apply joint latent class tree to a well-known data set (the PAQUID data set) and confirm its superior prediction performance and orders-of-magnitude speedup over joint latent class model.