Longitudinal and survival joint prediction: time reparameterization in amyotrophic lateral sclerosis context

International audience ; Joint modelling has been widely used to improve the estimation accuracy of both longitudinal and survival outcomes. Several have already been developed and they differ by the latent variables used to link the two processes. Shared random effects models are often using Generalized Linear Models (GLM). A non-linear relation for random effects, named time reparameterization, has been shown to offer good performance and interpretability in longitudinal modelling[1]. This work aimed to extend time reparameterization to univariate joint modelling in the context of Amyotrophic Lateral Sclerosis (ALS), for which death or tracheotomy is often associated with the study of the clinical score ALSFRSr. The proposed model (PropM) was benchmarked against three models: the longitudinal model alone (LongMA), a Cox model (CoxM) and a GLM, using the JMbayes2 package[2]. We used 5-fold cross-validation on simulated and real ALS data. Prediction performances were measured using signed error, absolute error, C-index (at 1, 1.5, 2 years), and Integrated Brier score (IBS). The interpretability of the intercept estimated by the model was assessed by the intra-class correlation between this intercept and, on simulated data, the one used for simulation, or, on real data, the age at first symptoms. On simulation data, the PM reduces the bias on signed error compared to LongMA. No performance was significantly different between PropM and CoxM. Compared to GLM, PropM got significantly better results for absolute error and C-index at each time. The agreement, between the simulated and the PropM estimated random effects, was at least 0.703 (CI95%=[0.67,0.74]) for the intercept and at least 0.228 (CI95%=[0.16,0.29]) for the log speed. On real data, PropM reduces the bias for longitudinal metrics compared to both GLM and LongMA. For survival modelling, PropM was significantly better for IBS compared to GLM. CoxM was significantly better, compared to PropM, for C-index whatever the time. Finally, PropM estimated intercept ...