Joint model with latent disease age: Overcoming the need for reference time

Abstract

Heterogeneity of the progression of neurodegenerative diseases is one of the main challenges faced in developing therapies. Thanks to the increasing number of clinical databases, progression models have allowed a better understanding of this heterogeneity. Joint models have proven their effectiveness by combining longitudinal and survival data. Nevertheless, they require a reference time, which is ill-defined for neurodegenerative diseases, where biological underlying processes start before the first symptoms. In this work, we propose a joint non-linear mixed-effect model with a latent disease age, to overcome this need for a precise reference time. We used a longitudinal model with a latent disease age as a longitudinal sub-model. We associated it with a survival sub-model that estimates a Weibull distribution from the latent disease age. We validated our model on simulated data and benchmarked it with a state-of-the-art joint model on data from patients with Amyotrophic Lateral Sclerosis (ALS). Finally, we showed how the model could be used to describe ALS heterogeneity. Our model got significantly better results than the state-of-the-art joint model for absolute bias on ALS functional rating scale revised score (4.21(SD 4.41) versus 4.24(SD 4.14)( $p$ -value $=$ 1.4 $\times {10}^{-17}$ )), and mean-cumulative-AUC for right-censored events on death (0.67(0.07) versus 0.61(0.09)( $p$ -value $=$ 1.7 $\times {10}^{-03}$ )). To conclude, we propose a new model better suited in the context of unreliable reference time.