Introduction: Heterogeneity of the progression of neurodegenerative diseases is one of the main challenges faced in developing effective therapies. With the increasing number of large clinical databases, disease progression models have led to a better understanding of this heterogeneity. Nevertheless, these diseases may have no clear onset and biological underlying processes may start before the first symptoms. Such an ill-defined disease reference time is an issue for current joint models, which have proven their effectiveness by combining longitudinal and survival data. Objective 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. Method: To do so, we utilized an existing longitudinal model with a latent disease age as a longitudinal sub-model and associated it with a survival sub-model that estimates a Weibull distribution from the latent disease age. We then validated our model on different simulated scenarios. Finally, we benchmarked our model with a state-of-the-art joint model and reference survival and longitudinal models on simulated and real data in the context of Amyotrophic Lateral Sclerosis (ALS). Results: On real data, our model got significantly better results than the state-of-the-art joint model for absolute bias (4.21(4.41) versus 4.24(4.14)(p-value=1.4e-17)), and mean cumulative AUC for right censored events (0.67(0.07) versus 0.61(0.09)(p-value=1.7e-03)). Conclusion: We showed that our approach is better suited than the state-of-the-art in the context where the reference time is not reliable. This work opens up the perspective to design predictive and personalized therapeutic strategies.

翻译：引言：神经退行性疾病进展的异质性是开发有效疗法面临的主要挑战之一。随着大型临床数据库数量的增加，疾病进展模型使人们对此异质性有了更深入的理解。然而，这些疾病可能没有明确的发病时间，且潜在的生物学过程可能在首次症状出现前就已开始。这种不明确的疾病参考时间是当前联合模型面临的问题，尽管这些模型通过结合纵向数据和生存数据已证明其有效性。目标：在本研究中，我们提出了一种具有潜在病程年龄的联合非线性混合效应模型，以克服对精确参考时间的需求。方法：为此，我们采用了一个现有的具有潜在病程年龄的纵向模型作为纵向子模型，并将其与一个生存子模型相关联，该生存子模型从潜在病程年龄估计威布尔分布。随后，我们在不同的模拟场景中验证了我们的模型。最后，我们在肌萎缩侧索硬化症（ALS）背景下，使用模拟数据和真实数据，将我们的模型与最先进的联合模型以及参考生存模型和纵向模型进行了基准测试。结果：在真实数据上，我们的模型在绝对偏差（4.21(4.41) 对比 4.24(4.14)（p值=1.4e-17））和右删失事件的平均累积AUC（0.67(0.07) 对比 0.61(0.09)（p值=1.7e-03））方面均取得了显著优于最先进联合模型的结果。结论：我们证明了在参考时间不可靠的情况下，我们的方法比现有最先进方法更适用。这项工作为设计预测性和个性化的治疗策略开辟了前景。