Spatial joint models through Bayesian structured piecewise additive joint modelling for longitudinal and time-to-event data

Joint models for longitudinal and time-to-event data simultaneously model longitudinal and time-to-event information to avoid bias by combining usually a linear mixed model with a proportional hazards model. This model class has seen many developments in recent years, yet joint models including a spatial predictor are still rare and the traditional proportional hazards formulation of the time-to-event part of the model is accompanied by computational challenges. We propose a joint model with a piecewise exponential formulation of the hazard using the counting process representation of a hazard and structured additive predictors able to estimate (non-)linear, spatial and random effects. Its capabilities are assessed in a simulation study comparing our approach to an established one and highlighted by an example on physical functioning after cardiovascular events from the German Ageing Survey. The Structured Piecewise Additive Joint Model yielded good estimation performance, also and especially in spatial effects, while being double as fast as the chosen benchmark approach and performing stable in an imbalanced data setting with few events.