Nonlinear association structures in flexible Bayesian additive joint models

TL;DR

This paper introduces a flexible Bayesian additive joint modeling framework that captures nonlinear and covariate-specific associations between longitudinal biomarkers and survival outcomes, enhancing modeling accuracy.

Contribution

It extends existing joint models by incorporating Bayesian P-splines for nonlinear association estimation, implemented in the R package bamlss.

Findings

Successfully captures linear and nonlinear associations in simulations.

Demonstrates application on primary biliary cirrhosis data.

Provides flexible modeling of time-varying effects.

Abstract

Joint models of longitudinal and survival data have become an important tool for modeling associations between longitudinal biomarkers and event processes. The association between marker and log-hazard is assumed to be linear in existing shared random effects models, with this assumption usually remaining unchecked. We present an extended framework of flexible additive joint models that allows the estimation of nonlinear, covariate specific associations by making use of Bayesian P-splines. Our joint models are estimated in a Bayesian framework using structured additive predictors for all model components, allowing for great flexibility in the specification of smooth nonlinear, time-varying and random effects terms for longitudinal submodel, survival submodel and their association. The ability to capture truly linear and nonlinear associations is assessed in simulations and illustrated on the widely studied biomedical data on the rare fatal liver disease primary biliary cirrhosis. All methods are implemented in the R package bamlss to facilitate the application of this flexible joint model in practice.