The joint modeling of multiple longitudinal biomarkers together with a time-to-event outcome is a challenging modeling task of continued scientific interest. In particular, the computational complexity of high dimensional (generalized) mixed effects models often restricts the flexibility of shared parameter joint models, even when the subject-specific marker trajectories follow highly nonlinear courses. We propose a parsimonious multivariate functional principal components representation of the shared random effects. This allows better scalability, as the dimension of the random effects does not directly increase with the number of markers, only with the chosen number of principal component basis functions used in the approximation of the random effects. The functional principal component representation additionally allows to estimate highly flexible subject-specific random trajectories without parametric assumptions. The modeled trajectories can thus be distinctly different for each biomarker. We build on the framework of flexible Bayesian additive joint models implemented in the R-package 'bamlss', which also supports estimation of nonlinear covariate effects via Bayesian P-splines. The flexible yet parsimonious functional principal components basis used in the estimation of the joint model is first estimated in a preliminary step. We validate our approach in a simulation study and illustrate its advantages by analyzing a study on primary biliary cholangitis.

翻译：多生物标志物纵向数据与时间事件结局的联合建模是一项持续受学界关注且富有挑战性的建模任务。特别地，高维（广义）混合效应模型的计算复杂度常限制共享参数联合模型的灵活性，即使受试者特异性标志物轨迹呈现高度非线性变化。我们提出了一种简约的多元函数主成分分析表征共享随机效应的方法。该方法通过仅依赖选定的随机效应近似主成分基函数数量（而非标志物数量）来提升可扩展性，使随机效应维度不会随标志物数量直接增长。函数主成分表征还允许在无需参数假设条件下估计高度灵活的受试者特异性随机轨迹，因此每个生物标志物的建模轨迹可呈现显著差异。我们基于R语言包"bamlss"中实现的柔性贝叶斯加性联合模型框架，该框架同时支持通过贝叶斯P样条估计非线性协变量效应。用于联合模型估计的柔性简约函数主成分基函数在初步步骤中预先估算。我们通过模拟研究验证了该方法，并通过原发性胆汁性胆管炎研究实例分析展示了其优势。