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：将多个纵向生物标志物与时间至事件结局进行联合建模是一项具有持续科学意义且充满挑战性的建模任务。特别地，高维（广义）混合效应模型的计算复杂度往往限制了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过程。我们提出了一种简约的多元函数主成分分析表示方法用于共享随机效应。这种方法实现了更好的可扩展性，因为随机效应的维度不会随标志物数量直接增加，仅取决于近似随机效应时选用的主成分基函数数量。函数主成分表示法还允许在无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，不同生物标志物的建模轨迹可以呈现显著差异。我们基于R包"bamlss"中实现的柔性贝叶斯加性联合模型框架构建，该框架支持通过贝叶斯P样条估计非线性协变量效应。用于联合模型估计的柔性且简约的函数主成分基需通过初步步骤预先估计。我们通过模拟研究验证该方法，并通过分析原发性胆汁性胆管炎研究数据展示其优势。