Institute of Medical Biometry and Statistics, Faculty of Medicine and Medical Center, University of Freiburg, Freiburg, Germany.
Freiburg Center for Data Analysis and Modelling, University of Freiburg, Freiburg, Germany.
Biom J. 2023 Aug;65(6):e2100381. doi: 10.1002/bimj.202100381. Epub 2023 Mar 17.
When modeling longitudinal biomedical data, often dimensionality reduction as well as dynamic modeling in the resulting latent representation is needed. This can be achieved by artificial neural networks for dimension reduction and differential equations for dynamic modeling of individual-level trajectories. However, such approaches so far assume that parameters of individual-level dynamics are constant throughout the observation period. Motivated by an application from psychological resilience research, we propose an extension where different sets of differential equation parameters are allowed for observation subperiods. Still, estimation for intra-individual subperiods is coupled for being able to fit the model also with a relatively small dataset. We subsequently derive prediction targets from individual dynamic models of resilience in the application. These serve as outcomes for predicting resilience from characteristics of individuals, measured at baseline and a follow-up time point, and selecting a small set of important predictors. Our approach is seen to successfully identify individual-level parameters of dynamic models that allow to stably select predictors, that is, resilience factors. Furthermore, we can identify those characteristics of individuals that are the most promising for updates at follow-up, which might inform future study design. This underlines the usefulness of our proposed deep dynamic modeling approach with changes in parameters between observation subperiods.
在对纵向生物医学数据进行建模时，通常需要进行降维和在所得潜在表示中进行动态建模。这可以通过人工神经网络进行降维和通过微分方程对个体轨迹的动态建模来实现。然而，到目前为止，此类方法假设个体动态的参数在整个观察期间是恒定的。受来自心理弹性研究的应用启发，我们提出了一种扩展，允许在观察子期间允许不同的微分方程参数集。尽管如此，为了能够使用相对较小的数据集拟合模型，个体子期间的估计仍然是耦合的。随后，我们从应用中的弹性个体动态模型中推导出预测目标。这些作为从个体特征预测弹性的结果，这些特征在基线和随访时间点进行测量，并选择一小部分重要的预测因子。我们的方法成功地确定了允许稳定选择预测因子（即弹性因素）的个体动态模型的个体水平参数。此外，我们可以确定那些在随访时最有希望更新的个体特征，这可能为未来的研究设计提供信息。这强调了我们提出的具有观察子期间参数变化的深度动态建模方法的有用性。
