Sten Willemsen | Searcharxiv

arXiv2026

Deep Generalised Mixed Models: a Novel Neural Network Structure for Analysing Hierarchical Data

The experience sampling method (ESM) is a longitudinal research design where participants report their thoughts, emotional states and behaviours multiple times a day. Our work is motivated by such data collected by the GrowIt! app, which was released to investigate daily emotions among adolescents during the COVID-19 pandemic. Current procedures to analyse ESM data face various challenges. While standard statistical techniques may not scale well to a high-dimensional setting, machine learning procedures can give biased results due to selection bias introduced by missingness. In our motivating dataset, adolescents dropped out due to previous strong feelings of negative emotions. Hence, the implied missing data are of the missing-at-random type that standard machine learning procedures cannot accommodate. We develop a novel neural network architecture that generalises mixed effects models to deep learning to overcome these challenges. It allows semi-parametric and flexible modelling of data's mean and correlation structure through fixed and random effects. For estimation, we use an adaptation of variational auto-encoders and a Bayesian data augmentation algorithm. Through this approach, the model can accommodate longitudinal outcomes following generic distributions, scale well to high-dimensional settings and provide valid inference when data are missing-at-random. We applied the Deep Generalised Mixed Model to the GrowIt! study and various simulations. The results show potential for the Deep Generalised Mixed Model, yet suboptimal performance due to model instability.

stat.ML↗

arXiv2026

Ensemble Machine Learning and Statistical Procedures for Dynamic Predictions of Time-to-Event Outcomes

Dynamic predictions for longitudinal and time-to-event outcomes have become a versatile tool in precision medicine. Our work is motivated by the application of dynamic predictions in the decision-making process for primary biliary cholangitis patients. For these patients, serial biomarker measurements (e.g., bilirubin and alkaline phosphatase levels) are routinely collected to inform treating physicians of the risk of liver failure and guide clinical decision-making. Two popular statistical approaches to derive dynamic predictions are joint modelling and landmarking. However, recently, machine learning techniques have also been proposed. Each approach has its merits, and no single method exists to outperform all others. Consequently, obtaining the best possible survival estimates is challenging. Therefore, we extend the Super Learner framework to combine dynamic predictions from different models and procedures. Super Learner is an ensemble learning technique that allows users to combine different prediction algorithms to improve predictive accuracy and flexibility. It uses cross-validation and different objective functions of performance (e.g., squared loss) that suit specific applications to build the optimally weighted combination of predictions from a library of candidate algorithms. In our work, we pay special attention to appropriate objective functions for Super Learner to obtain the most optimal weighted combination of dynamic predictions. In our primary biliary cholangitis application, Super Learner presented unique benefits due to its ability to flexibly combine outputs from a diverse set of models with varying assumptions for equal or better predictive performance than any model fit separately.

stat.ML↗