Speaker
Description
In clinical registries, longitudinal patient data are often sparse,
noisy, and irregularly sampled, yet an important practical question is
how an individual patient’s health status is likely to change from the current visit to the next.
Regression-based approaches to longitudinal data analysis typically
provide a global fit over the full observed time course, but are not
directly aimed at modeling such temporally local, patient-specific
changes. Ordinary differential equations ODEs provide a natural
framework for describing local dynamics based on current status, where
parameters can be informed by external knowledge, but their use in
clinical cohort settings remains limited. This is potentially due to a
larger number of variables to be modeled and a higher noise level, as
an ODE solution strongly depends on the initial value and jointly modeling many variables is challenging.
To address this, we propose an ODE-based modeling approach for
multivariate longitudinal cohort data. Each observation is used as an
initial value to obtain multiple local ODE solutions, which are then
combined into a single estimator, enabling prediction from arbitrary
time points while improving robustness to noise. To accommodate a
larger number of observed variables, we learn a low-dimensional
latent space using neural networks, and infer individual-specific ODE parameters from patients' baseline characteristics.
Differentiable programming allows for simultaneous estimation of the
latent representation and the dynamic model.
We illustrate the approach in an application on data from patients
with spinal muscular atrophy and compare it with global regression-based function fitting.
The application highlights how different modeling strategies address
different scientific and clinical questions, and shows the potential
of combining mechanistic and statistical modeling ideas for longitudinal registry data.