From Noise to Signal: Unveiling Treatment Effects from Digital Health Data through Pharmacology-Informed Neural-SDE

TL;DR

The paper tackles extracting treatment effects from noisy digital health time-series by introducing a pharmacology-informed neural-SDE that couples an ODE-based PK input with a stochastic PD process. It learns a population dynamical system with patient-specific latent descriptors $p$ via a GRU encoder and neural networks for drift $\nu_{\theta}$ and diffusion $\sigma_{\theta}$, trained on snapshots and a likelihood derived from the Euler-Maruyama scheme. The model enables counterfactual PD simulations, such as trajectories in the absence of dosing, yielding individualized treatment effect estimates. Experiments on synthetic PK–PD data demonstrate the approach can reproduce dose–response patterns and capture inter-individual variability, supporting its potential for causal inference and personalized medicine using digital health data.

Abstract

Digital health technologies (DHT), such as wearable devices, provide personalized, continuous, and real-time monitoring of patient. These technologies are contributing to the development of novel therapies and personalized medicine. Gaining insight from these technologies requires appropriate modeling techniques to capture clinically-relevant changes in disease state. The data generated from these devices is characterized by being stochastic in nature, may have missing elements, and exhibits considerable inter-individual variability - thereby making it difficult to analyze using traditional longitudinal modeling techniques. We present a novel pharmacology-informed neural stochastic differential equation (SDE) model capable of addressing these challenges. Using synthetic data, we demonstrate that our approach is effective in identifying treatment effects and learning causal relationships from stochastic data, thereby enabling counterfactual simulation.

Figures (6)

• Figure 1: The Neural-SDE architecture including the GRU encoder.
• Figure 2: Comparison of the true and predicted SDE trajectories in the test dataset. Left panel: the colored lines represent the observed stochastic trajectories in the test data. Right panel: blue line and shaded region represent the median and the $10^{th}$ to $90^{th}$ percentile respectively of the ground truth trajectories; similarly, the orange lines and shade region represent those from the model.
• Figure 3: Comparison of the true and predicted SDE trajectories in the test datase for 50, 100 and 400 mg doses. Blue lines represent the median of the ground truth trajectories; orange dashed lines and shaded regions represent median and the $10^{th}$ to $90^{th}$ percentile of trajectories from the model.
• Figure 4: Patient-specific trajectories and counterfactual simulations. Each subplot represents a random patient from the respective dosages. The solid blue line represents the true drift; the orange dashed line and shaded region represent the mean and mean $\rm \pm$ standard deviation (std) of 250 posterior samples; the green dashed lines represent counterfactual simulations assuming no dosing (i.e., $\rm PK=0$).
• Figure 5: Synthetic data trajectories without the diffusivity component under different simulated doses.