# Patient-Specific Effects of Medication Using Latent Force Models with Gaussian Processes

arXiv: https://arxiv.org/abs/1906.00226 · HTML: https://mlsanity.com/paper/1906.00226/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jun 2019.

## Built on by (most cited first, 6 of 6)

- [DoFlow: Flow-based Generative Models for Interventional and Counterfactual Forecasting on Time Series](https://mlsanity.com/paper/2511.02137/) (2025)
- [Causal Modeling of Policy Interventions From Sequences of Treatments and Outcomes](https://mlsanity.com/paper/2209.04142/) (2022)
- [Approximate Latent Force Model Inference](https://mlsanity.com/paper/2109.11851/) (2021)
- [Multi-Task Dynamical Systems](https://mlsanity.com/paper/2210.04023/) (2022)
- [Temporal Causal Mediation through a Point Process: Direct and Indirect Effects of Healthcare Interventions](https://mlsanity.com/paper/2306.09656/) (2023)
- [Nonparametric modeling of the composite effect of multiple nutrients on blood glucose dynamics](https://mlsanity.com/paper/2311.03129/) (2023)

## Abstract (arXiv)

Multi-output Gaussian processes (GPs) are a flexible Bayesian nonparametric framework that has proven useful in jointly modeling the physiological states of patients in medical time series data. However, capturing the short-term effects of drugs and therapeutic interventions on patient physiological state remains challenging. We propose a novel approach that models the effect of interventions as a hybrid Gaussian process composed of a GP capturing patient physiology convolved with a latent force model capturing effects of treatments on specific physiological features. This convolution of a multi-output GP with a GP including a causal time-marked kernel leads to a well-characterized model of the patients' physiological state responding to interventions. We show that our model leads to analytically tractable cross-covariance functions, allowing scalable inference. Our hierarchical model includes estimates of patient-specific effects but allows sharing of support across patients. Our approach achieves competitive predictive performance on challenging hospital data, where we recover patient-specific response to the administration of three common drugs: one antihypertensive drug and two anticoagulants.