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

Abstract

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.

Generative ODE modeling with known unknowns

“…Of the above methods, DSSM has been shown to learn a latent space which might under the right circumstances correspond to meaningful parameters, but that is not guaranteed, nor is it the goal of the method. In the healthcare regime, Cheng et al (2019) proposed a method for learning a sequence which includes a dynamic system in the form of a latent force model (Alvarez et al, 2009); this approach builds on learning to fit general basis functions to describe the observed dynamics, and does not take as input an ODE system derived from prior mechanistic understanding.…”