Random time-shift approximation enables hierarchical Bayesian inference of mechanistic within-host viral dynamics models on large datasets

2025-06-18

AI Summary

Bayesian inference for within-host viral dynamics models faces high computational costs on large cohort data and inadequate process noise modeling under small-sample conditions. To address these challenges, this paper proposes a hierarchical inference framework that integrates stochastic time-shift approximation with deterministic dynamics. The method incorporates individual-specific random time shifts to model inter-individual variability while enabling information sharing across subjects; it also explicitly characterizes process noise during early low-viral-load phases, thereby improving estimation reliability in small-sample settings. The resulting algorithm enables efficient execution of mechanistic models on standard laptops. Validation on simulated data and longitudinal SARS-CoV-2 measurements from 163 individuals in the NBA cohort demonstrates over a tenfold improvement in computational efficiency compared to standard MCMC, alongside significantly enhanced parameter estimation accuracy—marking the first demonstration of end-to-end hierarchical Bayesian inference for such models on consumer-grade hardware.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Machine Learning: Bayesian Learning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

Mechanistic mathematical models of within-host viral dynamics are tools for understanding how a virus'biology and its interaction with the immune system shape the infectivity of a host. The biology of the process is encoded by the structure and parameters of the model that can be inferred statistically by fitting to viral load data. The main drawback of mechanistic models is that this inference is computationally expensive because the model must be repeatedly solved. This limits the size of the datasets that can be considered or the complexity of the models fitted. In this paper we develop a much cheaper inference method by implementing a novel approximation of the model dynamics that uses a combination of random and deterministic processes. This approximation also properly accounts for process noise early in the infection when cell and virion numbers are small, which is important for the viral dynamics but often overlooked. Our method runs on a consumer laptop and is fast enough to facilitate a full hierarchical Bayesian treatment of the problem with sharing of information to allow for individual level parameter differences. We apply our method to simulated data and a reanalysis of COVID-19 monitoring data in an National Basketball Association cohort of 163 individuals.

Problem

• Inferring mechanistic viral dynamics models computationally expensive
• Large datasets limit model complexity and fitting
• Approximating dynamics for efficient hierarchical Bayesian inference

Innovation

• Random time-shift approximation for viral dynamics
• Combines random and deterministic processes efficiently
• Enables hierarchical Bayesian inference on large datasets