Estimating Mean Viral Load Trajectory from Intermittent Longitudinal Data and Unknown Time Origins

TL;DR

This paper presents a likelihood-based method using an EM algorithm to estimate the average viral load trajectory over time from incomplete, irregularly timed data with unknown infection start dates, exemplified on SARS-CoV-2 data.

Contribution

It introduces a novel EM algorithm for modeling viral load trajectories with unknown infection times and incomplete data, applicable to real-world infectious disease studies.

Findings

Successfully reconstructed SARS-CoV-2 viral load trajectory.

Demonstrated the method's effectiveness on real patient data.

Provided insights into viral dynamics despite data limitations.

Abstract

Viral load (VL) in the respiratory tract is the leading proxy for assessing infectiousness potential. Understanding the dynamics of disease-related VL within the host is very important and help to determine different policy and health recommendations. However, often only partial followup data are available with unknown infection date. In this paper we introduce a discrete time likelihood-based approach to modeling and estimating partial observed longitudinal samples. We model the VL trajectory by a multivariate normal distribution that accounts for possible correlation between measurements within individuals. We derive an expectation-maximization (EM) algorithm which treats the unknown time origins and the missing measurements as latent variables. Our main motivation is the reconstruction of the daily mean SARS-Cov-2 VL, given measurements performed on random patients, whose VL was measured multiple times on different days. The method is applied to SARS-Cov-2 cycle-threshold-value data collected in Israel.