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Viral load (VL) in the respiratory tract is the leading proxy for assessinginfectiousness potential. Understanding the dynamics of disease-related VLwithin the host is very important and help to determine different policy andhealth recommendations. However, often only partial followup data are availablewith unknown infection date. In this paper we introduce a discrete timelikelihood-based approach to modeling and estimating partial observedlongitudinal samples. We model the VL trajectory by a multivariate normaldistribution that accounts for possible correlation between measurements withinindividuals. We derive an expectation-maximization (EM) algorithm which treatsthe unknown time origins and the missing measurements as latent variables. Ourmain motivation is the reconstruction of the daily mean SARS-Cov-2 VL, givenmeasurements performed on random patients, whose VL was measured multiple timeson different days. The method is applied to SARS-Cov-2 cycle-threshold-valuedata collected in Israel.

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