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.

翻译：病毒载量（VL）是评估呼吸道传染潜力的主要指标。了解宿主体内疾病相关病毒载量的动态变化至关重要，有助于制定不同的政策和健康建议。然而，通常只能获得部分随访数据，且感染日期未知。本文提出一种基于离散时间似然的方法，用于建模和估算部分观测的纵向样本。我们通过多元正态分布对病毒载量轨迹进行建模，该分布可解释个体内测量值之间可能存在的相关性。我们推导出一种期望最大化（EM）算法，将未知时间起点和缺失测量值视为潜在变量。本文的主要动机是基于对随机患者进行的多次不同日期的病毒载量测量，重建每日平均SARS-Cov-2病毒载量。该方法已应用于以色列收集的SARS-Cov-2阈值循环值数据。