Regression Models for Understanding COVID-19 Epidemic Dynamics With Incomplete Data

Modeling infectious disease dynamics has been critical throughout the COVID-19 pandemic. Of particular interest are the incidence, prevalence, and effective reproductive number (Rt ). Estimating these quantities is challenging due to under-ascertainment, unreliable reporting, and time lags between infection, onset, and testing. We propose a Multilevel Epidemic Regression Model to Account for Incomplete Data (MERMAID) to jointly estimate Rt , ascertainment rates, incidence, and prevalence over time in one or multiple regions. Specifically, MERMAID allows for a flexible regression model of Rt that can incorporate geographic and time-varying covariates. To account for under-ascertainment, we (a) model the ascertainment probability over time as a function of testing metrics and (b) jointly model data on confirmed infections and population-based serological surveys. To account for delays between infection, onset, and reporting, we model stochastic lag times as missing data, and develop an EM algorithm to estimate the model parameters. We evaluate the performance of MERMAID in simulation studies, and assess its robustness by conducting sensitivity analyses in a range of scenarios of model misspecifications. We apply the proposed method to analyze COVID-19 daily confirmed infection counts, PCR testing data, and serological survey data across the United States. Based on our model, we estimate an overall COVID-19 prevalence of 12.5% (ranging from 2.4% in Maine to 20.2% in New York) and an overall ascertainment rate of 45.5% (ranging from 22.5% in New York to 81.3% in Rhode Island) in the United States from March to December 2020. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.