Beyond linear regression: Modeling COVID-19 clinical cases with wastewater surveillance of SARS-CoV-2 for the city of Athens and Ohio University campus

Wastewater-based surveillance has emerged as a detection tool for population-wide infectious diseases, including coronavirus disease 2019 (COVID-19), caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Infected individuals shed the virus, which can be detected in wastewater using molecular techniques such as reverse transcription-digital polymerase chain reaction (RT-dPCR). This study examined the association between the number of clinical cases and the concentration of SARS-CoV-2 in wastewater beyond linear regression and for various normalizations of viral loads. Viral loads were measured in a total of 446 wastewater samples during the period from August 2021 to April 2022. These samples were collected from nine different locations, with 220 samples taken from four specific sites within the city of Athens and 226 samples from five sites within Ohio University. The correlation between COVID-19 cases and wastewater viral concentrations, which was estimated using the Pearson correlation coefficient, was statistically significant and ranged from 0.6 to 0.9. In addition, time-lagged cross correlation was applied to identify the lag time between clinical and wastewater data, estimated 4 to 7 days. While we also explored the effect on the correlation coefficients of various normalizations of viral loads accounting for procedural loss or amount of fecal material and of estimated lag times, these alternative specifications did not change our substantive conclusions. Additionally, several linear and non-linear regression models were applied to predict the COVID-19 cases given wastewater data as input. The non-linear approach was found to yield the highest R-squared and Pearson correlation and lowest Mean Absolute Error values between the predicted and actual number of COVID-19 cases for both aggregated OHIO Campus and city data. Our results provide support for previous studies on correlation and time lag and new evidence that non-linear models, approximated with artificial neural networks, should be implemented for WBS of contagious diseases.