Modeling the relationship between SARS-CoV-2 RNA in wastewater or sludge and COVID-19 cases in three New England regions

Background: We aimed to compare statistical techniques estimating the association between SARS-CoV-2 RNA in untreated wastewater and sludge and reported coronavirus disease 2019 (COVID-19) cases. Methods: SARS-CoV-2 RNA concentrations (copies/mL) were measured from 24-h composite samples of wastewater in Massachusetts (MA) (daily; 8/19/2020–1/19/2021) and Maine (ME) (weekly; 9/1/2020–3/2/2021) and sludge samples in Connecticut (CT) (daily; 3/1/2020–6/1/2020). We fit linear, generalized additive with a cubic regression spline (GAM), Poisson, and negative binomial models to estimate the association between SARS-CoV-2 RNA concentration and reported COVID-19 cases. Results: The models that fit the data best were linear [adjusted R2=0.85 (MA), 0.16 (CT) 0.63 (ME); root-mean-square error (RMSE)=0.41 (MA), 1.14 (CT), 0.99 (ME)), GAM (adjusted R2=0.86 (MA), 0.16 (CT) 0.65 (ME); RMSE=0.39 (MA), 1.14 (CT), 0.97 (ME)], and Poisson [pseudo R2=0.84 (MA), 0.21 (CT), 0.52 (ME); RMSE=0.39 (MA), 0.67 (CT), 0.79 (ME)]. Conclusions: Linear, GAM, and Poisson models outperformed negative binomial models when relating SARS-CoV-2 RNA in wastewater or sludge to reported COVID-19 cases.