Interpreting Wastewater SARS-CoV-2 Results using Bayesian Analysis

Wastewater surveillance of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has proven a practical complement to clinical data for assessing community-scale infection trends. Clinical assays, such as the CDC-promulgated N1, N2, and N3 have been used to detect and quantify viral RNA in wastewater but, to date, have not included estimates of reliability of true positive or true negative. Bayes Theorem was applied to estimate Type I and Type II error rates for detections of the virus in wastewater. Conditional probabilities of true positive or true negative were investigated when one assay was used, or multiple assays were run concurrently. Cumulative probability analysis was used to assess the likelihood of true SARS-CoV-2 detection using multiple samples. Results demonstrate highly reliable positive (>0.86 for priors >0.25) and negative (>0.80 for priors = 0.50) results using a single assay. Using N1 and N2 concurrently caused greater reliability (>0.99 for priors <0.05) when results concurred but generated potentially counterintuitive interpretations when results were discordant. Regional wastewater surveillance data was investigated as a means of setting prior probabilities. Probability of true detection with a single marker was investigated using cumulative probability across all combinations of positive and negative results for a set of three samples. Findings using a low (0.11) and uniformed (0.50) initial prior resulted in high probabilities of detection (>0.95) even when a set of samples included one or two negative results, demonstrating the influence of high sensitivity and specificity values. Analyses presented here provide a practical framework for understanding analytical results generated by wastewater surveillance programs.