Estimating Rates of Change to Interpret Quantitative Wastewater Surveillance of Disease Trends

Background: Wastewater monitoring data can be used to estimate disease trends to inform public health responses. One commonly estimated metric is the rate of change in pathogen quantity, which typically correlates with clinical surveillance in retrospective analyses. However, the accuracy of rate of change estimation approaches has not previously been evaluated. Objectives: We assessed the performance of approaches for estimating rates of change in wastewater pathogen loads by generating synthetic wastewater time series data for which rates of change were known. Each approach was also evaluated on real-world data. Methods: Smooth trends and their first derivatives were jointly sampled from Gaussian processes (GP) and independent errors were added to generate synthetic viral load measurements; the range hyperparameter and error variance were varied to produce nine simulation scenarios representing different potential disease patterns. The directions and magnitudes of the rate of change estimates from four estimation approaches (two established and two developed in this work) were compared to the GP first derivative to evaluate classification and quantitative accuracy. Each approach was also implemented for public SARS-CoV-2 wastewater monitoring data collected January 2021 - May 2024 at 25 sites in North Carolina, USA. Results: All four approaches inconsistently identified the correct direction of the trend given by the sign of the GP first derivative. Across all nine simulated disease patterns, between a quarter and a half of all estimates indicated the wrong trend direction, regardless of estimation approach. The proportion of trends classified as plateaus (statistically indistinguishable from zero) for the North Carolina SARS-CoV-2 data varied considerably by estimation method but not by site. Discussion: Our results suggest that wastewater measurements alone might not provide sufficient data to reliably track disease trends in real-time. Instead, wastewater viral loads could be combined with additional public health surveillance data to improve predictions of other outcomes. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement This work was supported by the CDC National Wastewater Surveillance System through the Epidemiology and Laboratory Capacity Cooperative Agreement with North Carolina Department of Health and Human Services, with additional support from the National Institute for Occupational Health and Safety (T42OH008673) and the NSF RAPID program (project #2029866). ### Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes The details of the IRB/oversight body that provided approval or exemption for the research described are given below: No human participants were involved in this research. All analyses were performed on synthetic or publicly available, aggregated data and did not require ethical approval. The code and data to perform these analyses are freely available in a permanent online repository at https://doi.org/10.17605/OSF.IO/BPGN4 (see Supplemental Material, Analysis Code). The original NC sewershed monitoring data may be accessed at https://covid19.ncdhhs.gov/dashboard/data-behind-dashboards. I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines, such as any relevant EQUATOR Network research reporting checklist(s) and other pertinent material, if applicable. Yes The code and data to perform these analyses are freely available in a permanent online repository at https://doi.org/10.17605/OSF.IO/BPGN4. The original NC sewershed monitoring data may be accessed at https://covid19.ncdhhs.gov/dashboard/data-behind-dashboards.