The impact of signal variability on epidemic growth rate estimation from wastewater surveillance data

Background Testing samples of waste water for markers of infectious disease became a widespread method of surveillance during the COVID-19 pandemic. While these data generally correlate well with other indicators of national prevalence, samples that cover localised regions tend to be highly variable over short time scales. Methods We introduce a procedure for estimating the realtime growth rate of pathogen prevalence using time series data from wastewater sampling. The number of copies of a target gene found in a sample is modelled as time-dependent random variable whose distribution is estimated using maximum likelihood. The output depends on a hyperparameter that controls the sensitivity to variability in the underlying data. We apply this procedure to data reporting the number of copies of the N1 gene of SARS-CoV-2 collected at water treatment works across Scotland between February 2021 and February 2023. Results The real-time growth rate of the SARS-CoV-2 prevalence is estimated at 121 wastewater sampling sites covering a diverse range of locations and population sizes. We find that the sensitivity of the fitting procedure to natural variability determines its reliability in detecting the early stages of an epidemic wave. Applying the procedure to hospital admissions data, we find that changes in the growth rate are detected an average of 2 days earlier in wastewater than in hospital admissions data. Conclusion We provide a robust method to generate reliable estimates of epidemic growth from highly variable data. Applying this method to samples collected at wastewater treatment works provides highly responsive situational awareness to inform public health. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement This study was funded by the National COVID-19 Wastewater Epidemiology Surveillance Programme. EC received funding from the Wellcome Trust ### 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: Edinburgh Medical School Research Ethics Committee (reference 22-EMREC-048) granted ethical approval for this work 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 Environmental data analysed in the present study are available at . Medical data were provided with restricted access subject to a data sharing agreement