Handling left-censored wastewater surveillance data at the city level: A state-space model incorporating a logistic function

Left-censored data (i.e., microbial non-detection data) in wastewater surveillance hinder accurate understanding of disease incidence and the early detection of epidemic signals in the initial stages. In this study, we propose state-space models incorporating a logistic model to handle left-censored data. Using simulation data, we show that the state-space models can provide accurate estimates of wastewater concentrations from detection rates. The models outperformed the substitution method (i.e., a method that replaces non-detection data with a specific value), lowering the mean of absolute percentage error from 0.39 to 0.053. We also found that the estimation accuracy of the models was improved by increasing the number of tested samples and sampling frequency. In the simulation analysis, higher sampling frequency was more critical than the number of daily analyzed samples, as long as weekly totals remained consistent. Subsequently, we applied the models to real-world data for influenza A virus (IAV) and respiratory syncytial viruses (RSV) in the USA, estimating wastewater concentration and wastewater-based effective reproduction number (R_e^ww). Estimated R_e^ww ranged from 0.80 to 1.36 for IAV and 0.74 to 1.66 for RSV, which was consistent with R_e reported in previous studies using clinical data. As a comparison, dynamics of wastewater concentration and R_e^ww were estimated using the substitution approach. We observed that the substitution approach underestimated concentrations in the period during which left-censored data were observed. The substitution approach also overestimated R_e^ww in early epidemic stages and underestimated R_e^ww in the end stage. These findings show the utility of the state-space models to handle left-censored data and enhance our ability to understand epidemic dynamics through wastewater surveillance. To facilitate its use, we provided a file for inputting wastewater-based data along with scripts. The state-space models can be run easily by adding wastewater-based data in a provided CSV file without advanced programming skills.