Improving inference in wastewater-based epidemiology by modelling the statistical features of digital PCR

Digital polymerase chain reaction (dPCR) is a powerful technique for quantifying gene targets in environmental samples, with various applications such as biodiversity monitoring and wastewater-based epidemiology. However, statistical analyses of environmental dPCR data often assume, explicitly or implicitly, that concentration measurements have a normal or log-normal error structure, which does not reflect the underlying partitioning statistics of dPCR. Using simulations and real-world environmental data, we show that (log-)normality assumptions are violated for dPCR measurements, leading to inaccurate estimates of gene concentrations and underlying biological processes. To enable reliable analyses of environmental dPCR data, we present a dPCR-specific likelihood model that accounts for concentration-dependent measurement noise and non-detects as characteristic of dPCR assays. We demonstrate that this approach overcomes biases in inference from environmental data, such as estimating free-eDNA decay in seawater or pathogen transmission from wastewater monitoring. Our method is implemented in the R packages "dPCRfit" for regression analyses and "EpiSewer" for wastewater surveillance.