Improving Inference from Reported Concentrations in Environmental Surveillance by Modeling the Statistical Features...

Digital polymerase chain reaction (dPCR) is a powerful technique for quantifying gene targets in environmental samples, with applications ranging from species monitoring to wastewater-based epidemiology. Although accurate statistical models for analyzing dPCR measurements exist, these require exact assay parameters and the number of positive and total PCR partitions. In practice, however, many environmental studies and monitoring programs analyze only concentration estimates, assuming normally or log-normally distributed measurements. Such assumptions ignore key statistical features of PCR assays, including concentration-dependent measurement noise and nondetects, leading to biased environmental estimates. In this work, we present a Bayesian model with a dPCR-specific likelihood that can be fitted directly to reported concentrations, while incorporating uncertainty in assay parameters through interpretable priors. Using real-world case studies of free-eDNA decay in seawater and pathogen transmission from wastewater, we show that our approach yields similar estimates as a fully informed model with partition counts, while avoiding biases from normal or log-normal approximations. This enables accurate inference from dPCR measurements even when partition count data and assay parameters are unavailable. The method is implemented in the R packages "dPCRfit" for regression analyses and "EpiSewer" for wastewater surveillance.