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

Abstract

The growing field of wastewater-based infectious disease surveillance relies on the quantification of pathogen concentrations in wastewater using polymerase chain reaction (PCR) techniques. However, existing models for monitoring pathogen spread using wastewater have often been adapted from methods for case count data and neglect the statistical features of PCR techniques. In this paper, we seek to overcome the widespread simplistic modelling of wastewater PCR measurements as normally or log-normally distributed by proposing an appropriate model for digital PCR (dPCR). Building on established statistical theory of dPCR, we derive approximations for the coefficient of variation of measurements and the probability of non-detection and propose a hurdle model-based likelihood for estimating concentrations from dPCR measurements. Using simulations and real-world data, we show that simple likelihoods based on normal or log-normal distributions are misspecified, affecting the estimation of pathogen concentrations and infection trends over time. In contrast, the proposed dPCR-specific likelihood accurately models the distribution of dPCR measurements, improving epidemiological estimates and forecasts even if details of the laboratory protocol are unknown. The method has been implemented in the open-source R package EpiSewer to improve wastewater-based monitoring of pathogens.