Improving estimates of epidemiological quantities by combining reported cases with wastewater data: a statistical framework with applications to COVID-19 in Aotearoa New Zealand (preprint)

ABSTRACT

Background: Timely and informed public health responses to infectious diseases such as COVID-19 necessitate reliable information about infection dynamics. The case ascertainment rate (CAR), the proportion of infections that are reported as cases, is typically much less than one and varies with testing practices and behaviours, making reported cases unreliable as the sole source of data. The concentration of viral RNA in wastewater samples provides an alternate measure of infection prevalence that is not affected by human behaviours. Here, we investigated how these two data sources can be combined to inform estimates of the instantaneous reproduction number, R, and track changes in the CAR over time. Methods: We constructed a state-space model that we solved using sequential Monte Carlo methods. The observed data are the levels of SARS-CoV-2 in wastewater and reported case incidence. The hidden states that we estimate are R and CAR. Model parameters are estimated using the particle marginal Metropolis Hastings algorithm. Findings: We analysed data from 1 January 2022 to 31 March 2023 from Aotearoa New Zealand. Our model estimates that R peaked at 2.76 (95% CrI 2.20, 3.83) around 18 February 2022 and the CAR peaked around 12 March 2022. Accounting for reduced CAR, we estimate that New Zealand's second Omicron wave in July 2022 was similar in size to the first, despite fewer reported cases. We estimate that the CAR in the BA.5 Omicron wave in July 2022 was approximately 50% lower than in the BA.1/BA.2 Omicron wave in March 2022. The CAR in subsequent waves around November 2022 and April 2023 was estimated to be comparable to that in the second Omicron wave. Interpretation: This work on wastewater-based epidemiology (WBE) can be used to give insight into key epidemiological quantities. Estimating R, CAR, and cumulative number of infections provides useful information for planning public health responses and understanding the state of immunity in the population. This model is a useful disease surveillance tool, improving situational awareness of infectious disease dynamics in real-time, which may be increasingly useful as intensive pandemic surveillance programmes are wound down.