Quantifying the information in noisy epidemic curves

Abstract

Reliably estimating the dynamics of transmissible diseases from noisy surveillance data is an enduring problem in modern epidemiology. Key parameters, such as the time-varying reproduction number, Rt at time t, are often inferred from incident time series, with the aim of informing policymakers on the growth rate of outbreaks or testing hypotheses about the effectiveness of public health interventions. However, the reliability of these inferences depends critically on reporting errors and latencies innate to those time series. While studies have proposed corrections for these issues, methodology for formally assessing how these noise sources degrade Rt estimate quality is lacking. By adapting Fisher information and experimental design theory, we develop an analytical framework to quantify the uncertainty induced by under-reporting and delays in reporting infections. This yields a novel metric, defined by the geometric means of reporting and cumulative delay probabilities, for ranking surveillance data informativeness. We apply this metric to two primary data sources for inferring Rt: epidemic case and death curves. We show that the assumption of death curves as more reliable, commonly made for acute infectious diseases such as COVID-19 and influenza, is not obvious and possibly untrue in many settings. Our framework clarifies and quantifies how actionable information about pathogen transmissibility is lost due to surveillance limitations.

Risk averse reproduction numbers improve resurgence detection

“…These are reasonable given high fidelity surveillance in Israel during this wave and are consistent with the analyses of [34,35]. As we only focus on relative trends, we make no further corrections to the dataset but note that accounting for issues such as testing delays generally cause incidence curves to be back-shifted and increase uncertainty, but necessitate auxiliary data [28,38]. Figure 5 demonstrates that all reproduction numbers agree that the wave was curbed across the booster period and that the epidemic was eventually controlled.…”

“…Since the α j are design variables subject to the conservation constraint in Eq. (4) , we can leverage experimental design theory [20,29] to derive novel consensus statistics to replace the default formulation from Eq. (2) .…”

“…If p = 2, this uncertainty can be circumscribed by an ellipse in the space spanned by R 1 and R 2 , and designs have a geometric interpretation as in Figure 1 . A -optimal designs minimise the bounding box of the ellipse, while D and E -optimal designs minimise its area (or volume, when extending to higher dimensions) and largest chord respectively [29,30]. These designs yield optimal versions of Λ j , , computed as shown in Eq.…”

“…Although this is an almost universal definition, other measures (e.g., the early warning signals of [43]) may circumvent some of the problems of 𝑅 as a metric for informing decision-making. Third, 𝐸 requires infection time and incidence data (or proxies [28]) at the resolution of the local scale. While this is becoming the norm with improved surveillance [44], it is not guaranteed, and may be scarce for emerging infectious diseases.…”

Quantifying the information in noisy epidemic curves

“…All data and source code (MATLAB v2021a) for reproducing the analyses and figures in this manuscript, as well as for applying the methodology we have developed here, are freely available at https://github.com/kpzoo/information-inepidemic-curves with a citable release at ref. 65 . We include a template function (in MATLAB and R) that can be easily modified to compute our metrics with userdefined noise estimates.…”