Improving early epidemiological assessment of emerging Aedes-transmitted epidemics using historical data

An approximate Bayesian approach for estimation of the instantaneous reproduction number under misreported epidemic data

In epidemic models, the effective reproduction number is of central importance to assess the transmission dynamics of an infectious disease and to orient health intervention strategies. Publicly shared data during an outbreak often suffers from two sources of misreporting (underreporting and delay in reporting) that should not be overlooked when estimating epidemiological parameters. The main statistical challenge in models that intrinsically account for a misreporting process lies in the joint estimation of the time-varying reproduction number and the delay/underreporting parameters. Existing Bayesian approaches typically rely on Markov chain Monte Carlo algorithms that are extremely costly from a computational perspective. We propose a much faster alternative based on Laplacian-P-splines (LPS) that combines Bayesian penalized B-splines for flexible and smooth estimation of the instantaneous reproduction number and Laplace approximations to selected posterior distributions for fast computation. Assuming a known generation interval distribution, the incidence at a given calendar time is governed by the epidemic renewal equation and the delay structure is specified through a composite link framework. Laplace approximations to the conditional posterior of the spline vector are obtained from analytical versions of the gradient and Hessian of the log-likelihood, implying a drastic speed-up in the computation of posterior estimates. Furthermore, the proposed LPS approach can be used to obtain point estimates and approximate credible intervals for the delay and reporting probabilities. Simulation of epidemics with different combinations for the underreporting rate and delay structure (one-day, two-day, and weekend delays) show that the proposed LPS methodology delivers fast and accurate estimates outperforming existing methods that do not take into account underreporting and delay patterns. Finally, LPS is illustrated in two real case studies of epidemic outbreaks.

Estimation of SARS-CoV-2 mortality during the early stages of an epidemic: A modeling study in Hubei, China, and six regions in Europe

BACKGROUND

As of 16 May 2020, more than 4.5 million cases and more than 300,000 deaths from disease caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) have been reported. Reliable estimates of mortality from SARS-CoV-2 infection are essential for understanding clinical prognosis, planning healthcare capacity, and epidemic forecasting. The case-fatality ratio (CFR), calculated from total numbers of reported cases and reported deaths, is the most commonly reported metric, but it can be a misleading measure of overall mortality. The objectives of this study were to (1) simulate the transmission dynamics of SARS-CoV-2 using publicly available surveillance data and (2) infer estimates of SARS-CoV-2 mortality adjusted for biases and examine the CFR, the symptomatic case-fatality ratio (sCFR), and the infection-fatality ratio (IFR) in different geographic locations.

METHOD AND FINDINGS

We developed an age-stratified susceptible-exposed-infected-removed (SEIR) compartmental model describing the dynamics of transmission and mortality during the SARS-CoV-2 epidemic. Our model accounts for two biases: preferential ascertainment of severe cases and right-censoring of mortality. We fitted the transmission model to surveillance data from Hubei Province, China, and applied the same model to six regions in Europe: Austria, Bavaria (Germany), Baden-Württemberg (Germany), Lombardy (Italy), Spain, and Switzerland. In Hubei, the baseline estimates were as follows: CFR 2.4% (95% credible interval [CrI] 2.1%-2.8%), sCFR 3.7% (3.2%-4.2%), and IFR 2.9% (2.4%-3.5%). Estimated measures of mortality changed over time. Across the six locations in Europe, estimates of CFR varied widely. Estimates of sCFR and IFR, adjusted for bias, were more similar to each other but still showed some degree of heterogeneity. Estimates of IFR ranged from 0.5% (95% CrI 0.4%-0.6%) in Switzerland to 1.4% (1.1%-1.6%) in Lombardy, Italy. In all locations, mortality increased with age. Among individuals 80 years or older, estimates of the IFR suggest that the proportion of all those infected with SARS-CoV-2 who will die ranges from 20% (95% CrI 16%-26%) in Switzerland to 34% (95% CrI 28%-40%) in Spain. A limitation of the model is that count data by date of onset are required, and these are not available in all countries.

CONCLUSIONS

We propose a comprehensive solution to the estimation of SARS-Cov-2 mortality from surveillance data during outbreaks. The CFR is not a good predictor of overall mortality from SARS-CoV-2 and should not be used for evaluation of policy or comparison across settings. Geographic differences in IFR suggest that a single IFR should not be applied to all settings to estimate the total size of the SARS-CoV-2 epidemic in different countries. The sCFR and IFR, adjusted for right-censoring and preferential ascertainment of severe cases, are measures that can be used to improve and monitor clinical and public health strategies to reduce the deaths from SARS-CoV-2 infection.

Estimation of SARS-CoV-2 mortality during the early stages of an epidemic: A modeling study in Hubei, China, and six regions in Europe

BACKGROUND

As of 16 May 2020, more than 4.5 million cases and more than 300,000 deaths from disease caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) have been reported. Reliable estimates of mortality from SARS-CoV-2 infection are essential for understanding clinical prognosis, planning healthcare capacity, and epidemic forecasting. The case-fatality ratio (CFR), calculated from total numbers of reported cases and reported deaths, is the most commonly reported metric, but it can be a misleading measure of overall mortality. The objectives of this study were to (1) simulate the transmission dynamics of SARS-CoV-2 using publicly available surveillance data and (2) infer estimates of SARS-CoV-2 mortality adjusted for biases and examine the CFR, the symptomatic case-fatality ratio (sCFR), and the infection-fatality ratio (IFR) in different geographic locations.

METHOD AND FINDINGS

We developed an age-stratified susceptible-exposed-infected-removed (SEIR) compartmental model describing the dynamics of transmission and mortality during the SARS-CoV-2 epidemic. Our model accounts for two biases: preferential ascertainment of severe cases and right-censoring of mortality. We fitted the transmission model to surveillance data from Hubei Province, China, and applied the same model to six regions in Europe: Austria, Bavaria (Germany), Baden-Württemberg (Germany), Lombardy (Italy), Spain, and Switzerland. In Hubei, the baseline estimates were as follows: CFR 2.4% (95% credible interval [CrI] 2.1%-2.8%), sCFR 3.7% (3.2%-4.2%), and IFR 2.9% (2.4%-3.5%). Estimated measures of mortality changed over time. Across the six locations in Europe, estimates of CFR varied widely. Estimates of sCFR and IFR, adjusted for bias, were more similar to each other but still showed some degree of heterogeneity. Estimates of IFR ranged from 0.5% (95% CrI 0.4%-0.6%) in Switzerland to 1.4% (1.1%-1.6%) in Lombardy, Italy. In all locations, mortality increased with age. Among individuals 80 years or older, estimates of the IFR suggest that the proportion of all those infected with SARS-CoV-2 who will die ranges from 20% (95% CrI 16%-26%) in Switzerland to 34% (95% CrI 28%-40%) in Spain. A limitation of the model is that count data by date of onset are required, and these are not available in all countries.

CONCLUSIONS

We propose a comprehensive solution to the estimation of SARS-Cov-2 mortality from surveillance data during outbreaks. The CFR is not a good predictor of overall mortality from SARS-CoV-2 and should not be used for evaluation of policy or comparison across settings. Geographic differences in IFR suggest that a single IFR should not be applied to all settings to estimate the total size of the SARS-CoV-2 epidemic in different countries. The sCFR and IFR, adjusted for right-censoring and preferential ascertainment of severe cases, are measures that can be used to improve and monitor clinical and public health strategies to reduce the deaths from SARS-CoV-2 infection.