Accounting for Uncertainty During a Pandemic

We discuss several issues of statistical design, data collection, analysis, communication, and decision making that have arisen in recent and ongoing coronavirus studies, focusing on tools for assessment and propagation of uncertainty. This paper does not purport to be a comprehensive survey of the research literature; rather, we use examples to illustrate statistical points that we think are important.Comment: 16 page

Bayesian workflow for disease transmission modeling in Stan

This tutorial shows how to build, fit, and criticize disease transmission models in Stan, and should be useful to researchers interested in modeling the SARS-CoV-2 pandemic and other infectious diseases in a Bayesian framework. Bayesian modeling provides a principled way to quantify uncertainty and incorporate both data and prior knowledge into the model estimates. Stan is an expressive probabilistic programming language that abstracts the inference and allows users to focus on the modeling. As a result, Stan code is readable and easily extensible, which makes the modeler's work more transparent. Furthermore, Stan's main inference engine, Hamiltonian Monte Carlo sampling, is amiable to diagnostics, which means the user can verify whether the obtained inference is reliable. In this tutorial, we demonstrate how to formulate, fit, and diagnose a compartmental transmission model in Stan, first with a simple Susceptible-Infected-Recovered (SIR) model, then with a more elaborate transmission model used during the SARS-CoV-2 pandemic. We also cover advanced topics which can further help practitioners fit sophisticated models; notably, how to use simulations to probe the model and priors, and computational techniques to scale-up models based on ordinary differential equations

Estimating the cumulative incidence of SARS-CoV-2 with imperfect serological tests: Exploiting cutoff-free approaches.

Large-scale serological testing in the population is essential to determine the true extent of the current SARS-CoV-2 pandemic. Serological tests measure antibody responses against pathogens and use predefined cutoff levels that dichotomize the quantitative test measures into sero-positives and negatives and use this as a proxy for past infection. With the imperfect assays that are currently available to test for past SARS-CoV-2 infection, the fraction of seropositive individuals in serosurveys is a biased estimator of the cumulative incidence and is usually corrected to account for the sensitivity and specificity. Here we use an inference method-referred to as mixture-model approach-for the estimation of the cumulative incidence that does not require to define cutoffs by integrating the quantitative test measures directly into the statistical inference procedure. We confirm that the mixture model outperforms the methods based on cutoffs, leading to less bias and error in estimates of the cumulative incidence. We illustrate how the mixture model can be used to optimize the design of serosurveys with imperfect serological tests. We also provide guidance on the number of control and case sera that are required to quantify the test's ambiguity sufficiently to enable the reliable estimation of the cumulative incidence. Lastly, we show how this approach can be used to estimate the cumulative incidence of classes of infections with an unknown distribution of quantitative test measures. This is a very promising application of the mixture-model approach that could identify the elusive fraction of asymptomatic SARS-CoV-2 infections. An R-package implementing the inference methods used in this paper is provided. Our study advocates using serological tests without cutoffs, especially if they are used to determine parameters characterizing populations rather than individuals. This approach circumvents some of the shortcomings of cutoff-based methods at exactly the low cumulative incidence levels and test accuracies that we are currently facing in SARS-CoV-2 serosurveys

Direct and indirect effects of the COVID-19 pandemic on mortality in Switzerland.

The direct and indirect impact of the COVID-19 pandemic on population-level mortality is of concern to public health but challenging to quantify. Using data for 2011-2019, we applied Bayesian models to predict the expected number of deaths in Switzerland and compared them with laboratory-confirmed COVID-19 deaths from February 2020 to April 2022 (study period). We estimated that COVID-19-related mortality was underestimated by a factor of 0.72 (95% credible interval [CrI]: 0.46-0.78). After accounting for COVID-19 deaths, the observed mortality was -4% (95% CrI: -8 to 0) lower than expected. The deficit in mortality was concentrated in age groups 40-59 (-12%, 95%CrI: -19 to -5) and 60-69 (-8%, 95%CrI: -15 to -2). Although COVID-19 control measures may have negative effects, after subtracting COVID-19 deaths, there were fewer deaths in Switzerland during the pandemic than expected, suggesting that any negative effects of control measures were offset by the positive effects. These results have important implications for the ongoing debate about the appropriateness of COVID-19 control measures

Socio-demographic characteristics associated with COVID-19 vaccination uptake in Switzerland: longitudinal analysis of the CoMix study.

BACKGROUND Vaccination is an effective strategy to reduce morbidity and mortality from coronavirus disease 2019 (COVID-19). However, the uptake of COVID-19 vaccination has varied across and within countries. Switzerland has had lower levels of COVID-19 vaccination uptake in the general population than many other high-income countries. Understanding the socio-demographic factors associated with vaccination uptake can help to inform future vaccination strategies to increase uptake. METHODS We conducted a longitudinal online survey in the Swiss population, consisting of six survey waves from June to September 2021. Participants provided information on socio-demographic characteristics, history of testing for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), social contacts, willingness to be vaccinated, and vaccination status. We used a multivariable Poisson regression model to estimate the adjusted rate ratio (aRR) and 95% confidence intervals (CI) of COVID-19 vaccine uptake. RESULTS We recorded 6,758 observations from 1,884 adults. For the regression analysis, we included 3,513 observations from 1,883 participants. By September 2021, 600 (75%) of 806 study participants had received at least one vaccine dose. Participants who were older, male, and students, had a higher educational level, household income, and number of social contacts, and lived in a household with a medically vulnerable person were more likely to have received at least one vaccine dose. Female participants, those who lived in rural areas and smaller households, and people who perceived COVID-19 measures as being too strict were less likely to be vaccinated. We found no significant association between previous SARS-CoV-2 infections and vaccination uptake. CONCLUSIONS Our results suggest that socio-demographic factors as well as individual behaviours and attitudes played an important role in COVID-19 vaccination uptake in Switzerland. Therefore, appropriate communication with the public is needed to ensure that public health interventions are accepted and implemented by the population. Tailored COVID-19 vaccination strategies in Switzerland that aim to improve uptake should target specific subgroups such as women, people from rural areas or people with lower socio-demographic status

Impact of cross-border-associated cases on the SARS-CoV-2 epidemic in Switzerland during summer 2020 and 2021

During the summers of 2020 and 2021, the number of confirmed cases of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infections in Switzerland remained at relatively low levels, but grew steadily over time. It remains unclear to what extent epidemic growth during these periods was a result of the relaxation of local control measures or increased traveling and subsequent importation of cases. A better understanding of the role of cross-border-associated cases (imports) on the local epidemic dynamics will help to inform future surveillance strategies. We analyzed routine surveillance data of confirmed cases of SARS-CoV-2 in Switzerland from 1 June to 30 September 2020 and 2021. We used a stochastic branching process model that accounts for superspreading of SARS-CoV-2 to simulate epidemic trajectories in absence and in presence of imports during summer 2020 and 2021. The Swiss Federal Office of Public Health reported 22,919 and 145,840 confirmed cases of SARS-CoV-2 from 1 June to 30 September 2020 and 2021, respectively. Among cases with known place of exposure, 27% (3,276 of 12,088) and 25% (1,110 of 4,368) reported an exposure abroad in 2020 and 2021, respectively. Without considering the impact of imported cases, the steady growth of confirmed cases during summer periods would be consistent with a value of that is significantly above the critical threshold of 1. In contrast, we estimated at 0.84 (95% credible interval, CrI: 0.78–0.90) in 2020 and 0.82 (95% CrI: 0.74–0.90) in 2021 when imported cases were taken into account, indicating that the local was below the critical threshold of 1 during summer. In Switzerland, cross-border-associated SARS-CoV-2 cases had a considerable impact on the local transmission dynamics and can explain the steady growth of the epidemic during the summers of 2020 and 2021

A mechanistic model for long-term immunological outcomes in South African HIV-infected children and adults receiving ART.

Long-term effects of the growing population of HIV-treated people in Southern Africa on individuals and the public health sector at large are not yet understood. This study proposes a novel 'ratio' model that relates CD4+ T-cell counts of HIV-infected individuals to the CD4+ count reference values from healthy populations. We use mixed-effects regression to fit the model to data from 1616 children (median age 4.3 years at ART initiation) and 14,542 adults (median age 36 years at ART initiation). We found that the scaled carrying capacity, maximum CD4+ count relative to an HIV-negative individual of similar age, and baseline scaled CD4+ counts were closer to healthy values in children than in adults. Post-ART initiation, CD4+ growth rate was inversely correlated with baseline CD4+ T-cell counts, and consequently higher in adults than children. Our results highlight the impacts of age on dynamics of the immune system of healthy and HIV-infected individuals

Drivers of HIV-1 drug resistance to non-nucleoside reverse-transcriptase inhibitors (NNRTIs) in nine southern African countries: a modelling study.

INTRODUCTION: The rise of HIV-1 drug resistance to non-nucleoside reverse-transcriptase inhibitors (NNRTI) threatens antiretroviral therapy's long-term success (ART). NNRTIs will remain an essential drug for the management of HIV-1 due to safety concerns associated with integrase inhibitors. We fitted a dynamic transmission model to historical data from 2000 to 2018 in nine countries of southern Africa to understand the mechanisms that have shaped the HIV-1 epidemic and the rise of pretreatment NNRTI resistance. METHODS: We included data on HIV-1 prevalence, ART coverage, HIV-related mortality, and survey data on pretreatment NNRTI resistance from nine southern Africa countries from a systematic review, UNAIDS and World Bank. Using a Bayesian hierarchical framework, we developed a dynamic transmission model linking data on the HIV-1 epidemic to survey data on NNRTI drug resistance in each country. We estimated the proportion of resistance attributable to unregulated, off-programme use of ART. We examined each national ART programme's vulnerability to NNRTI resistance by defining a fragility index: the ratio of the rate of NNRTI resistance emergence during first-line ART over the rate of switching to second-line ART. We explored associations between fragility and characteristics of the health system of each country. RESULTS: The model reliably described the dynamics of the HIV-1 epidemic and NNRTI resistance in each country. Predicted levels of resistance in 2018 ranged between 3.3% (95% credible interval 1.9-7.1) in Mozambique and 25.3% (17.9-33.8) in Eswatini. The proportion of pretreatment NNRTI resistance attributable to unregulated antiretroviral use ranged from 6% (2-14) in Eswatini to 64% (26-85) in Mozambique. The fragility index was low in Botswana (0.01; 0.0-0.11) but high in Namibia (0.48; 0.16-10.17), Eswatini (0.64; 0.23-11.8) and South Africa (1.21; 0.83-9.84). The combination of high fragility of ART programmes and high ART coverage levels was associated with a sharp increase in pretreatment NNRTI resistance. CONCLUSIONS: This comparison of nine countries shows that pretreatment NNRTI resistance can be controlled despite high ART coverage levels. This was the case in Botswana, Mozambique, and Zambia, most likely because of better HIV care delivery, including rapid switching to second-line ART of patients failing first-line ART

Survival among people hospitalized with COVID-19 in Switzerland: a nationwide population-based analysis

Background: Increasing age, male sex, and pre-existing comorbidities are associated with lower survival from SARS-CoV-2 infection. The interplay between different comorbidities, age, and sex is not fully understood, and it remains unclear if survival decreases linearly with higher ICU occupancy or if there is a threshold beyond which survival falls. Method: This national population-based study included 22,648 people who tested positive for SARS-CoV-2 infection and were hospitalized in Switzerland between February 24, 2020, and March 01, 2021. Bayesian survival models were used to estimate survival after positive SARS-CoV-2 test among people hospitalized with COVID-19 by epidemic wave, age, sex, comorbidities, and ICU occupancy. Two-way interactions between age, sex, and comorbidities were included to assess the differential risk of death across strata. ICU occupancy was modeled using restricted cubic splines to allow for a non-linear association with survival. Results: Of 22,648 people hospitalized with COVID-19, 4785 (21.1%) died. The survival was lower during the first epidemic wave than in the second (predicted survival at 40 days after positive test 76.1 versus 80.5%). During the second epidemic wave, occupancy among all available ICU beds in Switzerland varied between 51.7 and 78.8%. The estimated survival was stable at approximately 81.5% when ICU occupancy was below 70%, but worse when ICU occupancy exceeded this threshold (survival at 80% ICU occupancy: 78.2%; 95% credible interval [CrI] 76.1 to 80.1%). Periods with higher ICU occupancy (>70 vs 70%) were associated with an estimated number of 137 (95% CrI 27 to 242) excess deaths. Comorbid conditions reduced survival more in younger people than in older people. Among comorbid conditions, hypertension and obesity were not associated with poorer survival. Hypertension appeared to decrease survival in combination with cardiovascular disease. Conclusions: Survival after hospitalization with COVID-19 has improved over time, consistent with improved management of severe COVID-19. The decreased survival above 70% national ICU occupancy supports the need to introduce measures for prevention and control of SARS-CoV-2 transmission in the population well before ICUs are full