The interaction of disease transmission, mortality, and economic output over the first 2 years of the COVID-19 pandemic.

BACKGROUND: The COVID-19 pandemic has caused over 7.02 million deaths as of January 2024 and profoundly affected most countries' Gross Domestic Product (GDP). Here, we study the interaction of SARS-CoV-2 transmission, mortality, and economic output between January 2020 and December 2022 across 25 European countries. METHODS: We use a Bayesian mixed effects model with auto-regressive terms to estimate the temporal relationships between disease transmission, excess deaths, changes in economic output, transit mobility and non-pharmaceutical interventions (NPIs) across countries. RESULTS: Disease transmission intensity (logRt) decreases GDP and increases excess deaths, where the latter association is longer-lasting. Changes in GDP as well as prior week transmission intensity are both negatively associated with each other (-0.241, 95% CrI: -0.295 - -0.189). We find evidence of risk-averse behaviour, as changes in transit and prior week transmission intensity are negatively associated (-0.055, 95% CrI: -0.074 to -0.036). Our results highlight a complex cost-benefit trade-off from individual NPIs. For example, banning international travel is associated with both increases in GDP (0.014, 0.002-0.025) and decreases in excess deaths (-0.014, 95% CrI: -0.028 - -0.001). Country-specific random effects, such as the poverty rate, are positively associated with excess deaths while the UN government effectiveness index is negatively associated with excess deaths. INTERPRETATION: The interplay between transmission intensity, excess deaths, population mobility and economic output is highly complex, and none of these factors can be considered in isolation. Our results reinforce the intuitive idea that significant economic activity arises from diverse person-to-person interactions. Our analysis quantifies and highlights that the impact of disease on a given country is complex and multifaceted. Long-term economic impairments are not fully captured by our model, as well as long-term disease effects (Long COVID).

Differential responses of SARS-CoV-2 variants to environmental drivers during their selective sweeps.

Previous work has shown that environmental variables affect SARS-CoV-2 transmission, but it is unclear whether different strains show similar environmental responses. Here we leverage genetic data on the transmission of three (Alpha, Delta and Omicron BA.1) variants of SARS-CoV-2 throughout England, to unpick the roles that climate and public-health interventions play in the circulation of this virus. We find evidence for enhanced transmission of the virus in colder conditions in the first variant selective sweep (of Alpha, in winter), but limited evidence of an impact of climate in either the second (of Delta, in the summer, when vaccines were prevalent) or third sweep (of Omicron, in the winter, during a successful booster-vaccination campaign). We argue that the results for Alpha are to be expected if the impact of climate is non-linear: we find evidence of an asymptotic impact of temperature on the alpha variant transmission rate. That is, at lower temperatures, the influence of temperature on transmission is much higher than at warmer temperatures. As with the initial spread of SARS-CoV-2, however, the overwhelming majority of variation in disease transmission is explained by the intrinsic biology of the virus and public-health mitigation measures. Specifically, when vaccination rates are high, a major driver of the spread of a new variant is it's ability to evade immunity, and any climate effects are secondary (as evidenced for Delta and Omicron). Climate alone cannot describe the transmission dynamics of emerging SARS-CoV-2 variants.

Comparative impact assessment of COVID-19 policy interventions in five South Asian countries using reported and estimated unreported death counts during 2020-2021.

There has been raging discussion and debate around the quality of COVID death data in South Asia. According to WHO, of the 5.5 million reported COVID-19 deaths from 2020-2021, 0.57 million (10%) were contributed by five low and middle income countries (LMIC) countries in the Global South: India, Pakistan, Bangladesh, Sri Lanka and Nepal. However, a number of excess death estimates show that the actual death toll from COVID-19 is significantly higher than the reported number of deaths. For example, the IHME and WHO both project around 14.9 million total deaths, of which 4.5-5.5 million were attributed to these five countries in 2020-2021. We focus our gaze on the COVID-19 performance of these five countries where 23.5% of the world population lives in 2020 and 2021, via a counterfactual lens and ask, to what extent the mortality of one LMIC would have been affected if it adopted the pandemic policies of another, similar country? We use a Bayesian semi-mechanistic model developed by Mishra et al. (2021) to compare both the reported and estimated total death tolls by permuting the time-varying reproduction number (Rt) across these countries over a similar time period. Our analysis shows that, in the first half of 2021, mortality in India in terms of reported deaths could have been reduced to 96 and 102 deaths per million compared to actual 170 reported deaths per million had it adopted the policies of Nepal and Pakistan respectively. In terms of total deaths, India could have averted 481 and 466 deaths per million had it adopted the policies of Bangladesh and Pakistan. On the other hand, India had a lower number of reported COVID-19 deaths per million (48 deaths per million) and a lower estimated total deaths per million (80 deaths per million) in the second half of 2021, and LMICs other than Pakistan would have lower reported mortality had they followed India's strategy. The gap between the reported and estimated total deaths highlights the varying level and extent of under-reporting of deaths across the subcontinent, and that model estimates are contingent on accuracy of the death data. Our analysis shows the importance of timely public health intervention and vaccines for lowering mortality and the need for better coverage infrastructure for the death registration system in LMICs.

Application of referenced thermodynamic integration to Bayesian model selection.

Evaluating normalising constants is important across a range of topics in statistical learning, notably Bayesian model selection. However, in many realistic problems this involves the integration of analytically intractable, high-dimensional distributions, and therefore requires the use of stochastic methods such as thermodynamic integration (TI). In this paper we apply a simple but under-appreciated variation of the TI method, here referred to as referenced TI, which computes a single model's normalising constant in an efficient way by using a judiciously chosen reference density. The advantages of the approach and theoretical considerations are set out, along with pedagogical 1 and 2D examples. The approach is shown to be useful in practice when applied to a real problem -to perform model selection for a semi-mechanistic hierarchical Bayesian model of COVID-19 transmission in South Korea involving the integration of a 200D density.

Unifying incidence and prevalence under a time-varying general branching process.

Renewal equations are a popular approach used in modelling the number of new infections, i.e., incidence, in an outbreak. We develop a stochastic model of an outbreak based on a time-varying variant of the Crump-Mode-Jagers branching process. This model accommodates a time-varying reproduction number and a time-varying distribution for the generation interval. We then derive renewal-like integral equations for incidence, cumulative incidence and prevalence under this model. We show that the equations for incidence and prevalence are consistent with the so-called back-calculation relationship. We analyse two particular cases of these integral equations, one that arises from a Bellman-Harris process and one that arises from an inhomogeneous Poisson process model of transmission. We also show that the incidence integral equations that arise from both of these specific models agree with the renewal equation used ubiquitously in infectious disease modelling. We present a numerical discretisation scheme to solve these equations, and use this scheme to estimate rates of transmission from serological prevalence of SARS-CoV-2 in the UK and historical incidence data on Influenza, Measles, SARS and Smallpox.

Machine learning models of healthcare expenditures predicting mortality: A cohort study of spousal bereaved Danish individuals.

BACKGROUND: The ability to accurately predict survival in older adults is crucial as it guides clinical decision making. The added value of using health care usage for predicting mortality remains unexplored. The aim of this study was to investigate if temporal patterns of healthcare expenditures, can improve the predictive performance for mortality, in spousal bereaved older adults, next to other widely used sociodemographic variables. METHODS: This is a population-based cohort study of 48,944 Danish citizens 65 years of age and older suffering bereavement within 2013-2016. Individuals were followed from date of spousal loss until death from all causes or 31st of December 2016, whichever came first. Healthcare expenditures were available on weekly basis for each person during the follow-up and used as predictors for mortality risk in Extreme Gradient Boosting models. The extent to which medical spending trajectories improved mortality predictions compared to models with sociodemographics, was assessed with respect to discrimination (AUC), overall prediction error (Brier score), calibration, and clinical benefit (decision curve analysis). RESULTS: The AUC of age and sex for mortality the year after spousal loss was 70.8% [95% CI 68.8, 72.8]. The addition of sociodemographic variables led to an increase of AUC ranging from 0.9% to 3.1% but did not significantly reduce the overall prediction error. The AUC of the model combining the variables above plus medical spending usage was 80.8% [79.3, 82.4] also exhibiting smaller Brier score and better calibration. Overall, patterns of healthcare expenditures improved mortality predictions the most, also exhibiting the highest clinical benefit among the rest of the models. CONCLUSION: Temporal patterns of medical spending have the potential to significantly improve our assessment on who is at high risk of dying after suffering spousal loss. The proposed methodology can assist in a more efficient risk profiling and prognosis of bereaved individuals.

Predicting mortality risk after a fall in older adults using health care spending patterns: a population-based cohort study.

OBJECTIVE: To develop a prognostic model of 1-year mortality for individuals aged 65+ presenting at the emergency department (ED) with a fall based on health care spending patterns to guide clinical decision-making. DESIGN: Population-based cohort study (n = 35,997) included with a fall in 2013 and followed 1 year. METHODS: Health care spending indicators (dynamical indicators of resilience, DIORs) 2 years before admission were evaluated as potential predictors, along with age, sex and other clinical and sociodemographic covariates. Multivariable logistic regression models were developed and internally validated (10-fold cross-validation). Performance was assessed via discrimination (area under the receiver operating characteristic curve, AUC), Brier scores, calibration and decision curve analysis. RESULTS: The AUC of age and sex for mortality was 72.5% [95% confidence interval 71.8 to 73.2]. The best model included age, sex, number of medications and health care spending DIORs. It exhibited high discrimination (AUC: 81.1 [80.5 to 81.6]), good calibration and potential clinical benefit for various threshold probabilities. Overall, health care spending patterns improved predictive accuracy the most while also exhibiting superior performance and clinical benefit. CONCLUSIONS: Patterns of health care spending have the potential to significantly improve assessments on who is at high risk of dying following admission to the ED with a fall. The proposed methodology can assist in predicting the prognosis of fallers, emphasising the added predictive value of longitudinal health-related information next to clinical and sociodemographic predictors.

Effectiveness assessment of non-pharmaceutical interventions: lessons learned from the COVID-19 pandemic.

Effectiveness of non-pharmaceutical interventions (NPIs), such as school closures and stay-at-home orders, during the COVID-19 pandemic has been assessed in many studies. Such assessments can inform public health policies and contribute to evidence-based choices of NPIs during subsequent waves or future epidemics. However, methodological issues and no standardised assessment practices have restricted the practical value of the existing evidence. Here, we present and discuss lessons learned from the COVID-19 pandemic and make recommendations for standardising and improving assessment, data collection, and modelling. These recommendations could contribute to reliable and policy-relevant assessments of the effectiveness of NPIs during future epidemics.

Sex differences in health care expenditures and mortality after spousal bereavement: A register-based Danish cohort study.

BACKGROUND: Spousal bereavement is a life event that affects older people differently. We investigated the impact of spousal bereavement on medical expenditures and mortality in the general population, emphasizing on age and sex. METHODS: Data are from a population-based, retrospective cohort study following 924,958 Danish citizens over the age of 65 years, within 2011-2016. Changes in health care expenditures in those who suffer bereavement were compared with time matched changes among those who did not. Mortality hazards were analysed with time to event analysis. RESULTS: A total of 77,722 (~8.4%) individuals experienced bereavement, 65.8% being females. Among males, bereavement was associated with increase of expenditures the year after, that was 42 Euros per week (95% CI, 36 to 48) larger than the non-bereaved group. The corresponding increase for females was 35 Euros per week (95% CI, 30 to 40). The increase of mortality hazards was highest in the first year after bereavement, higher in males than females, in young old and almost absent in the oldest old. Compared with the reference, mortality the year after spousal loss was 70% higher (HR 1.70 [95% CI 1.40 to 2.08]) for males aged 65-69 years and remained elevated for a period of six years. Mortality for females aged 65-69 years was 27% higher in the first year (HR 1.27, [1.07 to 1.52]), normalizing thereafter. CONCLUSION: Bereavement affects older people differently with younger males being most frail with limited recovery potential.

Assessment of COVID-19 as the Underlying Cause of Death Among Children and Young People Aged 0 to 19 Years in the US.

Importance: COVID-19 was the underlying cause of death for more than 940 000 individuals in the US, including at least 1289 children and young people (CYP) aged 0 to 19 years, with at least 821 CYP deaths occurring in the 1-year period from August 1, 2021, to July 31, 2022. Because deaths among US CYP are rare, the mortality burden of COVID-19 in CYP is best understood in the context of all other causes of CYP death. Objective: To determine whether COVID-19 is a leading (top 10) cause of death in CYP in the US. Design, Setting, and Participants: This national population-level cross-sectional epidemiological analysis for the years 2019 to 2022 used data from the US Centers for Disease Control and Prevention Wide-Ranging Online Data for Epidemiologic Research (WONDER) database on underlying cause of death in the US to identify the ranking of COVID-19 relative to other causes of death among individuals aged 0 to 19 years. COVID-19 deaths were considered in 12-month periods between April 1, 2020, and August 31, 2022, compared with deaths from leading non-COVID-19 causes in 2019, 2020, and 2021. Main Outcomes and Measures: Cause of death rankings by total number of deaths, crude rates per 100 000 population, and percentage of all causes of death, using the National Center for Health Statistics 113 Selected Causes of Death, for ages 0 to 19 and by age groupings (<1 year, 1-4 years, 5-9 years, 10-14 years, 15-19 years). Results: There were 821 COVID-19 deaths among individuals aged 0 to 19 years during the study period, resulting in a crude death rate of 1.0 per 100 000 population overall; 4.3 per 100 000 for those younger than 1 year; 0.6 per 100 000 for those aged 1 to 4 years; 0.4 per 100 000 for those aged 5 to 9 years; 0.5 per 100 000 for those aged 10 to 14 years; and 1.8 per 100 000 for those aged 15 to 19 years. COVID-19 mortality in the time period of August 1, 2021, to July 31, 2022, was among the 10 leading causes of death in CYP aged 0 to 19 years in the US, ranking eighth among all causes of deaths, fifth in disease-related causes of deaths (excluding unintentional injuries, assault, and suicide), and first in deaths caused by infectious or respiratory diseases when compared with 2019. COVID-19 deaths constituted 2% of all causes of death in this age group. Conclusions and Relevance: The findings of this study suggest that COVID-19 was a leading cause of death in CYP. It caused substantially more deaths in CYP annually than any vaccine-preventable disease historically in the recent period before vaccines became available. Various factors, including underreporting and not accounting for COVID-19's role as a contributing cause of death from other diseases, mean that these estimates may understate the true mortality burden of COVID-19. The findings of this study underscore the public health relevance of COVID-19 to CYP. In the likely future context of sustained SARS-CoV-2 circulation, appropriate pharmaceutical and nonpharmaceutical interventions (eg, vaccines, ventilation, air cleaning) will continue to play an important role in limiting transmission of the virus and mitigating severe disease in CYP.

Intrinsic randomness in epidemic modelling beyond statistical uncertainty.

Uncertainty can be classified as either aleatoric (intrinsic randomness) or epistemic (imperfect knowledge of parameters). The majority of frameworks assessing infectious disease risk consider only epistemic uncertainty. We only ever observe a single epidemic, and therefore cannot empirically determine aleatoric uncertainty. Here, we characterise both epistemic and aleatoric uncertainty using a time-varying general branching process. Our framework explicitly decomposes aleatoric variance into mechanistic components, quantifying the contribution to uncertainty produced by each factor in the epidemic process, and how these contributions vary over time. The aleatoric variance of an outbreak is itself a renewal equation where past variance affects future variance. We find that, superspreading is not necessary for substantial uncertainty, and profound variation in outbreak size can occur even without overdispersion in the offspring distribution (i.e. the distribution of the number of secondary infections an infected person produces). Aleatoric forecasting uncertainty grows dynamically and rapidly, and so forecasting using only epistemic uncertainty is a significant underestimate. Therefore, failure to account for aleatoric uncertainty will ensure that policymakers are misled about the substantially higher true extent of potential risk. We demonstrate our method, and the extent to which potential risk is underestimated, using two historical examples.

π VAE: a stochastic process prior for Bayesian deep learning with MCMC.

Stochastic processes provide a mathematically elegant way to model complex data. In theory, they provide flexible priors over function classes that can encode a wide range of interesting assumptions. However, in practice efficient inference by optimisation or marginalisation is difficult, a problem further exacerbated with big data and high dimensional input spaces. We propose a novel variational autoencoder (VAE) called the prior encoding variational autoencoder ( π VAE). π VAE is a new continuous stochastic process. We use π VAE to learn low dimensional embeddings of function classes by combining a trainable feature mapping with generative model using a VAE. We show that our framework can accurately learn expressive function classes such as Gaussian processes, but also properties of functions such as their integrals. For popular tasks, such as spatial interpolation, π VAE achieves state-of-the-art performance both in terms of accuracy and computational efficiency. Perhaps most usefully, we demonstrate an elegant and scalable means of performing fully Bayesian inference for stochastic processes within probabilistic programming languages such as Stan.

PriorVAE: encoding spatial priors with variational autoencoders for small-area estimation.

Gaussian processes (GPs), implemented through multivariate Gaussian distributions for a finite collection of data, are the most popular approach in small-area spatial statistical modelling. In this context, they are used to encode correlation structures over space and can generalize well in interpolation tasks. Despite their flexibility, off-the-shelf GPs present serious computational challenges which limit their scalability and practical usefulness in applied settings. Here, we propose a novel, deep generative modelling approach to tackle this challenge, termed PriorVAE: for a particular spatial setting, we approximate a class of GP priors through prior sampling and subsequent fitting of a variational autoencoder (VAE). Given a trained VAE, the resultant decoder allows spatial inference to become incredibly efficient due to the low dimensional, independently distributed latent Gaussian space representation of the VAE. Once trained, inference using the VAE decoder replaces the GP within a Bayesian sampling framework. This approach provides tractable and easy-to-implement means of approximately encoding spatial priors and facilitates efficient statistical inference. We demonstrate the utility of our VAE two-stage approach on Bayesian, small-area estimation tasks.

Estimating the COVID-19 infection fatality ratio accounting for seroreversion using statistical modelling.

Background: The infection fatality ratio (IFR) is a key statistic for estimating the burden of coronavirus disease 2019 (COVID-19) and has been continuously debated throughout the COVID-19 pandemic. The age-specific IFR can be quantified using antibody surveys to estimate total infections, but requires consideration of delay-distributions from time from infection to seroconversion, time to death, and time to seroreversion (i.e. antibody waning) alongside serologic test sensitivity and specificity. Previous IFR estimates have not fully propagated uncertainty or accounted for these potential biases, particularly seroreversion. Methods: We built a Bayesian statistical model that incorporates these factors and applied this model to simulated data and 10 serologic studies from different countries. Results: We demonstrate that seroreversion becomes a crucial factor as time accrues but is less important during first-wave, short-term dynamics. We additionally show that disaggregating surveys by regions with higher versus lower disease burden can inform serologic test specificity estimates. The overall IFR in each setting was estimated at 0.49-2.53%. Conclusion: We developed a robust statistical framework to account for full uncertainties in the parameters determining IFR. We provide code for others to apply these methods to further datasets and future epidemics.

Spatial and temporal fluctuations in COVID-19 fatality rates in Brazilian hospitals.

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) Gamma variant of concern has spread rapidly across Brazil since late 2020, causing substantial infection and death waves. Here we used individual-level patient records after hospitalization with suspected or confirmed coronavirus disease 2019 (COVID-19) between 20 January 2020 and 26 July 2021 to document temporary, sweeping shocks in hospital fatality rates that followed the spread of Gamma across 14 state capitals, during which typically more than half of hospitalized patients aged 70 years and older died. We show that such extensive shocks in COVID-19 in-hospital fatality rates also existed before the detection of Gamma. Using a Bayesian fatality rate model, we found that the geographic and temporal fluctuations in Brazil's COVID-19 in-hospital fatality rates were primarily associated with geographic inequities and shortages in healthcare capacity. We estimate that approximately half of the COVID-19 deaths in hospitals in the 14 cities could have been avoided without pre-pandemic geographic inequities and without pandemic healthcare pressure. Our results suggest that investments in healthcare resources, healthcare optimization and pandemic preparedness are critical to minimize population-wide mortality and morbidity caused by highly transmissible and deadly pathogens such as SARS-CoV-2, especially in low- and middle-income countries.

A dataset of non-pharmaceutical interventions on SARS-CoV-2 in Europe.

During the second half of 2020, many European governments responded to the resurging transmission of SARS-CoV-2 with wide-ranging non-pharmaceutical interventions (NPIs). These efforts were often highly targeted at the regional level and included fine-grained NPIs. This paper describes a new dataset designed for the accurate recording of NPIs in Europe's second wave to allow precise modelling of NPI effectiveness. The dataset includes interventions from 114 regions in 7 European countries during the period from the 1st August 2020 to the 9th January 2021. The paper includes NPI definitions tailored to the second wave following an exploratory data collection. Each entry has been extensively validated by semi-independent double entry, comparison with existing datasets, and, when necessary, discussion with local epidemiologists. The dataset has considerable potential for use in disentangling the effectiveness of NPIs and comparing the impact of interventions across different phases of the pandemic.

A COVID-19 model for local authorities of the United Kingdom.

We propose a new framework to model the COVID-19 epidemic of the United Kingdom at the local authority level. The model fits within a general framework for semi-mechanistic Bayesian models of the epidemic based on renewal equations, with some important innovations, including a random walk modelling the reproduction number, incorporating information from different sources, including surveys to estimate the time-varying proportion of infections that lead to reported cases or deaths, and modelling the underlying infections as latent random variables. The model is designed to be updated daily using publicly available data. We envisage the model to be useful for now-casting and short-term projections of the epidemic as well as estimating historical trends. The model fits are available on a public website: https://imperialcollegelondon.github.io/covid19local. The model is currently being used by the Scottish government to inform their interventions.

Report 46: Factors driving extensive spatial and temporal fluctuations in COVID-19 fatality rates in Brazilian hospitals.

The SARS-CoV-2 Gamma variant spread rapidly across Brazil, causing substantial infection and death waves. We use individual-level patient records following hospitalisation with suspected or confirmed COVID-19 to document the extensive shocks in hospital fatality rates that followed Gamma's spread across 14 state capitals, and in which more than half of hospitalised patients died over sustained time periods. We show that extensive fluctuations in COVID-19 in-hospital fatality rates also existed prior to Gamma's detection, and were largely transient after Gamma's detection, subsiding with hospital demand. Using a Bayesian fatality rate model, we find that the geographic and temporal fluctuations in Brazil's COVID-19 in-hospital fatality rates are primarily associated with geographic inequities and shortages in healthcare capacity. We project that approximately half of Brazil's COVID-19 deaths in hospitals could have been avoided without pre-pandemic geographic inequities and without pandemic healthcare pressure. Our results suggest that investments in healthcare resources, healthcare optimization, and pandemic preparedness are critical to minimize population wide mortality and morbidity caused by highly transmissible and deadly pathogens such as SARS-CoV-2, especially in low- and middle-income countries. NOTE: The following manuscript has appeared as 'Report 46 - Factors driving extensive spatial and temporal fluctuations in COVID-19 fatality rates in Brazilian hospitals' at https://spiral.imperial.ac.uk:8443/handle/10044/1/91875 . ONE SENTENCE SUMMARY: COVID-19 in-hospital fatality rates fluctuate dramatically in Brazil, and these fluctuations are primarily associated with geographic inequities and shortages in healthcare capacity.