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A central pillar of the UK's response to the SARS-CoV-2 pandemic was the provision of up-to-the moment nowcasts and short term projections to monitor current trends in transmission and associated healthcare burden. Here we present a detailed deconstruction of one of the 'real-time' models that was key contributor to this response, focussing on the model adaptations required over three pandemic years characterised by the imposition of lockdowns, mass vaccination campaigns and the emergence of new pandemic strains. The Bayesian model integrates an array of surveillance and other data sources including a novel approach to incorporating prevalence estimates from an unprecedented large-scale household survey. We present a full range of estimates of the epidemic history and the changing severity of the infection, quantify the impact of the vaccination programme and deconstruct contributing factors to the reproduction number. We further investigate the sensitivity of model-derived insights to the availability and timeliness of prevalence data, identifying its importance to the production of robust estimates., Comment: 35 pages, 7 figures, 3 tables

Nosocomial infections have important consequences for patients and hospital staff: they worsen patient outcomes and their management stresses already overburdened health systems. Accurate judgements of whether an infection is nosocomial helps staff make appropriate choices to protect other patients within the hospital. Nosocomiality cannot be properly assessed without considering whether the infected patient came into contact with high risk potential infectors within the hospital. We developed a Bayesian model that integrates epidemiological, contact and pathogen genetic data to determine how likely an infection is to be nosocomial and the probability of given infection candidates being the source of the infection.

Health-policy planning requires evidence on the burden that epidemics place on healthcare systems. Multiple, often dependent, datasets provide a noisy and fragmented signal from the unobserved epidemic process including transmission and severity dynamics. This paper explores important challenges to the use of state-space models for epidemic inference when multiple dependent datasets are analysed. We propose a new semi-stochastic model that exploits deterministic approximations for large-scale transmission dynamics while retaining stochasticity in the occurrence and reporting of relatively rare severe events. This model is suitable for many real-time situations including large seasonal epidemics and pandemics. Within this context, we develop algorithms to provide exact parameter inference and test them via simulation. Finally, we apply our joint model and the proposed algorithm to several surveillance data on the 2017-18 influenza epidemic in England to reconstruct transmission dynamics and estimate the daily new influenza infections as well as severity indicators such as the case-hospitalisation risk and the hospital-intensive care risk., Comment: 23 pages, 6 figures, 4 tables, 1 algorithm. Submitted to the Annals of Applied Statistics

Widespread vaccination campaigns have changed the landscape for COVID-19, vastly altering symptoms and reducing morbidity and mortality. We estimate trends in mortality by month of admission and vaccination status among those hospitalised with COVID-19 in England between March 2020 to September 2021, controlling for demographic factors and hospital load. Among 259,727 hospitalised COVID-19 cases, 51,948 (20.0%) experienced mortality in hospital. Hospitalised fatality risk ranged from 40.3% (95% confidence interval 39.4-41.3%) in March 2020 to 8.1% (7.2-9.0%) in June 2021. Older individuals and those with multiple co-morbidities were more likely to die or else experienced longer stays prior to discharge. Compared to unvaccinated people, the hazard of hospitalised mortality was 0.71 (0.67-0.77) with a first vaccine dose, and 0.56 (0.52-0.61) with a second vaccine dose. Compared to hospital load at 0-20% of the busiest week, the hazard of hospitalised mortality during periods of peak load (90-100%), was 1.23 (1.12-1.34). The prognosis for people hospitalised with COVID-19 in England has varied substantially throughout the pandemic and according to case-mix, vaccination, and hospital load. Our estimates provide an indication for demands on hospital resources, and the relationship between hospital burden and outcomes.

Assessing the impact of an intervention using time-series observational data on multiple units and outcomes is a frequent problem in many fields of scientific research. In this paper, we present a novel method to estimate intervention effects in such a setting by generalising existing approaches based on the factor analysis model and developing a Bayesian algorithm for inference. Our method is one of the few that can simultaneously: deal with outcomes of mixed type (continuous, binomial, count); increase efficiency in the estimates of the causal effects by jointly modelling multiple outcomes affected by the intervention; easily provide uncertainty quantification for all causal estimands of interest. We use the proposed approach to evaluate the impact that local tracing partnerships (LTP) had on the effectiveness of England's Test and Trace (TT) programme for COVID-19. Our analyses suggest that, overall, LTPs had a small positive impact on TT. However, there is considerable heterogeneity in the estimates of the causal effects over units and time.

Objective: To evaluate the relationship between coronavirus disease 2019 (COVID-19) diagnosis with SARS-CoV-2 variant B.1.1.7 (also known as Variant of Concern 202012/01) and the risk of hospitalisation compared to diagnosis with wildtype SARS-CoV-2 variants. Design: Retrospective cohort, analysed using stratified Cox regression. Setting: Community-based SARS-CoV-2 testing in England, individually linked with hospitalisation data. Participants: 839,278 laboratory-confirmed COVID-19 patients, of whom 36,233 had been hospitalised within 14 days, tested between 23rd November 2020 and 31st January 2021 and analysed at a laboratory with an available TaqPath assay that enables assessment of S-gene target failure (SGTF). SGTF is a proxy test for the B.1.1.7 variant. Patient data were stratified by age, sex, ethnicity, deprivation, region of residence, and date of positive test. Main outcome measures: Hospitalisation between 1 and 14 days after the first positive SARS-CoV-2 test. Results: 27,710 of 592,409 SGTF patients (4.7%) and 8,523 of 246,869 non-SGTF patients (3.5%) had been hospitalised within 1-14 days. The stratum-adjusted hazard ratio (HR) of hospitalisation was 1.52 (95% confidence interval [CI] 1.47 to 1.57) for COVID-19 patients infected with SGTF variants, compared to those infected with non-SGTF variants. The effect was modified by age (P<0.001), with HRs of 0.93-1.21 for SGTF compared to non-SGTF patients below age 20 years, 1.29 in those aged 20-29, and 1.45-1.65 in age groups 30 years or older. Conclusions: The results suggest that the risk of hospitalisation is higher for individuals infected with the B.1.1.7 variant compared to wildtype SARS-CoV-2, likely reflecting a more severe disease. The higher severity may be specific to adults above the age of 30., Comment: 29 pages, 9 figures

Clinical trials of a vaccine during an epidemic face particular challenges, such as the pressure to identify an effective vaccine quickly to control the epidemic, and the effect that time-space-varying infection incidence has on the power of a trial. We illustrate how the operating characteristics of different trial design elements may be evaluated using a network epidemic and trial simulation model, based on COVID-19 and individually randomised two-arm trials with a binary outcome. We show that "ring" recruitment strategies, prioritising participants at high risk of infection, can result in substantial improvement in terms of power, if sufficiently many contacts of observed cases are at high risk. In addition, we introduce a novel method to make more efficient use of the data from the earliest cases of infection observed in the trial, whose infection may have been too early to be vaccine-preventable. Finally, we compare several methods of response-adaptive randomisation, discussing their advantages and disadvantages in this two-arm context and identifying particular adaptation strategies that preserve power and estimation properties, while slightly reducing the number of infections, given an effective vaccine.

Background: Trends in hospitalised case-fatality risk (HFR), risk of intensive care unit (ICU) admission and lengths of stay for patients hospitalised for COVID-19 in England over the pre-vaccination era are unknown. Methods: Data on hospital and ICU admissions with COVID-19 at 31 NHS trusts in England were collected by Public Health England's Severe Acute Respiratory Infections surveillance system and linked to death information. We applied parametric multi-state mixture models, accounting for censored outcomes and regressing risks and times between events on month of admission, geography, and baseline characteristics. Findings: 20,785 adults were admitted with COVID-19 in 2020. Between March and June/July/August estimated HFR reduced from 31.9% (95% confidence interval 30.3-33.5%) to 10.9% (9.4-12.7%), then rose steadily from 21.6% (18.4-25.5%) in September to 25.7% (23.0-29.2%) in December, with steeper increases among older patients, those with multi-morbidity and outside London/South of England. ICU admission risk reduced from 13.9% (12.8-15.2%) in March to 6.2% (5.3-7.1%) in May, rising to a high of 14.2% (11.1-17.2%) in September. Median length of stay in non-critical care increased during 2020, from 6.6 to 12.3 days for those dying, and from 6.1 to 9.3 days for those discharged. Interpretation: Initial improvements in patient outcomes, corresponding to developments in clinical practice, were not sustained throughout 2020, with HFR in December approaching the levels seen at the start of the pandemic, whilst median hospital stays have lengthened. The role of increased transmission, new variants, case-mix and hospital pressures in increasing COVID-19 severity requires urgent further investigation., Comment: 45 pages, 12 figures

A target to eliminate Human Immuno-deficiency Virus (HIV) transmission in England by 2030 was set in early 2019. Estimates of recent trends in HIV prevalence, particularly the number of people living with undiagnosed HIV, by exposure group, ethnicity, gender, age group and region, are essential to monitor progress towards elimination. A Bayesian synthesis of evidence from multiple surveillance, demographic and survey datasets relevant to HIV in England is employed to estimate trends in: the number of people living with HIV (PLWH); the proportion of these people unaware of their HIV infection; and the corresponding prevalence of undiagnosed HIV. All estimates are stratified by exposure group, ethnicity, gender, age group (15-34, 35-44, 45-59, 60-74), region (London, outside London) and year (2012-2017). The total number of PLWH aged 15-74 in England increased from 82,400 (95% credible interval, CrI, 78,700 to 89,100) in 2012 to 89,500 (95% CrI 87,400 to 93,300) in 2017. The proportion diagnosed steadily increased from 84% (95% CrI 77 to 88%) to 92% (95% CrI 89 to 94%) over the same time period, corresponding to a halving in the number of undiagnosed infections from 13,500 (95% CrI 9,800 to 20,200) to 6,900 (95% CrI 4,900 to 10,700). This decrease is equivalent to a halving in prevalence of undiagnosed infection and is reflected in all sub-groups of gay, bisexual and other men who have sex with men and most sub-groups of black African heterosexuals. However, decreases were not detected for some sub-groups of other ethnicity heterosexuals, particularly outside London. In 2016, the Joint United Nations Programme on HIV/ AIDS target of diagnosing 90% of people living with HIV was reached in England. To achieve HIV elimination by 2030, current testing efforts should be enhanced to address the numbers of heterosexuals living with undiagnosed HIV, especially outside London.

Evidence-based knowledge of infectious disease burden, including prevalence, incidence, severity and transmission, in different population strata and locations, and possibly in real time, is crucial to the planning and evaluation of public health policies. Direct observation of a disease process is rarely possible. However, latent characteristics of an epidemic and its evolution can often be inferred from the synthesis of indirect information from various routine data sources, as well as expert opinion. The simultaneous synthesis of multiple data sources, often conveniently carried out in a Bayesian framework, poses a number of statistical and computational challenges: the heterogeneity in type, relevance and granularity of the data, together with selection and informative observation biases, lead to complex probabilistic models that are difficult to build and fit, and challenging to criticize. Using motivating case studies of influenza, this chapter illustrates the cycle of model development and criticism in the context of Bayesian evidence synthesis, highlighting the challenges of complex model building, computationally efficient inference, and conflicting evidence., Comment: This manuscript is a preprint of a Chapter to appear in the "Handbook of Infectious Disease Data Analysis", Held, L., Hens, N., O'Neill, P.D. and Wallinga, J. (Eds.). Chapman & Hall/CRC, 2018. Please use the book for possible citations

Researchers are often challenged with assessing the impact of an intervention on an outcome of interest in situations where the intervention is non-randomised, the intervention is only applied to one or few units, the intervention is binary, and outcome measurements are available at multiple time points. In this paper, we review existing methods for causal inference in these situations. We detail the assumptions underlying each method, emphasize connections between the different approaches and provide guidelines regarding their practical implementation. Several open problems are identified thus highlighting the need for future research.

Knowledge of the time at which an HIV-infected individual seroconverts, when the immune system starts responding to HIV infection, plays a vital role in the design and implementation of interventions to reduce the impact of the HIV epidemic. A number of biomarkers have been developed to distinguish between recent and long-term HIV infection, based on the antibody response to HIV. To quantify the recency of infection at an individual level, we propose characterising the growth of such biomarkers from observations from a panel of individuals with known seroconversion time, using Bayesian mixed effect models. We combine this knowledge of the growth patterns with observations from a newly diagnosed individual, to estimate the probability seroconversion occurred in the X months prior to diagnosis. We explore, through a simulation study, the characteristics of different biomarkers that affect our ability to estimate recency, such as the growth rate. In particular, we find that predictive ability is improved by using joint models of two biomarkers, accounting for their correlation, rather than univariate models of single biomarkers.

Influenza remains a significant burden on health systems. Effective responses rely on the timely understanding of the magnitude and the evolution of an outbreak. For monitoring purposes, data on severe cases of influenza in England are reported weekly to Public Health England. These data are both readily available and have the potential to provide valuable information to estimate and predict the key transmission features of seasonal and pandemic influenza. We propose an epidemic model that links the underlying unobserved influenza transmission process to data on severe influenza cases. Within a Bayesian framework, we infer retrospectively the parameters of the epidemic model for each seasonal outbreak from 2012 to 2015, including: the effective reproduction number; the initial susceptibility; the probability of admission to intensive care given infection; and the effect of school closure on transmission. The model is also implemented in real time to assess whether early forecasting of the number of admission to intensive care is possible. Our model of admissions data allows reconstruction of the underlying transmission dynamics revealing: increased transmission during the season 2013/14 and a noticeable effect of Christmas school holiday on disease spread during season 2012/13 and 2014/15. When information on the initial immunity of the population is available, forecasts of the number of admissions to intensive care can be substantially improved. Readily available severe case data can be effectively used to estimate epidemiological characteristics and to predict the evolution of an epidemic, crucially allowing real-time monitoring of the transmission and severity of the outbreak., Comment: 17 pages, 6 Figures, 3 tables and one ancillary file (Additional_File_1) Replacement of "Monitoring and predicting influenza epidemics from routinely collected severe case data" with the following changes: we used a continuous-time system to describe transmission; we used a time varying transmission; we improved the analysis of the waiting time from symptoms to ICU admissions

Suppose we have a Bayesian model which combines evidence from several different sources. We want to know which model parameters most affect the estimate or decision from the model, or which of the parameter uncertainties drive the decision uncertainty. Furthermore we want to prioritise what further data should be collected. These questions can be addressed by Value of Information (VoI) analysis, in which we estimate expected reductions in loss from learning specific parameters or collecting data of a given design. We describe the theory and practice of VoI for Bayesian evidence synthesis, using and extending ideas from health economics, computer modelling and Bayesian design. The methods are general to a range of decision problems including point estimation and choices between discrete actions. We apply them to a model for estimating prevalence of HIV infection, combining indirect information from several surveys, registers and expert beliefs. This analysis shows which parameters contribute most of the uncertainty about each prevalence estimate, and provides the expected improvements in precision from collecting specific amounts of additional data.

A prompt public health response to a new epidemic relies on the ability to monitor and predict its evolution in real time as data accumulate. The 2009 A/H1N1 outbreak in the UK revealed pandemic data as noisy, contaminated, potentially biased, and originating from multiple sources. This seriously challenges the capacity for real-time monitoring. Here we assess the feasibility of real-time inference based on such data by constructing an analytic tool combining an age-stratified SEIR transmission model with various observation models describing the data generation mechanisms. As batches of data become available, a sequential Monte Carlo (SMC) algorithm is developed to synthesise multiple imperfect data streams, iterate epidemic inferences and assess model adequacy amidst a rapidly evolving epidemic environment, substantially reducing computation time in comparison to standard MCMC, to ensure timely delivery of real-time epidemic assessments. In application to simulated data designed to mimic the 2009 A/H1N1 epidemic, SMC is shown to have additional benefits in terms of assessing predictive performance and coping with parameter non-identifiability., Comment: 30 pages, 8 figures

Analysing multiple evidence sources is often feasible only via a modular approach, with separate submodels specified for smaller components of the available evidence. Here we introduce a generic framework that enables fully Bayesian analysis in this setting. We propose a generic method for forming a suitable joint model when joining submodels, and a convenient computational algorithm for fitting this joint model in stages, rather than as a single, monolithic model. The approach also enables splitting of large joint models into smaller submodels, allowing inference for the original joint model to be conducted via our multi-stage algorithm. We motivate and demonstrate our approach through two examples: joining components of an evidence synthesis of A/H1N1 influenza, and splitting a large ecology model.

Knowledge of the severity of an influenza outbreak is crucial for informing and monitoring appropriate public health responses, both during and after an epidemic. However, case-fatality, case-intensive care admission and case-hospitalisation risks are difficult to measure directly. Bayesian evidence synthesis methods have previously been employed to combine fragmented, under-ascertained and biased surveillance data coherently and consistently, to estimate case-severity risks in the first two waves of the 2009 A/H1N1 influenza pandemic experienced in England. We present in detail the complex probabilistic model underlying this evidence synthesis, and extend the analysis to also estimate severity in the third wave of the pandemic strain during the 2010/2011 influenza season. We adapt the model to account for changes in the surveillance data available over the three waves. We consider two approaches: (a) a two-stage approach using posterior distributions from the model for the first two waves to inform priors for the third wave model; and (b) a one-stage approach modelling all three waves simultaneously. Both approaches result in the same key conclusions: (1) that the age-distribution of the case-severity risks is "u"-shaped, with children and older adults having the highest severity; (2) that the age-distribution of the infection attack rate changes over waves, school-age children being most affected in the first two waves and the attack rate in adults over 25 increasing from the second to third waves; and (3) that when averaged over all age groups, case-severity appears to increase over the three waves. The extent to which the final conclusion is driven by the change in age-distribution of those infected over time is subject to discussion., Comment: Published in at http://dx.doi.org/10.1214/14-AOAS775 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Whole genome sequencing of pathogens from multiple hosts in an epidemic offers the potential to investigate who infected whom with unparalleled resolution, potentially yielding important insights into disease dynamics and the impact of control measures. We considered disease outbreaks in a setting with dense genomic sampling, and formulated stochastic epidemic models to investigate person-to-person transmission, based on observed genomic and epidemiological data. We constructed models in which the genetic distance between sampled genotypes depends on the epidemiological relationship between the hosts. A data augmented Markov chain Monte Carlo algorithm was used to sample over the transmission trees, providing a posterior probability for any given transmission route. We investigated the predictive performance of our methodology using simulated data, demonstrating high sensitivity and specificity, particularly for rapidly mutating pathogens with low transmissibility. We then analyzed data collected during an outbreak of methicillin-resistant Staphylococcus aureus in a hospital, identifying probable transmission routes and estimating epidemiological parameters. Our approach overcomes limitations of previous methods, providing a framework with the flexibility to allow for unobserved infection times, multiple independent introductions of the pathogen, and within-host genetic diversity, as well as allowing forward simulation.

Multi-parameter evidence synthesis (MPES) is receiving growing attention from the epidemiological community as a coherent and flexible analytical framework to accommodate a disparate body of evidence available to inform disease incidence and prevalence estimation. MPES is the statistical methodology adopted by the Health Protection Agency in the UK for its annual national assessment of the HIV epidemic, and is acknowledged by the World Health Organization and UNAIDS as a valuable technique for the estimation of adult HIV prevalence from surveillance data. This paper describes the results of utilizing a Bayesian MPES approach to model HIV prevalence in the Netherlands at the end of 2007, using an array of field data from different study designs on various population risk subgroups and with a varying degree of regional coverage. Auxiliary data and expert opinion were additionally incorporated to resolve issues arising from biased, insufficient or inconsistent evidence. This case study offers a demonstration of the ability of MPES to naturally integrate and critically reconcile disparate and heterogeneous sources of evidence, while producing reliable estimates of HIV prevalence used to support public health decision-making., Comment: Published in at http://dx.doi.org/10.1214/11-AOAS488 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)