77 results found
Lamprinakou S, Barahona M, Flaxman S, et al., 2023, BART-based inference for Poisson processes, Computational Statistics and Data Analysis, Vol: 180, ISSN: 0167-9473
The effectiveness of Bayesian Additive Regression Trees (BART) has been demonstrated in a variety of contexts including non-parametric regression and classification. A BART scheme for estimating the intensity of inhomogeneous Poisson processes is introduced. Poisson intensity estimation is a vital task in various applications including medical imaging, astrophysics and network traffic analysis. The new approach enables full posterior inference of the intensity in a non-parametric regression setting. The performance of the novel scheme is demonstrated through simulation studies on synthetic and real datasets up to five dimensions, and the new scheme is compared with alternative approaches.
Huang KH, Liu X, Duncan AB, et al., 2023, A High-dimensional Convergence Theorem for U-statistics with Applications to Kernel-based Testing
We prove a convergence theorem for U-statistics of degree two, where the datadimension $d$ is allowed to scale with sample size $n$. We find that thelimiting distribution of a U-statistic undergoes a phase transition from thenon-degenerate Gaussian limit to the degenerate limit, regardless of itsdegeneracy and depending only on a moment ratio. A surprising consequence isthat a non-degenerate U-statistic in high dimensions can have a non-Gaussianlimit with a larger variance and asymmetric distribution. Our bounds are validfor any finite $n$ and $d$, independent of individual eigenvalues of theunderlying function, and dimension-independent under a mild assumption. As anapplication, we apply our theory to two popular kernel-based distributiontests, MMD and KSD, whose high-dimensional performance has been challenging tostudy. In a simple empirical setting, our results correctly predict how thetest power at a fixed threshold scales with $d$ and the bandwidth.
Hilbers AP, Brayshaw DJ, Gandy A, 2023, Reducing climate risk in energy system planning: A posteriori time series aggregation for models with storage, APPLIED ENERGY, Vol: 334, ISSN: 0306-2619
Lamprinakou S, Gandy A, McCoy E, 2023, Using a latent Hawkes process for epidemiological modelling., PLoS One, Vol: 18
Understanding the spread of COVID-19 has been the subject of numerous studies, highlighting the significance of reliable epidemic models. Here, we introduce a novel epidemic model using a latent Hawkes process with temporal covariates for modelling the infections. Unlike other models, we model the reported cases via a probability distribution driven by the underlying Hawkes process. Modelling the infections via a Hawkes process allows us to estimate by whom an infected individual was infected. We propose a Kernel Density Particle Filter (KDPF) for inference of both latent cases and reproduction number and for predicting the new cases in the near future. The computational effort is proportional to the number of infections making it possible to use particle filter type algorithms, such as the KDPF. We demonstrate the performance of the proposed algorithm on synthetic data sets and COVID-19 reported cases in various local authorities in the UK, and benchmark our model to alternative approaches.
Gandy A, Jana K, Veraart A, 2022, Scoring predictions at extreme quantiles, AStA Advances in Statistical Analysis, Vol: 106, Pages: 527-544, ISSN: 0002-6018
Prediction of quantiles at extreme tails is of interest in numerousapplications. Extreme value modelling provides various competing predictorsfor this point prediction problem. A common method of assessment of a setof competing predictors is to evaluate their predictive performance in a givensituation. However, due to the extreme nature of this inference problem, it canbe possible that the predicted quantiles are not seen in the historical records,particularly when the sample size is small. This situation poses a problem tothe validation of the prediction with its realisation. In this article, we proposetwo non-parametric scoring approaches to assess extreme quantile predictionmechanisms. The proposed assessment methods are based on predicting a sequence of equally extreme quantiles on different parts of the data. We thenuse the quantile scoring function to evaluate the competing predictors. Theperformance of the scoring methods is compared with the conventional scoring method and the superiority of the former methods are demonstrated in asimulation study. The methods are then applied to reanalyse cyber Netflowdata from Los Alamos National Laboratory and daily precipitation data at astation in California available from Global Historical Climatology Network.
Lamprinakou S, Gandy A, McCoy E, 2022, Can a latent Hawkes process be used for epidemiological modelling?
Understanding the spread of COVID-19 has been the subject of numerousstudies, highlighting the significance of reliable epidemic models. Here, weintroduce a novel epidemic model using a latent Hawkes process with temporalcovariates for modelling the infections. Unlike other models, we model thereported cases via a probability distribution driven by the underlying Hawkesprocess. Modelling the infections via a Hawkes process allows us to estimate bywhom an infected individual was infected. We propose a Kernel Density ParticleFilter (KDPF) for inference of both latent cases and reproduction number andfor predicting the new cases in the near future. The computational effort isproportional to the number of infections making it possible to use particlefilter type algorithms, such as the KDPF. We demonstrate the performance of theproposed algorithm on synthetic data sets and COVID-19 reported cases invarious local authorities in the UK, and benchmark our model to alternativeapproaches.
Gandy A, Matcham TJ, 2022, On concordance indices for models with time-varying risk
Harrel's concordance index is a commonly used discrimination metric forsurvival models, particularly for models where the relative ordering of therisk of individuals is time-independent, such as the proportional hazardsmodel. There are several suggestions, but no consensus, on how it could beextended to models where risk varies over time, e.g.\ in case of crossinghazard rates. We show that, in the limit, concordance is maximized if and onlyif the risk score is concordant with the hazard rate, in the sense that for acomparable pair where the first event time is observed, the risk score isconcordant with the hazard rate at this first event time. Thus, we suggestusing the hazard rate as the risk score when calculating concordance. Throughsimulations, we demonstrate situations in which other concordance indices canlead to incorrect models being selected over a true model, justifying the useof our suggested risk prediction in both model selection and in loss functionsin, e.g., machine learning models.
Faria NR, Mellan TA, Whittaker C, et al., 2021, Genomics and epidemiology of the P.1 SARS-CoV-2 lineage in Manaus, Brazil, Science, Vol: 372, Pages: 815-821, ISSN: 0036-8075
Cases of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection in Manaus, Brazil, resurged in late 2020 despite previously high levels of infection. Genome sequencing of viruses sampled in Manaus between November 2020 and January 2021 revealed the emergence and circulation of a novel SARS-CoV-2 variant of concern. Lineage P.1 acquired 17 mutations, including a trio in the spike protein (K417T, E484K, and N501Y) associated with increased binding to the human ACE2 (angiotensin-converting enzyme 2) receptor. Molecular clock analysis shows that P.1 emergence occurred around mid-November 2020 and was preceded by a period of faster molecular evolution. Using a two-category dynamical model that integrates genomic and mortality data, we estimate that P.1 may be 1.7- to 2.4-fold more transmissible and that previous (non-P.1) infection provides 54 to 79% of the protection against infection with P.1 that it provides against non-P.1 lineages. Enhanced global genomic surveillance of variants of concern, which may exhibit increased transmissibility and/or immune evasion, is critical to accelerate pandemic responsiveness.
Volz E, Mishra S, Chand M, et al., 2021, Assessing transmissibility of SARS-CoV-2 lineage B.1.1.7 in England, Nature, Vol: 593, Pages: 266-269, ISSN: 0028-0836
The SARS-CoV-2 lineage B.1.1.7, designated a Variant of Concern 202012/01 (VOC) by Public Health England1, originated in the UK in late Summer to early Autumn 20202. Whole genome SARS-CoV-2 sequence data collected from community-based diagnostic testing shows an unprecedentedly rapid expansion of the B.1.1.7 lineage during Autumn 2020, suggesting a selective advantage. We find that changes in VOC frequency inferred from genetic data correspond closely to changes inferred by S-gene target failures (SGTF) in community-based diagnostic PCR testing. Analysis of trends in SGTF and non-SGTF case numbers in local areas across England shows that the VOC has higher transmissibility than non-VOC lineages, even if the VOC has a different latent period or generation time. The SGTF data indicate a transient shift in the age composition of reported cases, with a larger share of under 20 year olds among reported VOC than non-VOC cases. Time-varying reproduction numbers for the VOC and cocirculating lineages were estimated using SGTF and genomic data. The best supported models did not indicate a substantial difference in VOC transmissibility among different age groups. There is a consensus among all analyses that the VOC has a substantial transmission advantage with a 50% to 100% higher reproduction number.
Hilbers AP, Brayshaw DJ, Gandy A, 2021, Efficient quantification of the impact of demand and weather uncertainty in power system models, IEEE Transactions on Power Systems, Vol: 36, Pages: 1771-1779, ISSN: 0885-8950
This paper introduces a novel approach to quantify the effect of forwardpropagated demand and weather uncertainty on power system planning andoperation model outputs. Recent studies indicate that such samplinguncertainty, originating from demand and weather time series inputs, should notbe ignored. However, established uncertainty quantification approaches fail inthis context due to the computational resources and additional data requiredfor Monte Carlo-based analysis. The method introduced here quantifiesuncertainty on model outputs using a bootstrap scheme with shorter time seriesthan the original, enhancing computational efficiency and avoiding the need forany additional data. It both quantifies output uncertainty and determines thesample length required for desired confidence levels. Simulations performed ontwo generation and transmission expansion planning models and one unitcommitment and economic dispatch model illustrate the method's efficacy. A testis introduced allowing users to determine whether estimated uncertainty boundsare valid. The models, data and code applying the method are provided asopen-source software.
Laydon D, Mishra S, Hinsley W, et al., 2021, Modelling the impact of the Tier system on SARS-CoV-2 transmission in the UK between the first and second national lockdowns, BMJ Open, Vol: 11, ISSN: 2044-6055
Objective To measure the effects of the tier system on the COVID-19 pandemic in the UK between the first and second national lockdowns, before the emergence of the B.1.1.7 variant of concern.Design This is a modelling study combining estimates of real-time reproduction number Rt (derived from UK case, death and serological survey data) with publicly available data on regional non-pharmaceutical interventions. We fit a Bayesian hierarchical model with latent factors using these quantities to account for broader national trends in addition to subnational effects from tiers.Setting The UK at lower tier local authority (LTLA) level. 310 LTLAs were included in the analysis.Primary and secondary outcome measures Reduction in real-time reproduction number Rt.Results Nationally, transmission increased between July and late September, regional differences notwithstanding. Immediately prior to the introduction of the tier system, Rt averaged 1.3 (0.9–1.6) across LTLAs, but declined to an average of 1.1 (0.86–1.42) 2 weeks later. Decline in transmission was not solely attributable to tiers. Tier 1 had negligible effects. Tiers 2 and 3, respectively, reduced transmission by 6% (5%–7%) and 23% (21%–25%). 288 LTLAs (93%) would have begun to suppress their epidemics if every LTLA had gone into tier 3 by the second national lockdown, whereas only 90 (29%) did so in reality.Conclusions The relatively small effect sizes found in this analysis demonstrate that interventions at least as stringent as tier 3 are required to suppress transmission, especially considering more transmissible variants, at least until effective vaccination is widespread or much greater population immunity has amassed.
Flaxman S, Mishra S, Scott J, et al., 2020, The effect of interventions on COVID-19 Reply, NATURE, Vol: 588, Pages: E29-E32, ISSN: 0028-0836
- Author Web Link
- Citations: 3
Unwin H, Mishra S, Bradley V, et al., 2020, State-level tracking of COVID-19 in the United States, Nature Communications, Vol: 11, Pages: 1-9, ISSN: 2041-1723
As of 1st June 2020, the US Centers for Disease Control and Prevention reported 104,232 confirmed or probable COVID-19-related deaths in the US. This was more than twice the number of deaths reported in the next most severely impacted country. We jointly model the US epidemic at the state-level, using publicly available deathdata within a Bayesian hierarchical semi-mechanistic framework. For each state, we estimate the number of individuals that have been infected, the number of individuals that are currently infectious and the time-varying reproduction number (the average number of secondary infections caused by an infected person). We use changes in mobility to capture the impact that non-pharmaceutical interventions and other behaviour changes have on therate of transmission of SARS-CoV-2. We estimate thatRtwas only below one in 23 states on 1st June. We also estimate that 3.7% [3.4%-4.0%] of the total population of the US had been infected, with wide variation between states, and approximately 0.01% of the population was infectious. We demonstrate good 3 week model forecasts of deaths with low error and good coverage of our credible intervals.
Mishra S, Scott J, Zhu H, et al., 2020, A COVID-19 Model for Local Authorities of the United Kingdom
<jats:title>Abstract</jats:title><jats:p>We propose a new framework to model the COVID-19 epidemic of the United Kingdom at the level of local authorities. The model fits within a general framework for semi-mechanistic Bayesian models of the epidemic, with some important innovations: we model the proportion of infections that result in reported deaths and cases as random variables. This is in contrast to standard frameworks that model the latent infection as a deterministic function of time varying reproduction number, <jats:italic>R</jats:italic><jats:sub><jats:italic>t</jats:italic></jats:sub>. The model is tailored and designed to be updated daily based on 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, <jats:ext-link xmlns:xlink="http://www.w3.org/1999/xlink" ext-link-type="uri" xlink:href="https://imperialcollegelondon.github.io/covid19local">https://imperialcollegelondon.github.io/covid19local</jats:ext-link>. The model is currently being used by the Scottish government in their decisions on interventions within Scotland [1, issue 24 to now].</jats:p>
Okell LC, Verity R, Katzourakis A, et al., 2020, Host or pathogen-related factors in COVID-19 severity? Reply, LANCET, Vol: 396, Pages: 1397-1397, ISSN: 0140-6736
- Author Web Link
- Citations: 2
Monod M, Blenkinsop A, Xi X, et al., 2020, Report 32: Age groups that sustain resurging COVID-19 epidemics in the United States
<jats:title>Summary</jats:title><jats:p>Following initial declines, in mid 2020, a resurgence in transmission of novel coronavirus disease (COVID-19) has occurred in the United States and parts of Europe. Despite the wide implementation of non-pharmaceutical interventions, it is still not known how they are impacted by changing contact patterns, age and other demographics. As COVID-19 disease control becomes more localised, understanding the age demographics driving transmission and how these impacts the loosening of interventions such as school reopening is crucial. Considering dynamics for the United States, we analyse aggregated, age-specific mobility trends from more than 10 million individuals and link these mechanistically to age-specific COVID-19 mortality data. In contrast to previous approaches, we link mobility to mortality via age specific contact patterns and use this rich relationship to reconstruct accurate transmission dynamics. Contrary to anecdotal evidence, we find little support for age-shifts in contact and transmission dynamics over time. We estimate that, until August, 63.4% [60.9%-65.5%] of SARS-CoV-2 infections in the United States originated from adults aged 20-49, while 1.2% [0.8%-1.8%] originated from children aged 0-9. In areas with continued, community-wide transmission, our transmission model predicts that re-opening kindergartens and elementary schools could facilitate spread and lead to additional COVID-19 attributable deaths over a 90-day period. These findings indicate that targeting interventions to adults aged 20-49 are an important consideration in halting resurgent epidemics and preventing COVID-19-attributable deaths when kindergartens and elementary schools reopen.</jats:p><jats:sec><jats:title>One sentence summary</jats:title><jats:p>Adults aged 20-49 are a main driver of the COVID-19 epidemic in the United States; yet, in areas with resurging epidemics, opening schools will lea
Monod M, Blenkinsop A, Xi X, et al., 2020, Report 32: Targeting interventions to age groups that sustain COVID-19 transmission in the United States, Pages: 1-32
Following inial declines, in mid 2020, a resurgence in transmission of novel coronavirus disease (COVID-19) has occurred in the United States and parts of Europe. Despite the wide implementaon of non-pharmaceucal inter-venons, it is sll not known how they are impacted by changing contact paerns, age and other demographics. As COVID-19 disease control becomes more localised, understanding the age demographics driving transmission and how these impact the loosening of intervenons such as school reopening is crucial. Considering dynamics for the United States, we analyse aggregated, age-speciﬁc mobility trends from more than 10 million individuals and link these mechaniscally to age-speciﬁc COVID-19 mortality data. In contrast to previous approaches, we link mobility to mortality via age speciﬁc contact paerns and use this rich relaonship to reconstruct accurate trans-mission dynamics. Contrary to anecdotal evidence, we ﬁnd lile support for age-shis in contact and transmission dynamics over me. We esmate that, unl August, 63.4% [60.9%-65.5%] of SARS-CoV-2 infecons in the United States originated from adults aged 20-49, while 1.2% [0.8%-1.8%] originated from children aged 0-9. In areas with connued, community-wide transmission, our transmission model predicts that re-opening kindergartens and el-ementary schools could facilitate spread and lead to considerable excess COVID-19 aributable deaths over a 90-day period. These ﬁndings indicate that targeng intervenons to adults aged 20-49 are an important con-sideraon in halng resurgent epidemics, and prevenng COVID-19-aributable deaths when kindergartens and elementary schools reopen.
Hilbers A, Brayshaw D, Gandy A, 2020, Importance subsampling for power system planning under multi-year demand and weather uncertainty, PMAPS 2020 (the 16th International Conference on Probabilistic Methods Applied to Power Systems), Publisher: IEEE, Pages: 1-6
This paper introduces a generalised version ofimportance subsamplingfor time series reduction/aggregation inoptimisation-based power system planning models. Recent studiesindicate that reliably determining optimal electricity (investment)strategy under climate variability requires the consideration ofmultiple years of demand and weather data. However, solvingplanning models over long simulation lengths is typically com-putationally unfeasible, and established time series reductionapproaches induce significant errors. Theimportance subsamplingmethod reliably estimates long-term planning model outputs atgreatly reduced computational cost, allowing the considerationof multi-decadal samples. The key innovation is a systematicidentification and preservation of relevant extreme events inmodeling subsamples. Simulation studies on generation andtransmission expansion planning models illustrate the method’senhanced performance over established “representative days”clustering approaches. The models, data and sample code aremade available as open-source software.
Ding D, Gandy A, Hahn G, 2020, A simple method for implementing Monte Carlo tests, Computational Statistics, Vol: 35, Pages: 1373-1392, ISSN: 0943-4062
We consider a statistical test whose p value can only be approximated using Monte Carlo simulations. We are interested in deciding whether the p value for an observed data set lies above or below a given threshold such as 5%. We want to ensure that the resampling risk, the probability of the (Monte Carlo) decision being different from the true decision, is uniformly bounded. This article introduces a simple open-ended method with this property, the confidence sequence method (CSM). We compare our approach to another algorithm, SIMCTEST, which also guarantees an (asymptotic) uniform bound on the resampling risk, as well as to other Monte Carlo procedures without a uniform bound. CSM is free of tuning parameters and conservative. It has the same theoretical guarantee as SIMCTEST and, in many settings, similar stopping boundaries. As it is much simpler than other methods, CSM is a useful method for practical applications.
Flaxman S, Mishra S, Gandy A, et al., 2020, Estimating the effects of non-pharmaceutical interventions on COVID-19 in Europe, Nature, Vol: 584, Pages: 257-261, ISSN: 0028-0836
Following the emergence of a novel coronavirus1 (SARS-CoV-2) and its spread outside of China, Europe has experienced large epidemics. In response, many European countries have implemented unprecedented non-pharmaceutical interventions such as closure of schools and national lockdowns. We study the impact of major interventions across 11 European countries for the period from the start of COVID-19 until the 4th of May 2020 when lockdowns started to be lifted. Our model calculates backwards from observed deaths to estimate transmission that occurred several weeks prior, allowing for the time lag between infection and death. We use partial pooling of information between countries with both individual and shared effects on the reproduction number. Pooling allows more information to be used, helps overcome data idiosyncrasies, and enables more timely estimates. Our model relies on fixed estimates of some epidemiological parameters such as the infection fatality rate, does not include importation or subnational variation and assumes that changes in the reproduction number are an immediate response to interventions rather than gradual changes in behavior. Amidst the ongoing pandemic, we rely on death data that is incomplete, with systematic biases in reporting, and subject to future consolidation. We estimate that, for all the countries we consider, current interventions have been sufficient to drive the reproduction number Rt below 1 (probability Rt< 1.0 is 99.9%) and achieve epidemic control. We estimate that, across all 11 countries, between 12 and 15 million individuals have been infected with SARS-CoV-2 up to 4th May, representing between 3.2% and 4.0% of the population. Our results show that major non-pharmaceutical interventions and lockdown in particular have had a large effect on reducing transmission. Continued intervention should be considered to keep transmission of SARS-CoV-2 under control.
Mishra S, Berah T, Mellan TA, et al., 2020, On the derivation of the renewal equation from an age-dependent branching process: an epidemic modelling perspective
Renewal processes are a popular approach used in modelling infectious diseaseoutbreaks. In a renewal process, previous infections give rise to futureinfections. However, while this formulation seems sensible, its application toinfectious disease can be difficult to justify from first principles. It hasbeen shown from the seminal work of Bellman and Harris that the renewalequation arises as the expectation of an age-dependent branching process. Inthis paper we provide a detailed derivation of the original Bellman Harrisprocess. We introduce generalisations, that allow for time-varying reproductionnumbers and the accounting of exogenous events, such as importations. We showhow inference on the renewal equation is easy to accomplish within a Bayesianhierarchical framework. Using off the shelf MCMC packages, we fit to SouthKorea COVID-19 case data to estimate reproduction numbers and importations. Ourderivation provides the mathematical fundamentals and assumptions underpinningthe use of the renewal equation for modelling outbreaks.
Okell LC, Verity R, Watson OJ, et al., 2020, Have deaths from COVID-19 in Europe plateaued due to herd immunity?, LANCET, Vol: 395, Pages: E110-E111, ISSN: 0140-6736
- Author Web Link
- Citations: 39
Gandy A, Veraart LAM, 2020, Compound poisson models for weighted networks with applications in finance, Mathematics and Financial Economics, Vol: 15, Pages: 131-153, ISSN: 1862-9660
We develop a modelling framework for estimating and predicting weighted network data. Theedge weights in weighted networks often arise from aggregating some individual relationships between the nodes. Motivated by this, we introduce a modelling framework for weighted networksbased on the compound Poisson distribution. To allow for heterogeneity between the nodes, weuse a regression approach for the model parameters. We test the new modelling framework on twotypes of financial networks: a network of financial institutions in which the edge weights representexposures from trading Credit Default Swaps and a network of countries in which the edge weightsrepresent cross-border lending. The compound Poisson Gamma distributions with regression fit thedata well in both situations. We illustrate how this modelling framework can be used for predictingunobserved edges and their weights in an only partially observed network. This is for examplerelevant for assessing systemic risk in financial networks.
Scott J, Gandy A, 2020, State-dependent Kernel selection for conditional sampling of graphs, Journal of Computational and Graphical Statistics, Vol: 29, Pages: 847-858, ISSN: 1061-8600
This article introduces new efficient algorithms for two problems: sampling conditional on vertex degrees in unweighted graphs, and conditional on vertex strengths in weighted graphs. The resulting conditional distributions provide the basis for exact tests on social networks and two-way contingency tables. The algorithms are able to sample conditional on the presence or absence of an arbitrary set of edges. Existing samplers based on MCMC or sequential importance sampling are generally not scalable; their efficiency can degrade in large graphs with complex patterns of known edges. MCMC methods usually require explicit computation of a Markov basis to navigate the state space; this is computationally intensive even for small graphs. Our samplers do not require a Markov basis, and are efficient both in sparse and dense settings. The key idea is to carefully select a Markov kernel on the basis of the current state of the chain. We demonstrate the utility of our methods on a real network and contingency table. Supplementary materials for this article are available online.
Mellan T, Hoeltgebaum H, Mishra S, et al., 2020, Report 21: Estimating COVID-19 cases and reproduction number in Brazil
Brazil is an epicentre for COVID-19 in Latin America. In this report we describe the Brazilian epidemicusing three epidemiological measures: the number of infections, the number of deaths and the reproduction number. Our modelling framework requires sufficient death data to estimate trends, and wetherefore limit our analysis to 16 states that have experienced a total of more than fifty deaths. Thedistribution of deaths among states is highly heterogeneous, with 5 states—São Paulo, Rio de Janeiro,Ceará, Pernambuco and Amazonas—accounting for 81% of deaths reported to date. In these states, weestimate that the percentage of people that have been infected with SARS-CoV-2 ranges from 3.3% (95%CI: 2.8%-3.7%) in São Paulo to 10.6% (95% CI: 8.8%-12.1%) in Amazonas. The reproduction number (ameasure of transmission intensity) at the start of the epidemic meant that an infected individual wouldinfect three or four others on average. Following non-pharmaceutical interventions such as school closures and decreases in population mobility, we show that the reproduction number has dropped substantially in each state. However, for all 16 states we study, we estimate with high confidence that thereproduction number remains above 1. A reproduction number above 1 means that the epidemic isnot yet controlled and will continue to grow. These trends are in stark contrast to other major COVID19 epidemics in Europe and Asia where enforced lockdowns have successfully driven the reproductionnumber below 1. While the Brazilian epidemic is still relatively nascent on a national scale, our resultssuggest that further action is needed to limit spread and prevent health system overload.
Vollmer M, Mishra S, Unwin H, et al., 2020, Report 20: A sub-national analysis of the rate of transmission of Covid-19 in Italy
Italy was the first European country to experience sustained local transmission of COVID-19. As of 1st May 2020, the Italian health authorities reported 28; 238 deaths nationally. To control the epidemic, the Italian government implemented a suite of non-pharmaceutical interventions (NPIs), including school and university closures, social distancing and full lockdown involving banning of public gatherings and non essential movement. In this report, we model the effect of NPIs on transmission using data on average mobility. We estimate that the average reproduction number (a measure of transmission intensity) is currently below one for all Italian regions, and significantly so for the majority of the regions. Despite the large number of deaths, the proportion of population that has been infected by SARS-CoV-2 (the attack rate) is far from the herd immunity threshold in all Italian regions, with the highest attack rate observed in Lombardy (13.18% [10.66%-16.70%]). Italy is set to relax the currently implemented NPIs from 4th May 2020. Given the control achieved by NPIs, we consider three scenarios for the next 8 weeks: a scenario in which mobility remains the same as during the lockdown, a scenario in which mobility returns to pre-lockdown levels by 20%, and a scenario in which mobility returns to pre-lockdown levels by 40%. The scenarios explored assume that mobility is scaled evenly across all dimensions, that behaviour stays the same as before NPIs were implemented, that no pharmaceutical interventions are introduced, and it does not include transmission reduction from contact tracing, testing and the isolation of confirmed or suspected cases. We find that, in the absence of additional interventions, even a 20% return to pre-lockdown mobility could lead to a resurgence in the number of deaths far greater than experienced in the current wave in several regions. Future increases in the number of deaths will lag behind the increase in transmission intensity and so a
Flaxman S, Mishra S, Gandy A, et al., 2020, Estimating the number of infections and the impact of non-pharmaceutical interventions on COVID-19 in European countries: technical description update
Following the emergence of a novel coronavirus (SARS-CoV-2) and its spreadoutside of China, Europe has experienced large epidemics. In response, manyEuropean countries have implemented unprecedented non-pharmaceuticalinterventions including case isolation, the closure of schools anduniversities, banning of mass gatherings and/or public events, and mostrecently, wide-scale social distancing including local and national lockdowns. In this technical update, we extend a semi-mechanistic Bayesian hierarchicalmodel that infers the impact of these interventions and estimates the number ofinfections over time. Our methods assume that changes in the reproductivenumber - a measure of transmission - are an immediate response to theseinterventions being implemented rather than broader gradual changes inbehaviour. Our model estimates these changes by calculating backwards fromtemporal data on observed to estimate the number of infections and rate oftransmission that occurred several weeks prior, allowing for a probabilistictime lag between infection and death. In this update we extend our original model [Flaxman, Mishra, Gandy et al2020, Report #13, Imperial College London] to include (a) population saturationeffects, (b) prior uncertainty on the infection fatality ratio, (c) a morebalanced prior on intervention effects and (d) partial pooling of the lockdownintervention covariate. We also (e) included another 3 countries (Greece, theNetherlands and Portugal). The model code is available athttps://github.com/ImperialCollegeLondon/covid19model/ We are now reporting the results of our updated model online athttps://mrc-ide.github.io/covid19estimates/ We estimated parameters jointly for all M=14 countries in a singlehierarchical model. Inference is performed in the probabilistic programminglanguage Stan using an adaptive Hamiltonian Monte Carlo (HMC) sampler.
Gandy A, Scott J, 2020, Unit Testing for MCMC and other Monte Carlo Methods
We propose approaches for testing implementations of Markov Chain Monte Carlomethods as well as of general Monte Carlo methods. Based on statisticalhypothesis tests, these approaches can be used in a unit testing framework to,for example, check if individual steps in a Gibbs sampler or a reversible jumpMCMC have the desired invariant distribution. Two exact tests for assessingwhether a given Markov chain has a specified invariant distribution arediscussed. These and other tests of Monte Carlo methods can be embedded into asequential method that allows low expected effort if the simulation shows thedesired behavior and high power if it does not. Moreover, the false rejectionprobability can be kept arbitrarily low. For general Monte Carlo methods, thisallows testing, for example, if a sampler has a specified distribution or if asampler produces samples with the desired mean. The methods have beenimplemented in the R-package MCUnit.
Hawryluk I, Mellan TA, Hoeltgebaum H, et al., 2020, Inference of COVID-19 epidemiological distributions from Brazilian hospital data, Journal of The Royal Society Interface, Vol: 17, Pages: 20200596-20200596, ISSN: 1742-5662
Knowing COVID-19 epidemiological distributions, such as the time from patient admission to death, is directly relevant to effective primary and secondary care planning, and moreover, the mathematical modelling of the pandemic generally. We determine epidemiological distributions for patients hospitalized with COVID-19 using a large dataset (N = 21 000 − 157 000) from the Brazilian Sistema de Informação de Vigilância Epidemiológica da Gripe database. A joint Bayesian subnational model with partial pooling is used to simultaneously describe the 26 states and one federal district of Brazil, and shows significant variation in the mean of the symptom-onset-to-death time, with ranges between 11.2 and 17.8 days across the different states, and a mean of 15.2 days for Brazil. We find strong evidence in favour of specific probability density function choices: for example, the gamma distribution gives the best fit for onset-to-death and the generalized lognormal for onset-to-hospital-admission. Our results show that epidemiological distributions have considerable geographical variation, and provide the first estimates of these distributions in a low and middle-income setting. At the subnational level, variation in COVID-19 outcome timings are found to be correlated with poverty, deprivation and segregation levels, and weaker correlation is observed for mean age, wealth and urbanicity.
Gandy A, Hahn G, Ding D, 2019, Implementing Monte Carlo tests with p-value buckets, SCANDINAVIAN JOURNAL OF STATISTICS, Vol: 47, Pages: 950-967, ISSN: 0303-6898
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