Statistical modelling of summary values leads to accurate Approximate Bayesian Computations

Approximate Bayesian Computation (ABC) methods rely on asymptotic arguments, implying that parameter inference can be systematically biased even when sufficient statistics are available. We propose to construct the ABC accept/reject step from decision theoretic arguments on a suitable auxiliary space. This framework, referred to as ABC*, fully specifies which test statistics to use, how to combine them, how to set the tolerances and how long to simulate in order to obtain accuracy properties on the auxiliary space. Akin to maximum-likelihood indirect inference, regularity conditions establish when the ABC* approximation to the posterior density is accurate on the original parameter space in terms of the Kullback-Leibler divergence and the maximum a posteriori point estimate. Fundamentally, escaping asymptotic arguments requires knowledge of the distribution of test statistics, which we obtain through modelling the distribution of summary values, data points on a summary level. Synthetic examples and an application to time series data of influenza A (H3N2) infections in the Netherlands illustrate ABC* in action.Comment: Videos can be played with Acrobat Reader. Manuscript under review and not accepte

Assessing optimal target populations for influenza vaccination programmes: an evidence synthesis and modelling study.

BACKGROUND: Influenza vaccine policies that maximise health benefit through efficient use of limited resources are needed. Generally, influenza vaccination programmes have targeted individuals 65 y and over and those at risk, according to World Health Organization recommendations. We developed methods to synthesise the multiplicity of surveillance datasets in order to evaluate how changing target populations in the seasonal vaccination programme would affect infection rate and mortality. METHODS AND FINDINGS: Using a contemporary evidence-synthesis approach, we use virological, clinical, epidemiological, and behavioural data to develop an age- and risk-stratified transmission model that reproduces the strain-specific behaviour of influenza over 14 seasons in England and Wales, having accounted for the vaccination uptake over this period. We estimate the reduction in infections and deaths achieved by the historical programme compared with no vaccination, and the reduction had different policies been in place over the period. We find that the current programme has averted 0.39 (95% credible interval 0.34-0.45) infections per dose of vaccine and 1.74 (1.16-3.02) deaths per 1,000 doses. Targeting transmitters by extending the current programme to 5-16-y-old children would increase the efficiency of the total programme, resulting in an overall reduction of 0.70 (0.52-0.81) infections per dose and 1.95 (1.28-3.39) deaths per 1,000 doses. In comparison, choosing the next group most at risk (50-64-y-olds) would prevent only 0.43 (0.35-0.52) infections per dose and 1.77 (1.15-3.14) deaths per 1,000 doses. CONCLUSIONS: This study proposes a framework to integrate influenza surveillance data into transmission models. Application to data from England and Wales confirms the role of children as key infection spreaders. The most efficient use of vaccine to reduce overall influenza morbidity and mortality is thus to target children in addition to older adults. Please see later in the article for the Editors' Summary

Extending the elderly- and risk-group programme of vaccination against seasonal influenza in England and Wales: a cost-effectiveness study.

BACKGROUND: The present study aims to evaluate the cost-effectiveness of extending the pre-2013 influenza immunisation programme for high-risk and elderly individuals to those at low risk of developing complications following infection with seasonal influenza. METHODS: We performed an economic evaluation comparing different extensions of the pre-2013 influenza programme to seven possible age groups of low-risk individuals (aged 2-4 years, 50-64 years, 5-16 years, 2-4 and 50-64 years, 2-16 years, 2-16 and 50-64 years, and 2-64 years). These extensions are evaluated incrementally on four base scenarios (no vaccination, risk group only with coverage as observed between 1995 and 2009, risk group and 65+, and risk group with 75% coverage and 65+). Impact of vaccination is assessed using a transmission model built and parameterised from a previously published study. The study population is all individuals of all ages in England and Wales representing an average total of 52.6 million people over 14 influenza seasons (1995-2009). RESULTS: The influenza programme (risk group and elderly) prior to 2013 is likely to be cost effective (incremental cost effectiveness ratio: 7,475 £/QALY, net benefit: 253 M£ [15-829]). Extension to any one of the low-risk target groups defined earlier is likely to be cost-effective. However, strategies that do not include vaccination of school-aged children are less likely to be cost-effective. The most efficient strategy is extension to the 5-16 year age group while universal vaccination (extension to all low-risk individuals over 2 years) will achieve the highest net benefit. While extension to the 2-16 year age group is likely to be very cost effective, the cost-effectiveness of extensions beyond 2-16 years is very uncertain. Extension to the 5-16 year age group would likely remain cost-effective even without herd immunity effects to other age groups. As our study includes a strong historical component, our results depend on the efficacy of the influenza vaccine remaining at levels similar to the ones achieved in the past over a long-period of time (assumed to vary between 28% and 70% depending of the circulating strains and age groups). CONCLUSIONS: Making use of surveillance data from over a decade in conjunction with a dynamic model, we find that vaccination of children in the United Kingdom is likely to be highly cost-effective, not only for their own benefit but also to reduce the disease burden in the rest of the community

Real-time forecasting of infectious disease dynamics with a stochastic semi-mechanistic model.

Real-time forecasts of infectious diseases can help public health planning, especially during outbreaks. If forecasts are generated from mechanistic models, they can be further used to target resources or to compare the impact of possible interventions. However, paremeterising such models is often difficult in real time, when information on behavioural changes, interventions and routes of transmission are not readily available. Here, we present a semi-mechanistic model of infectious disease dynamics that was used in real time during the 2013-2016 West African Ebola epidemic, and show fits to a Ebola Forecasting Challenge conducted in late 2015 with simulated data mimicking the true epidemic. We assess the performance of the model in different situations and identify strengths and shortcomings of our approach. Models such as the one presented here which combine the power of mechanistic models with the flexibility to include uncertainty about the precise outbreak dynamics may be an important tool in combating future outbreaks

Assessing the performance of real-time epidemic forecasts: A case study of Ebola in the Western Area Region of Sierra Leone, 2014–15

AbstractReal-time forecasts based on mathematical models can inform critical decision-making during infectious disease outbreaks. Yet, epidemic forecasts are rarely evaluated during or after the event, and there is little guidance on the best metrics for assessment. Here, we propose an evaluation approach that disentangles different components of forecasting ability using metrics that separately assess the calibration, sharpness and unbiasedness of forecasts. This makes it possible to assess not just how close a forecast was to reality but also how well uncertainty has been quantified. We used this approach to analyse the performance of weekly forecasts we generated in real time in Western Area, Sierra Leone, during the 2013–16 Ebola epidemic in West Africa. We investigated a range of forecast model variants based on the model fits generated at the time with a semi-mechanistic model, and found that good probabilistic calibration was achievable at short time horizons of one or two weeks ahead but models were increasingly inaccurate at longer forecasting horizons. This suggests that forecasts may have been of good enough quality to inform decision making requiring predictions a few weeks ahead of time but not longer, reflecting the high level of uncertainty in the processes driving the trajectory of the epidemic. Comparing forecasts based on the semi-mechanistic model to simpler null models showed that the best semi-mechanistic model variant performed better than the null models with respect to probabilistic calibration, and that this would have been identified from the earliest stages of the outbreak. As forecasts become a routine part of the toolkit in public health, standards for evaluation of performance will be important for assessing quality and improving credibility of mathematical models, and for elucidating difficulties and trade-offs when aiming to make the most useful and reliable forecasts.</jats:p

Measuring the impact of Ebola control measures in Sierra Leone.

Between September 2014 and February 2015, the number of Ebola virus disease (EVD) cases reported in Sierra Leone declined in many districts. During this period, a major international response was put in place, with thousands of treatment beds introduced alongside other infection control measures. However, assessing the impact of the response is challenging, as several factors could have influenced the decline in infections, including behavior changes and other community interventions. We developed a mathematical model of EVD transmission, and measured how transmission changed over time in the 12 districts of Sierra Leone with sustained transmission between June 2014 and February 2015. We used the model to estimate how many cases were averted as a result of the introduction of additional treatment beds in each area. Examining epidemic dynamics at the district level, we estimated that 56,600 (95% credible interval: 48,300-84,500) Ebola cases (both reported and unreported) were averted in Sierra Leone up to February 2, 2015 as a direct result of additional treatment beds being introduced. We also found that if beds had been introduced 1 month earlier, a further 12,500 cases could have been averted. Our results suggest the unprecedented local and international response led to a substantial decline in EVD transmission during 2014-2015. In particular, the introduction of beds had a direct impact on reducing EVD cases in Sierra Leone, although the effect varied considerably between districts

Estimating the probability of demonstrating vaccine efficacy in the declining Ebola epidemic: a Bayesian modelling approach.

OBJECTIVES: We investigate the chance of demonstrating Ebola vaccine efficacy in an individually randomised controlled trial implemented in the declining epidemic of Forécariah prefecture, Guinea. METHODS: We extend a previously published dynamic transmission model to include a simulated individually randomised controlled trial of 100,000 participants. Using Bayesian methods, we fit the model to Ebola case incidence before a trial and forecast the expected dynamics until disease elimination. We simulate trials under these forecasts and test potential start dates and rollout schemes to assess power to detect efficacy, and bias in vaccine efficacy estimates that may be introduced. RESULTS: Under realistic assumptions, we found that a trial of 100,000 participants starting after 1 August had less than 5% chance of having enough cases to detect vaccine efficacy. In particular, gradual recruitment precludes detection of vaccine efficacy because the epidemic is likely to go extinct before enough participants are recruited. Exclusion of early cases in either arm of the trial creates bias in vaccine efficacy estimates. CONCLUSIONS: The very low Ebola virus disease incidence in Forécariah prefecture means any individually randomised controlled trial implemented there is unlikely to be successful, unless there is a substantial increase in the number of cases

Duration of Ebola virus RNA persistence in semen of survivors: population-level estimates and projections.

Ebola virus can persist in semen after recovery, potentially for months, which may impact the duration of enhanced surveillance required after interruption of transmission. We combined recent data on viral RNA persistence with weekly disease incidence to estimate the current number of semen-positive men in affected West African countries. We find the number is low, and since few reported sexual transmission events have occurred, the future risk is also likely low, although sexual health promotion remains critical

A dynamic model of transmission and elimination of peste des petits ruminants in Ethiopia

Peste des petits ruminants (PPR), a devastating viral disease of sheep and goats, has been targeted by the global community for eradication within the next 15 years. Although an efficacious attenuated live vaccine is available, the lack of knowledge about the transmission potential of PPR virus (PPRV) may compromise eradication efforts. By fitting a metapopulation model simulating PPRV spread to the results of a nationwide serological survey in Ethiopia, we estimated the level of viral transmission in an endemic setting and the vaccination coverage required for elimination. Results suggest that the pastoral production system as a whole acts as a viral reservoir, from which PPRV spills over into the sedentary production system, where viral persistence is uncertain. Estimated levels of PPRV transmission indicate that viral spread could be prevented if the proportion of immune small ruminants is kept permanently above 37% in at least 71% of pastoral village populations. However, due to the high turnover of these populations, maintaining the fraction of immune animals above this threshold would require high vaccine coverage within villages, and vaccination campaigns to be conducted annually. Adapting vaccination strategies to the specific characteristics of the local epidemiological context and small ruminant population dynamics would result in optimized allocation of limited resources and increase the likelihood of PPR eradication

Aedes aegypti Control Through Modernized, Integrated Vector Management.

INTRODUCTION: In the context of the ongoing, unprecedented Zika virus outbreak in the Americas, the World Health Organization has expressed its support for developing and up-scaling three novel approaches to controlling the Aedes aegypti mosquito: the Sterile Insect Technique (SIT), the Release of Insects carrying Dominant Lethal genes (RIDL) and the release of Wolbachia-infected mosquitoes. Whereas the former two approaches are temporary insect population suppression strategies, Wolbachia infection is a self-sustaining, invasive strategy that uses inherited endosymbiotic bacteria to render natural mosquito populations arbovirus resistant. METHODS: A mathematical model is parameterised with new, Brazilian field data informing the mating competitiveness of mass-reared, released insects; and simulations compare and contrast projections of vector control achieved with the alternative approaches. RESULTS: Important disadvantages of Wolbachia and SIT are identified: both strategies result in mosquitoes ovipositing non-viable eggs and, by alleviating intense larval competition, can cause an overall increase in survival to the adult stage. However, it is demonstrated that strategically combining the suppression methods with Wolbachia can generate a sustained control while mitigating the risks of inadvertent exacerbation of the wild mosquito population. DISCUSSION: This initial analysis demonstrates potential for good synergy when combining novel mosquito approaches in a modernized, integrated vector control programme