Exploiting routinely collected severe case data to monitor and predict influenza outbreaks
Alice Corbella, Xu-Sheng Zhang, Paul J. Birrell, Nicky Boddington, Anne M. Presanis, Richard G. Pebody, Daniela De Angelis
EExploiting routinely collected severe case data to monitorand predict influenza outbreaks
A. Corbella †§ , X.-S. Zhang , P. J. Birrell , N. Boddington , A. M. Presanis ,R. G. Pebody , and D. De Angelis Medical Research Council, Biostatistics Unit - University of Cambridge, School of ClinicalMedicine Centre for Infectious Disease Surveillance and Control, Public Health England † Author for correspondence: [email protected] § Equal contributor
November 15, 2017
AbstractBackground
Influenza remains a significant burden on health systems. Effectiveresponses rely on the timely understanding of the magnitude and the evolution of anoutbreak. For monitoring purposes, data on severe cases of influenza in England arereported weekly to Public Health England. These data are both readily available andhave the potential to provide valuable information to estimate and predict the keytransmission features of seasonal and pandemic influenza.
Methods
We propose an epidemic model that links the underlying unobservedinfluenza transmission process to data on severe influenza cases. Within a Bayesianframework, we infer retrospectively the parameters of the epidemic model for eachseasonal outbreak from 2012 to 2015, including: the effective reproduction number; theinitial susceptibility; the probability of admission to intensive care given infection; andthe effect of school closure on transmission. The model is also implemented in realtime to assess whether early forecasting of the number of admission to intensive careis possible.
Results
Our model of admissions data allows reconstruction of the underlyingtransmission dynamics revealing: increased transmission during the season 2013/14and a noticeable effect of Christmas school holiday on disease spread during season2012/13 and 2014/15. When information on the initial immunity of the population isavailable, forecasts of the number of admissions to intensive care can be substantiallyimproved.
Conclusion
Readily available severe case data can be effectively used to estimateepidemiological characteristics and to predict the evolution of an epidemic, cruciallyallowing real-time monitoring of the transmission and severity of the outbreak.
Keywords
Epidemic monitoring, Bayesian inference, Epidemic models, Influenza,Reproduction number, Severe cases.
Background
Recent annual epidemics of influenza have resulted in about 3 to 5 million cases of severeillness each season worldwide [1]. Historically, influenza has always placed a large burden onmany national health systems [2], particularly as a result of severe cases in the most at riskgroups [3] (e.g. elderly [4], children and people with underlying chronic medical conditions[5], persons living in deprived areas[6], etc. ).Measures of different characteristics of an outbreak, whether from seasonal or a newlyemergent strain, are crucial to understand the healthcare burden and plan appropriate re-1 a r X i v : . [ s t a t . A P ] N ov ponse measures. For seasonal influenza, retrospective knowledge of severity and transmis-sibility provides a much valuable baseline measure against which to compare the severityand transmissibility of future pandemics. Prospectively, predictions of the likely extent oftransmission and the resulting number of severe cases are crucial to anticipate demandson health care facilities (e.g. number of beds in hospital) for each season. These timelypredictions are even more crucial to inform prompt targeted response in the event of a newemerging strain with the potential to cause a pandemic [7].Epidemic models are increasingly used to understand the effect of particular interventionsincluding: vaccination policies [8]; school closures to reduce transmission in a pandemic[9, 10, 11]; reinforced use of antiviral drugs [12]; or changes in hospital management policies.These models are generally applied to data, such as General Practitioner (GP) consul-tations for influenza-like illness (ILI) [13, 8] or health-related online queries [14] which areonly loosely related to the actual burden and are characterized by highly volatile noise.By contrast, more specific timely data on a sample of confirmed cases (e.g. confirmedinfluenza hospitalizations) might be collected routinely by national health systems. Anexample of these data is the UK Severe Influenza Surveillance System (USISS) [15] thatrecords counts of the weekly Intensive Care Unit (ICU) and High Dependence Unit (HDU)admissions and deaths with confirmed influenza in all hospital trusts in England.Only recently, and in the context of a pandemic, has some attention been paid to esti-mating and predicting pandemic transmission from routinely collected confirmed-case data[16]. This has entailed the development of a very complicated model which is difficult touse in a seasonal monitoring setting (when less effort is placed on data collection) with aprediction goal. Here we explore a much simpler model to be applied to seasonal influenza,and possibly during a pandemic, relying only on simpler data on severe cases alone, whichare timely available. We therefore investigate if data collected through USISS can charac-terise both seasonal and pandemic epidemics, aiming to achieve both the estimation and theprediction goal.We formulate an epidemic model that links the available USISS data to the underlyingunobserved dynamics of influenza in the UK. The model parameters are inferred using datafrom the seasonal epidemics in 2012-2015, to obtain nation-level estimates of transmission, asmeasured by R n , the average number of new cases generated by an infectious individual in apartially immune population, and severity, as measured by the probability of ICU admissiongiven infection.Additionally, to assess the predictive power of the model, we perform analyses at differentdates within each season. Finally, we study what would happen in the event of a pandemic,when the USISS surveillance scheme would be upgraded to collect more information. Methods
Data
Following the 2009 pandemic, the World Health Organization (WHO) declared the beginningof a post-pandemic phase [17], encouraging national public health agencies to establishhospital-based surveillance systems to monitor the epidemiology of severe influenza. Inresponse to these guidelines, and to understand the baseline epidemiology of severe influenza,the UK developed a surveillance system to monitor severe cases of influenza, the USISS [18,19]. After a pilot phase in 2010/11, USISS has run for each influenza season, providing dataon laboratory-confirmed ICU/HDU influenza cases and on laboratory-confirmed hospitalizedcases.According to the USISS protocol [18], all National Health Service (NHS) trusts reportthe weekly number of laboratory-confirmed influenza cases admitted to ICU/HDU and thenumber of confirmed influenza deaths in ICU/HDU via a web tool. An ICU/HDU case isdefined as a person who is admitted to ICU/HDU and has a laboratory-confirmed influenzaA (including H1, H3 or novel) or B infection.USISS runs annually from week 40 to week 20 of the following year but, in the event of apandemic, it can be activated out of this window and will collect the same data at all levels2f care, not only ICU/HDU.Data are broken down by age group and influenza type/subtype. Total ICU/HDU admis-sions between 2012 and 2015 are shown in Figure 1, varying substantially across seasons. Inthe 2012/13 season, mainly characterized by Influenza B and Influenza A(H3N2) outbreaks,the number of admissions peaks early, maintaining this plateau for several months [20]. In2013/14, when the predominant strain was A(H1N1), the time series displays a smootherincrease, a well localized peak and a subsequent regular decrease [21]. Lastly, in 2014/15,the number of ICU admissions peaks earlier and has a dramatic drop at the beginning of thenew year, which is followed by a smaller wave resulting in a time series characterized by adouble peak. During this season, Influenza A(H3N2) was the predominant virus circulatingand the total number of ICU admissions was higher; this strain is well-known to lead tomore severe outcomes, particularly in the elderly [22].
Season 2012/13 weeks ad m i ss i on s
40 45 50 3 8 13 182012 2013
Season 2013/14 weeks
40 45 50 3 8 13 182013 2014
Season 2014/15 weeks
40 45 50 3 8 13 182014 2015
Figure 1:
Weekly ICU/HDU admissions by season.
Time is measured in weeknumber as reported on the x axis.
Additional sources of information
In addition to the mandatory scheme, a subgroup of NHS trusts in England is recruited everyyear to participate in the USISS sentinel scheme [19, 23], which reports weekly number oflaboratory-confirmed influenza cases hospitalised at all levels of care. From this scheme,individual-level data on all ICU/HDU admissions (until season 2012/13) or on hospitaladmissions in the young ( ≤
17 years old) population (from season 2013/14 onwards) areavailable, including clinical details such as date of symptom onset, of hospital and ICUadmission, and date of discharge from ICU.These data provide useful information on the process between influenza infection andICU admission (e.g. the time elapsing from symptom onset to ICU admission). Furtherinformation on this process (e.g. proportion of symptomatic cases) can be found in theexisting literature about the incubation period of influenza [24] and the hospitalizationfatality rate [25].
Model
We used an epidemic model (Figure 2) to describe the spread of influenza in England [26].We assumed that the population changes according to a deterministic model in continuoustime. Time is measured in days and denoted by t .The population is divided according to health status into four compartments: susceptible( S ), exposed ( E ), infectious ( I ) and removed ( R ). The E and I compartment are furtherdivided into two ( E , E and I , I , respectively) leading to waiting times in the E and I states, distributed according to gamma distributions [27]. In the formulas below, the letters S, E , E , I , I , R denote the number of people in each compartment. The total size of the3opulation is fixed over every season and denoted by N . The change of compartment isdetermined by the transition rates: λ ( t ), σ and γ explained below.The infection rate λ ( t ) is proportional to the proportion of people in the infectiouscompartment at t , I ( t )+ I ( t ) N and a piecewise constant transmission rate β ∗ ( t ) (the rate atwhich new infections take place): λ ( t ) = β ∗ ( t ) I ( t ) + I ( t ) N . (1) β ∗ ( t ) is piecewise constant and it allows for a scaling factor κ ∈ (0 ,
1] that expresses thechange of the base contact rate β due to school closure [10] as reported in Equation 2. β ∗ ( t ) = (cid:40) κ · β, t ∈ school holidays β, otherwise . (2)The transition rates σ and γ are related to the mean latent period, d L , and the meaninfectious period, d I , by: σ = 2 /d L , γ = 2 /d I (3)The system of differential equations that defines the epidemic model is reported in Equa-tion 4. dSdt = − λ ( t ) · SdE dt = λ ( t ) · S − σ · E dE dt = σ · E − σ · E dI dt = σ · E − λ · I dI dt = λ · I − λ · I dRdt = λ · I (4)Here we have assumed homogeneous mixing among contacts (i.e. people are all equally likelyto meet, irrespective of their age class and residence, for example). S ( t ) E ( t ) E E I ( t ) I I R ( t ) λ ( t ) σ σ γ γICU t p ICU µ ICU | E σ ICU | E Figure 2: Schematic diagram representing the epidemic model and the model linkingtransmission to ICU/HDU admissions (in blue).This transmission model is linked to the data on ICU admissions through an observationalmodel that defines the time elapsing from infection to ICU admission and the probability ofICU admission conditional on infection. 4enote with f ICU | I ( w ) the probability that w weeks elapse from infection to ICU ad-mission, and with p ICU the probability of ICU admission given infection. We can link µ w ,the average number of ICU admissions during week w , to the weekly new infections in theprevious weeks via a convolution: µ w = w (cid:88) v =0 f ICU | I ( w − v ) · ∆ I v p ICU (5)where ∆ I v = ( S (7 v − − S (7 v )) is the count of the new infections during week v .To formulate the likelihood of the data, we assumed that the observed number of ICUadmissions is the realisation of a Negative Binomial random variable centred on µ w withover dispersion parameter η : ICU w ∼ NegBin( µ w , η ) , (6)i.e ICU w has density function: f ( ICU w = x ) = Γ( x + r w )Γ( x )Γ( x + r w ) (cid:18) η (cid:19) r w (cid:18) − η (cid:19) x (7)with r w = µ w η − .The Additional file contains the full specification of the transmission model, its re-parametrization and full derivation of f ICU | I ( w ). Parameter estimation
To define the epidemic we need to estimate or set both the transitions rates parameters (i.e. β, κ, σ, γ ) and the initial state of the epidemic (i.e. S (0) , E (0) , E (0) , I (0) , I (0) , R (0)).The epidemic model can be re-parametrized [27] and a number of quantities may bedefined, including: π , the initial proportion of non-immune people; I tot (0) = ( I (0) + I (0)),the total number of infectious people at t = 0; the basic reproduction number R that isthe average number of successful transmissions per infectious person in a fully susceptiblepopulation; and the effective reproduction number R n that is the average number of suc-cessful transmissions per infectious person in a partially susceptible population. All theseparameters are useful under a health-policy perspective.The parameters σ and γ are assumed known from previous studies [24, 13], as they can beinferred only with detailed information at the individual level. Likewise, the population size N is assumed known and fixed to the values estimated by the Office of National Statistics(ONS) [28].We used a Bayesian approach to draw inference on the other parameters. Bayesianinference consists in summarizing prior information on a general parameter θ in a distribution π ( θ ) and updating it with the information deriving from a set of data x , contained in itslikelihood L ( θ | x ), to derive the posterior distribution: p ( θ | x ) ∝ π ( θ ) · L ( θ | x ) . (8)We considered two scenarios. In the first one we assumed we have no prior information onthe values of the parameters except for lower and upper bounds, hence the prior distributionson all the parameters are non-informative (see Additional file 1). Table 1 lists the lower andupper limits of some transformations of the parameters and the values assumed known inthis scenario.In the second scenario we used sero-prevalence data from the 2010/11 season [29] toformulate a prior distribution for the initial susceptibility π . The use of sero-prevalencedata to describe the immunity of a population could be debatable, since the results maybe extendible only to seasons with similar predominant strains circulating. Here, sero-samples were taken during an H1 predominant season: this sub-type was prevalent alsoin the 2012/13 season, but not in 2014/15. However, combining this prior with the dataallows us to test how much prior knowledge is needed to overcome the lack of informationabout susceptibility from the data. We also derived an informative prior distribution on5able 1: Prior distributions of the parameters in the non-informative scenarioUnknown parameters definition Parameter Lower limit Upper limitSusceptibility π I tot (0) = ( I (0) + I (0)) 0 10000Transmission rate β η p ICU κ σ γ N N N p ICU by combining estimates of the probability of hospitalization given infection from aprevious severity study [25] with estimates of the probability of ICU/HDU admission givenhospitalization from the aggregate data of the USISS sentinel scheme. Table 2 lists the priordistributions of the two parameters that change in the informative scenario. The remainingparameters are again assumed to be uniformly distributed.Table 2: Prior distributions of the parameters that change in the informative scenarioParameter Distribution π ∼ LogNorm(log µ = log(0 . , log σ = 0 .
2) [29] p ICU ∼ LogNorm(log µ = log(0 . , log σ = 1) [25] Analyses
For both the prior settings we performed two types of analysis: firstly we considered all thedata reported in Figure 1 and we analysed them retrospectively. Secondly, to assess thepredictive ability of our model, we performed estimation and forecasting assuming only aninitial portion of the data are available. We used the data up to week w as a training datasetto estimate the parameters. Then we predicted the evolution of the epidemic after week w ,based on the estimates from the training dataset. We tested the following prediction timepoints: w = 3 , ,
13, and 18 from the beginning of the new year. An example of the sequenceof data used to analyse prospectively an epidemic (season 2014/15) is reported in Figure 3.To approximate the posterior distribution, we used a Metropolis Hastings block updatedsampling algorithm [30], coded using the R programming language [31]. The system ofdifferential equations 4 was solved using the R package deSolve [32]. Details on the algorithmare available in Additional file 1 and the code is available at . Results
Retrospective analysis
The retrospective analysis of the data was first performed in the uninformative scenario.The resulting posterior distributions are displayed in Figure 4 with the posterior medianand 95% Credible Intervals (CrI)s of some of the parameters reported in Table 3. Note thatthe posterior distribution of the initial susceptibility π and the basic reproduction number R are almost identical to the prior. This is due to the fact that the information containedin the data is not sufficient to determine separately the values of the parameters describing6 Season 2014/15: initial data weeks ad m i ss i on s
40 45 50 3 8 13 182014 2015
Season 2014/15... more data weeks
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Season 2014/15... more data weeks
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Season 2014/15... more data weeks
40 45 50 3 8 13 182014 2015
Figure 3:
Prospective analysis.
Sequential data on ICU admissions used in theprospective analysis in the season 2014/15.both the initial immunity and the transmission rate. This problem is explored in detail inAdditional file 1.Season 2012/13 Season 2013/14 Season 2014/15 . . . . . p n0 5 10 15 20 25 30 . . . h n0e+00 2e−04 4e−04 6e−04 8e−04 1e−03 p ICUn0.0 0.5 1.0 1.5 2.0 . . . . k n0 1 2 3 4 . . . . R n0.8 1.0 1.2 1.4 R n . . . . . p n0 5 10 15 20 25 30 . . . . . h n0e+00 2e−04 4e−04 6e−04 8e−04 1e−03 p ICUn0.0 0.5 1.0 1.5 2.0 k n0 1 2 3 4 . . . . R n0.8 1.0 1.2 1.4 R n . . . p n0 5 10 15 20 25 30 . . . h n0e+00 2e−04 4e−04 6e−04 8e−04 1e−03 p ICUn0.0 0.5 1.0 1.5 2.0 . . . . k n0 1 2 3 4 . . . . R n0.8 1.0 1.2 1.4 R n Figure 4:
Retrospective analysis.
Prior (red) and posterior (blue) distributions of:the initial susceptibility ( π ); the over-dispersion parameter ( η ); the probability of ICUadmission given infection ( p ICU ); the scaling parameter ( κ ); and the basic and effectivereproduction number ( R and R n ). The results are derived from season 2012/13 (leftcolumn), season 2013/14 (centre) and season 2014/15 (right column).7ata are much more informative about parameters η , p ICU and κ . The highly variablebehaviour of the ICU admissions count in season 2014/15 is reflected by the over-dispersionparameter η , whose distribution is significantly higher compared to the ones estimated fromthe 2012/13 and 2013/14 seasons. The range of the probability of going to ICU giveninfection, p ICU , is always between 0.04% and 0.4%. Its median is higher in season 2014/15,in agreement with the higher severity that was detected during this influenza season [23].The multiplicative factor κ introduced to allow for a school-closure effect is centred on 1for season 2013/14 and centred around higher values in the remaining seasons. A possibleexplanation for this counter-intuitive phenomenon relies on the age distribution of the samplepopulation. Our data have a different distribution compared to the English population ([23],[28]), with patients over 65 being over represented and children in school years being underrepresented. The elderly individual perhaps are more likely to meet other potential influenzaspreaders (e.g. children) during school closures, particularly over Christmas holiday. Itmakes sense, therefore, to observe an inverse relationship between school closure and thetransmission rate, in contrast to results that might be expected from a more representativesample of the population [10]. However, this piecewise increment in transmission rate mayincorporate other time-varying phenomena that affect the force of infection. The Christmasholiday often coincides with the beginning of a colder and more humid period and changesin vapour pressure, that might imply an increasing spread of influenza [33]. Lastly theposterior median of the effective reproduction number R n is equal to 1.152, 1.235, 1.089 inseasons 2012/13, 2013/14 and 2014/15 respectively.Table 3: Posterior medians and 95% CrIs from the retrospective analysis of the ICU admis-sions with uninformative priors.2012/13 2013/14 2014/15 π I tot β η p ICU ( · ) 0.084 (0.046 - 0.161) 0.071 (0.042 - 0.134) 0.175 (0.085 - 0.374) κ R n κ included 1, the posterior probability of it beinglarger than 1 (Pr( κ > π and on p ICU as defined in Table 2. The introduction of theseprior distributions compensate for the lack of information, allowing the identification of π and improving the precision of the posterior distribution of p ICU . This affects also otherparameters such as β and R . However, their the posterior distributions are driven by theprior distributions alone, and they do not learn from the data. In terms of fit there was noimprovement. Results are reported in Additional file 1. Prediction
The prospective analysis of the data in the uninformative scenario resulted in very widepredictions of the future dynamics, therefore we assumed the informative priors reported inTable 2. The performance of the model at different times is plotted in Figure 6 for each8 l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l
Season 2012/13 week I CU ad m i ss i on s
40 45 50 3 8 13 18 l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l
Season 2013/14 week I CU ad m i ss i on s
40 45 50 3 8 13 18 l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l
Season 2014/15 week I CU ad m i ss i on s
40 45 50 3 8 13 18 l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l
Figure 5:
Retrospective analysis.
Median (blue), 95 % CrI (light green) and quartile(dark green) of the posterior predictive distributions and observed values (red) for theweekly ICU/HDU admissions across seasons. The vertical dashed lines represent thebreakpoints for the piecewise transmissibility β ∗ ( t ) (i.e. start and end of each schoolholiday).season.Season 2013/14, despite displaying the most regular data, is the most difficult to predict:the well-defined initial growth biases the predictions towards a major outbreak. This leadsto overestimation of the median and the credible intervals of the posterior predictive distri-bution until mid-march (week 13 from the beginning of the year). For the other two seasons,the median predicted weekly ICU admissions is always very close to the data points, butthe credible intervals narrow to reasonable bounds only towards the end of February (week8 from the beginning of the year).In spite of the simplicity of our model, the flexibility introduced by the parameter κ allows for the correction “on the fly” of the prediction, adapting to new peaks (e.g. season2014/15) or periods of constant influenza circulation (e.g. season 2012/13). Further results
We simulated the weekly count of Hospital admissions in the case of a pandemic and weextended our model enabling the inference of the parameters from these data. Despitethe increased number of observations, the model performed very similarly to the case ofnon-pandemic ICU-counts data. We diagnosed identifiability problems in the uniform priorscenario and predictions were good only when more informative prior distributions (on thesusceptibility and probability of hospitalization) was included. Results from this analysisare reported in Section 5 of Additional file 1.Other analyses performed include: prospective analysis for the uninformative scenarioand retrospective analysis within the informative scenario. Results of these analysis arereported in Section 4 of Additional file 1.
Discussion
In this paper we proposed a model to estimate and predict influenza outbreaks from routinelycollected data on admissions to ICU/HDU.We investigated the performance of the proposed model both on simulated and on realdata. By fitting the model to simulated number of weekly ICU admissions, we discoveredthat, even with very vague prior information, we could obtain estimates of some of themain parameters, including the initial infection rate, the probability of going to ICU giveninfection, the effective reproduction number R n and the scaling factor for school holidays κ . When we injected information on the distribution of the average immunity (1 − π ) andon p ICU , estimates of the remaining parameters could be obtained. We were also able toforecast the evolution of the outbreak by analysing the first months of the epidemic usingdata up to the peak of influenza activity. 9eason 2012/13 Season 2013/14 Season 2014/15 llllllllllllllllllllllllllllllllll I CU ad m i ss i on s lllllllllllllllllllllllllllllllll weeks 40 45 50 3 8 13 18 llllllllllllllllllllllllllllllllll I CU ad m i ss i on s lllllllllllllllllllllllllllllllll weeks 40 45 50 3 8 13 18 llllllllllllllllllllllllllllllllll I CU ad m i ss i on s lllllllllllllllllllllllllllllllll weeks 40 45 50 3 8 13 18 llllllllllllllllllllllllllllllllll I CU ad m i ss i on s lllllllllllllllllllllllllllllllll weeks 40 45 50 3 8 13 18 llllllllllllllllllllllllllllllllll I CU ad m i ss i on s lllllllllllllllllllllllllllllllll weeks 40 45 50 3 8 13 18 llllllllllllllllllllllllllllllllll I CU ad m i ss i on s lllllllllllllllllllllllllllllllll weeks 40 45 50 3 8 13 18 llllllllllllllllllllllllllllllllll I CU ad m i ss i on s lllllllllllllllllllllllllllllllll weeks 40 45 50 3 8 13 18 llllllllllllllllllllllllllllllllll I CU ad m i ss i on s lllllllllllllllllllllllllllllllll weeks 40 45 50 3 8 13 18 llllllllllllllllllllllllllllllllll I CU ad m i ss i on s lllllllllllllllllllllllllllllllll weeks 40 45 50 3 8 13 18 llllllllllllllllllllllllllllllllll I CU ad m i ss i on s lllllllllllllllllllllllllllllllll weeks 40 45 50 3 8 13 18 llllllllllllllllllllllllllllllllll I CU ad m i ss i on s lllllllllllllllllllllllllllllllll weeks 40 45 50 3 8 13 18 llllllllllllllllllllllllllllllllll I CU ad m i ss i on s lllllllllllllllllllllllllllllllll weeks 40 45 50 3 8 13 18 Figure 6:
Prospective analysis.
The black line displays the analysis time; the blueline and green shaded area represent median, quartile (dark green) and 95% CrIs (lightgreen) of the posterior predictive distribution for the training dataset weeks. The pinkarea displays posterior quartiles (deep pink) and 95% CrIs (light pink) for the predictedfuture observations, and the purple line displays the median; the red dots are the trainingdata and the yellow dots are the observations we have predicted.The model was applied to real data on the weekly number of ICU admissions from sea-sons 2012/13, 2013/14 and 2014/15, confirming the performance obtained on the simulateddata. The estimated values of the effective reproduction number R n were similar to thoseestimated during the past decade of seasonal influenza [8]. A scaling parameter allowed thetransmission rate to vary between school and holiday/half-term periods, which resulted ina good fit of the model to the data.Recently, a similar analysis was performed on the Finnish influenza pandemic of 2009[16] using a more elaborate model, analysing confirmed data on both hospitalizations andGP consultation. Their inclusion of GP data enhances the performance of the inference.Nevertheless, these data are harder to collect in a larger population (England is almost10 times more populated than Finland) and out of pandemic emergencies. By contrast,the inference performed through our model is driven by few data, though readily available,even in real time, in seasonal settings. A further advance of the model by [16] is thatthe transmission parameter is time varying according to a Gaussian Process: this allows anaccurate description of the past dynamics but makes the prediction hard, since this temporalvariation cannot be forecast. By contrast, our simple piecewise constant model is able towell forecast the future trend and it includes enough flexibility to describe appropriately the10resent and the past data.Our work has also some limitations: firstly, our model is non-age-specific. This wasdictated by the very small data size which did not allow sub-grouping. Secondly, the qualityof some estimates and predictions strongly relies on prior information on the proportion ofnon-immune people. As this information is needed to overcome the lack of identifiability inthe parameters, we used sero-prevalence data following the 2010/11 epidemic. This is notlikely to be correct for all the three seasons analysed, as the predominant strain circulatingwas different across seasons. Likewise, the model that describes the time elapsing betweeninfection and ICU admission, is assumed to be fixed and mostly known, but this assumptionis not likely to be valid. The other element that defines the observational process, i.e.the probability of ICU admission given infection, is also sensible to the choice of priordistribution. Conclusion
The work presented here is a proof of concept of the potential for estimation and predictionof influenza transmission from USISS data. At the same time, the results highlight theneed of collecting external data to formulate appropriate prior distribution on the initialimmunity of the population, particularly in the event of a pandemic.The availability of this information, together with the tool we have provided here, allowsto retrospectively infer the epidemic parameters from routinely collected data on severe casesduring seasonal outbreaks and to predict the temporal dynamics of new epidemics.
Acronym
USISS
UK Severe Influenza Surveillance System
PHE
Public Health England
ILI influenza-like illness GP General Practitioner
NHS
National Health Service
ICU
Intensive Care Unit
HDU
High Dependence Unit
WHO
World Health Organization
ONS
Office of National Statistics
CrI
Credible Intervals
Declarations
Availability of data and material
The datasets used and/or analysed during the current study are available from the author onreasonable request at [email protected].
Competing interests
The authors declare that they have no competing interests.
Funding
AC, DDA, and AMP were supported by the Medical Research Council [grant number MC UI05260666,Program Core SLAH/001]. PJB was supported by the National Institute for Health Research (HTAProject:11/46/03). XSZ, NB, RP, PB and DDA were supported by Public Health England. uthor’s contributions AC wrote the paper, with help by XSZ DDA and AMP. XSZ and AC wrote the code, with supportby PJB and AMP in the formulation of the algorithm. NB provided the data and assisted withtheir interpretation. DDA and RGP conceived the study. All authors gave a final approval forpublication.
Acknowledgements
The authors would like to thank all the participants of the Armitage Lecture 2015. In particular,Prof. Leonard Held and Dr. Michael Hohle gave substantial advice for the implementation of thismodel. Likewise, during the Summer Institute on Statistics and Infectious Disease Modelling [ ? ],Prof. Pejman Rohani helped with suggestions on model evaluation. Finally, AC would like to thankProf. Rino Bellocco for his support from the very beginning of this project. References [1] World Health Organization (WHO). Influenza (seasonal) fact sheet;. Available from: .[2] Pitman RJ, Melegaro A, Gelb D, Siddiqui MR, Gay NJ, Edmunds WJ. Assessing theburden of influenza and other respiratory infections in England and Wales. J Infect.2007;54(6):530–538.[3] Hayward AC, Fragaszy EB, Bermingham A, Wang L, Copas A, Edmunds WJ, et al.Comparative community burden and severity of seasonal and pandemic influenza: Re-sults of the Flu Watch cohort study. 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