Baguelin, Marc and Flasche, Stefan and Camacho, Anton and Demiris, Nikolaos and Miller ...

20 Pages·2017·2.61 MB·English

Assessing Optimal Target Populations for Influenza
Vaccination Programmes: An Evidence Synthesis and
Modelling Study
Marc Baguelin1,2*, Stefan Flasche1,2,3, Anton Camacho1,2, Nikolaos Demiris4, Elizabeth Miller1,
W. John Edmunds1,2
1Immunisation,HepatitisandBloodSafetyDepartment,PublicHealthEngland,London,UnitedKingdom,2CentrefortheMathematicalModellingofInfectiousDiseases,
DepartmentofInfectiousDiseaseEpidemiology,LondonSchoolofHygiene&TropicalMedicine,London,UnitedKingdom,3DepartmentofMathematicsandStatistics,
UniversityofStrathclyde,Glasgow,UnitedKingdom,4DepartmentofStatistics,AthensUniversityofEconomicsandBusiness,Athens,Greece
Abstract
Background:Influenzavaccinepoliciesthatmaximisehealthbenefitthroughefficientuseoflimitedresourcesareneeded.
Generally,influenzavaccinationprogrammeshavetargetedindividuals65 yandoverandthoseatrisk,accordingtoWorld
Health Organization recommendations. We developed methods to synthesise the multiplicity of surveillance datasets in
ordertoevaluatehowchangingtargetpopulationsintheseasonalvaccinationprogrammewouldaffectinfectionrateand
mortality.
MethodsandFindings:Using a contemporary evidence-synthesis approach, we use virological, clinical, epidemiological,
andbehaviouraldatatodevelopanage-andrisk-stratifiedtransmissionmodelthatreproducesthestrain-specificbehaviour
of influenza over 14 seasons in England and Wales, having accounted for the vaccination uptake over this period. We
estimatethereductionininfectionsanddeathsachievedbythehistoricalprogrammecomparedwithnovaccination,and
the reductionhad differentpolicies beeninplaceover the period. Wefindthatthe current programme hasaverted0.39
(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,resultinginanoverallreductionof0.70(0.52–0.81)infectionsperdoseand1.95(1.28–3.39)deathsper1,000
doses.Incomparison,choosingthe nextgroup mostatrisk (50–64-y-olds) wouldpreventonly 0.43 (0.35–0.52)infections
perdose and 1.77 (1.15–3.14)deathsper 1,000doses.
Conclusions: This study proposes a framework to integrate influenza surveillance data into transmission models.
ApplicationtodatafromEnglandandWalesconfirmstheroleofchildrenaskeyinfectionspreaders.Themostefficientuse
ofvaccine toreduce overallinfluenza morbidity andmortality is thusto target children inadditionto olderadults.
Please see laterinthe articlefor the Editors’ Summary.
Citation:BaguelinM,FlascheS,CamachoA,DemirisN,MillerE,etal.(2013)AssessingOptimalTargetPopulationsforInfluenzaVaccinationProgrammes:An
EvidenceSynthesisandModellingStudy.PLoSMed10(10):e1001527.doi:10.1371/journal.pmed.1001527
AcademicEditor:GabrielM.Leung,UniversityofHongKong,HongKong
ReceivedMarch22,2013;AcceptedAugust29,2013;PublishedOctober8,2013
Copyright:(cid:2)2013Baguelinetal.Thisisanopen-accessarticledistributedunderthetermsoftheCreativeCommonsAttributionLicense,whichpermits
unrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalauthorandsourcearecredited.
Funding:WJEwassupportedbyagrantfromtheDHResearchandDevelopmentDirectorategrantnumber039/0031.MBandACreceivedfundingfromtheEU
FP7GrantEPIWORK(grantnumber231807),andACalsoreceivedfundingfromtheMRC(fellowshipMR/J01432X/1).Theviewsexpressedinthepublicationare
thoseoftheauthorsandnotnecessarilythoseoftheDepartmentofHealth,England.Thefundershadnoroleinstudydesign,datacollectionandanalysis,
decisiontopublish,orpreparationofthemanuscript.
CompetingInterests:NDisamemberoftheEditorialBoardofPLOSMedicinewhereheactsasastatisticaladviser.
Abbreviations:CFR,casefatalityratio;CI,confidenceinterval;GP,generalpractitioner;HPA/DH,HealthProtectionAgency/DepartmentofHealth;ILI,influenza-
like-illness;MCMC,MarkovchainMonteCarlo;RCGP,RoyalCollegeofGeneralPractitioners
*E-mail:[email protected]
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AssessingVaccinationofSeasonalInfluenza
Introduction quantify the amount of transmission due to each age group and
assess the impact of past and proposed changes to immunisation
Seasonal influenza is a serious public health problem globally. policy oncases and deaths.
In countries with an advanced health system, most of the deaths Thehypothesesweexaminearewhether,giventhevaccination
occur among elderly adults and those with co-morbid conditions coveragecurrentlyachievedinhigh-riskgroupsandelderlyadults
that place them at increased risk [1,2]. Immunisation strategies inindustrializedcountries,therehasbeenanymaterialimpacton
can target individuals at high risk of complications and/or key transmissionandwhethera moreefficientdeploymentofvaccine
spreaders in order to interrupt or reduce transmission. In most intermsofoverallpopulationmorbidityandmortalitywouldbeto
countries, influenza vaccination programmes have traditionally target children as the key infection spreaders. The incremental
targetedindividuals65yandolderandthoseinhigh-riskgroups, benefit of vaccinating low-risk children and/or adults as an
in line with World Health Organization recommendations [3]. addition to the existing risk/age-based policy is examined for
Following the experience with pandemic H1N1/2009 influenza, different coverage levels.
priority groups for vaccinationare nowbeing reconsidered [4].
Childrenhavebeenidentifiedasthemainspreadersofinfluenza Methods
infection[5,6]andthusapotentialtargetforvaccination,notonly
for their own protection but also for the indirect protection of Demography
others [7–9]. The annual mass vaccination of children presents For each of the seasons of the study, the number W of
i
major operational and resource challenges, and thus it is individualsinthepopulationwithageiistakenfromtheOfficefor
important for policy makers to be confident about the additional National Statistics (http://www.ons.gov.uk). Seven age groups
populationbenefitslikelytoaccruefrominducingherdprotection. were considered (,1, 1–4, 5–14, 15–24, 25–44, 45–64, 65+ y).
Theseverityofeachseasonalinfluenzaepidemicistheresultofa Eachoftheseagegroupsisdividedintoindividualsatloworhigh
complex interplay between background population immunity, risk of complications associated with influenza, later simply
which is partly a function of exposure to previously circulating referredtoasloworhighrisk.Individualsareconsideredathigh
cross-reactive viruses; the nature and extent of contact between risk if they have one of the following conditions: chronic
age groups; the pathogenicity of the circulating viruses; and the respiratory, heart, or renal disease; diabetes; or immunosuppres-
impactofvaccination,whichinturnisdependentoncoverageand sionduetodiseaseortreatment.Theproportionofpeopleinarisk
the match between wild and vaccine strains. While vaccination groupinaparticularagegroupisassumedtobeconstantoverthe
programmes are designed with a long-term perspective, some of periodofthestudy.Wederivedtheproportionofindividualsina
these parameters vary significantly from one season to another, risk group for each age group by analysing data from the Royal
necessitating longitudinal datasets to ensure that vaccine policy CollegeofGeneralPractitioners(RCGP)WeeklyReturnsService
decisionsarerobusttoyear-to-yearfluctuations.Inaddition,most over a period of 5y (2003–2008). The numbers of people in the
of the available surveillance data are designed for healthcare different age groups and the percent classified as high risk are
monitoring and are difficult to integrate directly in dynamic giveninTable1.Onthelastlineofthetable,theactualnumbers
transmission models (which require information on infection, resulting from theRCGPanalysiscan beseen.
rather than use of services). In the absence of quantitative
estimates derived from epidemiological data, models used to test Contact Survey
theimpactofalternativevaccinationprogrammeshavethusmade In2006,apan-Europeansurveywasconductedtomeasureand
substantialassumptions aboutbackgroundimmunity,structure of compare the structure of contacts in eight different European
contacts, and transmissibility of the virus [7–10]. Furthermore, countries (Belgium, Finland, Germany, United Kingdom, Italy,
given the importance of high-risk groups in contributing to the Luxembourg,theNetherlands,andPoland).Attentionwaspaidto
overall burden of disease, modelling of the impact of vaccine- recruiting participants representative in terms of geography, age,
induced changes in transmission on burden of disease needs to and sex [14]. Recruitment methods differed between countries,
takeaccountofthisadditionalpopulationheterogeneity.Recently, butwerebasedintheUnitedKingdomonface-to-faceinterviews.
modelsusingBayesianevidencesynthesishavebeendevelopedto Participantswereaskedtocompletediariesrecordingwithwhom
estimate the severity of influenza [11] and influenza infection they had contacts during a day. Diaries also recorded different
attackrates[12,13].WecombinesimilarBayesiantechniqueswith informationrelativetothosecontacts.Amongthem,theageofthe
transmissionmodelsinanovelapproachthatprovidesevidenceto contactwasrecorded,thenatureofthecontact(conversationalor
inform vaccinepolicy decisions. physicalcontact)andthenatureoftheday(weekday,weekend,or
Wethusapplyamodernstatisticalapproachtohelpdisentangle holiday).DetailsabouttheprojectcanbefoundinMossongetal.
theunderlyingbiological,epidemiological,andbehaviouralfactors [15].WeusedatafromtheUnitedKingdomarmofthestudy:the
that determine the annual patterns observed in surveillance data. final data consisted of 1,012 participants aged 0 to 79y who
We use theexperienceinEngland andWales, where vaccination recorded 11,876contacts in total.
was targeted at high-risk groups until 2000, then extended to all
individuals $65y, as an exemplar. Six different sources of data Consultations in General Practices
areused.Weusedemographicdatatodefinethestructureofthe SinceJanuary1967,theWeeklyReturnsServiceoftheRCGP
population in terms of age and risk groups. The structure of hasmonitoredtheactivityofacuterespiratoryinfectionsingeneral
contactsbetweenagegroupsisinferredfromacontactsurvey.The practices. As part of this scheme, the weekly number of persons
outcomes of the model are fitted to time series of healthcare consultingforinfluenza-like-illness(ILI)isrecorded.Foreachweek
consultations complemented by virological surveillance and of the studied period (from the influenza season 1995/1996 until
informed by vaccine uptake and match data. Finally, links 2008/2009), we obtained the size of the monitored population
between infections and consultations are given priors using includedintheRCGPWeeklyReturnServiceandthenumberof
serology data. By synthesising the evidence from these multiple individuals in that monitored population consulting for ILI
datasourcesacross14influenzaseasonsinEnglandandWales,we stratified in five age groups (0–4, 5–14, 15–44, 45–64, 65+ y).
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AssessingVaccinationofSeasonalInfluenza
Table1. Sizesofthe modelledpopulation compartments byageand risk group averagedover the periodof thestudy.
ModelledPopulation AgeGroup
,1y 1–4y 5–14y 15–24y 25–44y 45–64y 65+y
Averageagegroupsize 623,779 2,525,322 6,608,728 6,603,485 15,214,371 12,578,021 8,423,248
(2003–2008)
Percentathighrisk 2.1% 5.5% 9.8% 8.7% 9.2% 18.3% 45.0%
Proportionathighrisk, 723/33,780 15,837/287,075 77,197/783,844 63,206/724,292 165,827/1,803,008 301,562/1,647,783 456,654/1,013,979
fromRCGPsurveya
aNumberofindividualsathighriskofcomplicationsassociatedwithinfluenza/totalnumberofindividualssurveyed.
doi:10.1371/journal.pmed.1001527.t001
For a given season, we note by Nmon the size of the monitored Protection Agency/Department of Health (HPA/DH) annual
ij
populationandbym thenumberofpeoplerecordedasconsulting reports ontheinfluenza programme[18].
ij
for ILIinagegroupi at week jin that population. Inordertobeabletoderiveestimatesofthevaccineefficacyfor
In 2008, roughly 1.7% of the total population in England and each strain and season, data from the Health Protection Agency
WaleswasincludedintheRCGPnetworkofpractices.Although were used to establish the match between the circulating and
this number might seem small in comparison with other existing vaccinestrains (Table2).
surveillance networks, this sample is considered to be reasonably
representative of the whole population in terms of demography Serology for the Season 2003/2004 in A/H3N2
and geography[16]. During the winter of 2003/2004, the United Kingdom
experienced an unusual level of influenza activity following the
Respiratory Virus RCGP Surveillance emergence of A/Fujian/411/02-like antigenic variant strains. In
In order to complement the syndromic surveillance, a new ordertoinvestigatetheseverityofthesenewdriftedstrains,anage-
surveillanceactivityofvirologicalconfirmationofcaseswassetup stratified serological survey was conducted by the Health
starting from the 1995/1996 season. During weeks of potential ProtectionAgencyusingserasampledbeforeandaftertheseason
influenza activity, samples are taken from people presenting with [19].Resultingdatathuscontaininformationonhaemaglutination
ILIandsentfortestingtotheRespiratoryVirusUnitoftheHealth inhibition titres andRCGP age groupfor 875seracollected pre-
ProtectionAgency.Intheperiodconsidered(i.e.,fromthestartof and post-season. The haemaglutination inhibition assays were
the virological surveillance activity until the season 2008/2009), performed using the A/Wyoming/3/03 strain, antigenically
thedatasetincludes12,575virologicalsampleswithrecordedage equivalent to the A/Fujian/411/02 strain that was circulating in
grouptested,whichcorrespondstoanaverageof900samplesper theUnited Kingdomduring the2003/2004season.
season. In total, however, during the last season, because of the
novelH1N1pandemic,3,395samplesweretested.Ifthisseasonis Methods Overview
excluded, thedataset hasan average of700samples perseason. Based on these data sources, an inference and modelling
The predominant strain in the period investigated was A/ frameworkembeddingsocial,immunisation,epidemiological,and
H3N2. In every season except 2000/2001, A/H3N2 was surveillance components was developed. A Bayesian approach to
identified, while in several seasons either A/H1N1 or B was statistical inference was adopted, as it provides the most suitable
absent. In any given week, the number of confirmed samples by framework for synthesising diverse sources of evidence in a
agegroupwasrelativelysmall.Inaddition,nosamplesweretaken coherent manner [20]. Specifically, we utilised adaptive Markov
intheagegroup,1 y;mostofthesamples(47.7%)weretakenin chain Monte Carlo (MCMC) techniques [21], which represent a
the 15–44-y age group, while the younger age groups—though generic tool for inference from complex stochastic systems. An
highertransmitters—arelessrepresented(9.6%and13.7%forthe attractive aspect of the Bayesian approach when coupled to the
agegroups1–4yand5–14y,respectively).Elderlyadults(65+y) MCMC methodology is its particular suitability for the natural
areunder-represented(7.8%),whichisaproblemastheincidence propagationofuncertainty.Thisisespeciallycrucialinthepresent
appearstobesmallerinthisagegroup.Positivityratesaredifficult analysis since the quantities of interest, like the final numbers of
toaccurately quantifyin thisagegroup. individuals infected under different scenarios, are non-linear
Amongthesetestedsamples,17.3%werepositiveforinfluenza functionals of the basic model parameters. Additionally, MCMC
(H3N2:53.8%,H1N1:11.9%,H1N2:0.9%,H1N1pdm:10%,B: is highly modular, thus accommodating the inclusion of a novel
18.9%).Inthe2002/2003season,onlysevensamplesweretaken, algorithmforexploringthespaceofcontactmatrices(i.e.,ratesof
among which five were positive. However, three out of the five epidemiologically relevant contacts).
samples were taken in one age group (1–4 y) at a time when the We use a directed acyclic graph [22] to represent the model
level ofILIwas extremely low (middle ofMay 2003). structure and the way the data streams are integrated in the
In the rest of the manuscript, we note by nz the number of inference scheme (Figure 1). In what follows we refer to the
ij
positivesamplesfromagivensubtype(A/H1N1,A/H3N2,orB) notation adopted in Figure 1 in order to identify the different
taken among the n samples testedat week jin theagegroupi. processes operating at the different levels (transmission, vaccina-
ij
tion,epidemiology, andobservational processes) ofthemodel.
Vaccination Uptake and Match
CoveragebyageandriskgroupbyweekwastakenfromJoseph Transmission Model
etal.[17]fortheseasonsbefore2003/2004.Figuresforthe65+-y A series of studies have linked routes of transmission for
agegroup from2004/2005onwards weretaken fromtheHealth infectiousdiseaseswiththestructureofcontactsinthecommunity
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AssessingVaccinationofSeasonalInfluenza
[15,23].Theassumptionisthatwhenincontactwithasusceptible
9
00 individual, an infectious individual will have a probability q of
2
8/ transmitting the disease. This transmission probability q will
0
20 M M U depend on the type of contact involved (e.g., in the case of a
respiratory virus, a physical contact might be more effective in
08 transmitting than a conversational contact of the same duration)
0
2 andthetype of pathogen.
7/
0 Sociological surveys can thus replace expert opinion [24] to
20 M M U
characterise transmission matrices. However, though well estab-
7 lishedforsexuallytransmitteddiseases,wheretheimplicationand
0
0 interpretation of ‘‘contacts’’ is more obvious, the notion of
2
6/ ‘‘contact’’ is problematic for other diseases such as respiratory
0
20 M M U infections. Additionally, because of sample size or biases, the
results may need some reworking in order to become directly
6
0 interpretable. For example, we demonstrated previously that the
0
2
5/ transmission matrix of the A/H1N1/2009 virus directly inferred
0
20 M M U fromthemeancontactmatrixderivedfromthePOLYMODstudy
could not explain the change of dynamics during the summer
5 holidays[25].However,usingmatricesproducedfromresampling
0
0
2 (withreplacement)theoriginaldatadidallowthedynamicstobe
4/
0 accurately captured.
09. 20 U M U Wethusassumeherethatthereexistsamongthepossiblesetsa
0
2 set of resampled participants (with some participants sampled
8/ 04
0 0 several times)that representsan appropriate structureofcontacts
0 2
2 3/ inthepopulationintermsofdiseasetransmission.Themixingin
to 200 U M U ourmodelisthusdescribedbyaresampledsubsetofparticipants
96 from the original UK POLYMOD dataset. From this list of
9 3
1 0 participants, we uniquely derive a mixing matrix using the
d1995/ 2002/20 M M U mWeatlhliondgoaloegtyal.de[2v3el]oapneddHbeelnoswet(saiml.i[la1r4]t)o. the one described in
o For a set of entries resampled from the original POLYMOD
eri 02 dataset,letT bethenumberofparticipantsinclassj,A and(cid:2)Ni(cid:3)
p 0 j k k
gthe 2001/2 M M U strains. bgreo,urpesipefocrtivaenlyd,btyhepaargteiciapnadntnku.mWbeercaonf tchoenntaacstssomciaatdeetoineaacghe
urin 01 onal preacrotircdipedanitnktahewdeiigahryt:wkdependingonparticipantageandtheday
d 20 eas
gseasonalstrains 1999/20002000/ MU UM UU ccineandcirculatings 8>>><>>>:wwkk~~WWTTAAjjkkNN52wwde,,ffoorraawweeeekkednady,, ð1Þ
n a
thecirculati 1998/1999 M U U U,unmatchedv nwreuistTmphehbceetirNrveoew-lfndyoi,nardmdniudvarildiinsueNgadlwsawevoeefterhkaaeggeedtoaAnytukas.ml abnneudrmobwfeceroeknoetfancdctoss,npteaarncdtdsayWredcAijokmrdatehddee,
to 998 ns; by participants from age group j with persons in age group i
MatchofthevaccinestrainsTable2. SeasonStrain 1995/19961996/19971997/1 A/H3N2UMU A/H1N1MUM BUUU M,matchedvaccineandcirculatingseasonalstraidoi:10.1371/journal.pmed.1001527.t002 mgpusicApnitrjesoasda=ouopndiuacpuvdcelpoljilliaeday.nbrtiutBd.ifybaaoriyIceoslnpfsetmuedawrimosnceiefpahnsaouglgigkreceelriatvonaitflenhgruggldorgepecomiisjbfuadiretnpiosdahracydmegineajmjc~eudwtipmspsgeerfjPeroeoetooghPkortbpuremkdefait:lpacAkberus,:yikeiAalnjlsf[apitkmrjtmho[oiycNscejermoeijwttkein=inhanwtktasuaiagdnkgtmcitgje:/hottb,wTerwgewoirrpi,noteahusruoryamgpftpmniecbecdtimiooepombrpneamylttteeoarileoyyfscftyntricsmnswooegbmiimlnnleilatwceaasnðttticeheg2rtotshdyeeÞst.
Toachieve symmetry of thecontactmatrix {c },wethusset
ij
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AssessingVaccinationofSeasonalInfluenza
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AssessingVaccinationofSeasonalInfluenza
Figure1.Directedacyclicgraphshowingthelinkbetweenthedifferentmodellingcomponents,data,andparameters.Doubleand
simplearrowsindicate,respectively,deterministicandstochasticrelationships,ellipsesindicatevariables,andrectanglesindicatedata.Thecircled
lettersindicatewhichrelationshipconnectsthevariablesordatainvolved.Theserelationshipsareasfollows:processa,drawingwithreplacement;
processb,calculationofthetransmissionmatrixbyrescalingthemixingmatrixobtainedbyreweightingforageandweekdayandweekenddays;
processc,derivationoftheimmunisationratefromuptakedataandmatchofvaccine;processd,integrationoftheSEIRmodeloftransmission;
processe,ascertainmentofcasesthroughILIrecordingatGPs;processf,virologicaltestingschemefollowingahypergeometricdistribution.
doi:10.1371/journal.pmed.1001527.g001
[28]onseasonalinfluenzavaccineefficacysuggestedthatefficacy
1(cid:4)d d (cid:5) was lower in elderly (46%) compared to younger adults (70%).
cij~2 TijzTji : ð3Þ Since all of the studies included in the Cochrane review were
i j performed on healthy young adults, we assume that efficacy was
70%and46%inthoseunder65yand65yorolder,respectively,
Toobtainthetransmissionmatrix,wefinallymultiplythismixing
in a well-matched year, which was reduced to 42% and 28% in
matrixbyq,describingthetransmissibilityofthevirus,whichisthe
poorlymatchingyears.Weassumethatchildrenwereimmunised
probability that a contact between an infectious person and a
with a live attenuated influenza vaccine and that this type of
susceptible personleads totransmission.Thetransmission matrix
isthus broken downintoitsbiological andsocial components. vaccineproducedprotectionsimilartothatofthecurrenttrivalent
inactivated vaccineinadults.
In this study, we consider an average contact matrix over the
epidemic season, thus not considering holiday periods or Whentheagegroupingofthecoveragedatadifferedfromthat
weekends. When the epidemic is simultaneous with long periods used in our model, we reweighted the coverage values propor-
ofholidays(asduringtheA/H1N1/2009pandemicintheUnited tionally to the population sizes. Figures for the 65+-y age group
Kingdom), it is necessary to make the distinction between term from 2004/2005 onwards are taken from the HPA/DH annual
and holidaycontactmatrices[25]. reportontheinfluenzaprogramme[29].Forthecoverageinhigh-
At each step in the MCMC chain the matrix is updated by riskindividualsunder65yfortheseason2007/2008,weusedthe
resamplingfromthePOLYMODdatawithreplacement(Figure1, HPA/DHreportreweighteddependingontheriskgroup.Forthe
processa)andisthusinferredwithintheMCMCalgorithmviaa seasons2004/2005,2005/2006,and2006/2007,thecoveragein
novelrandom-walktypeofproposalonthematrixspacewherethe eachagegroupistakenasthefigurefrom2007/2008rescaledby
number of contacts between distinct age groups is re-normalised, theratioofcoverageinthetotalnon-riskunder-65-ypopulationin
reducingpotentialreportingorparticipationbiasesviasymmetry. each year and in 2007/2008. S1 in Text S1 gives the final
The contact matrix is combined with the demographic data and coverage by age/risk groupandseason assumedin theanalysis.
scaled by the transmissibility of the virus to give the transmission Only infants over 6 mo received vaccination. Infants under
matrix of thevirus(Figure 1,process b). 6 mowereassumedtobefullysusceptible.Possibleprotectionby
remaining maternalantibodies was not considered.
Vaccination Model
Epidemiological Model
The different epidemiological compartments of the model are
split into two types of compartments based on vaccine history The transmission matrix, the immunisation rate, the suscepti-
(indexedby NfornaiveorVforvaccinated;seeFigureS1inText bility profile, and the initial number of infections in the different
S1). As the vaccine is not 100% effective, a proportion a of the agegroupsfeedintotheepidemiologicalmodel(Figure1,process
i
vaccineesbecomeprotected(weassumefullprotection),whilethe d). The susceptibility profiles and initial number of infections are
rest12a remainfullysusceptible.Thevaccineefficacya depends derivedfromtheinferenceprocedure.Theepidemiologicalmodel
i i
on age group and the degree of match between the strain in the usesanage-andrisk-specificSEIR(susceptible–exposed–infected–
vaccineand thecirculating strain inthat year. recovered) epidemic model [25] with gamma-distributed latent
As in [25], we assume a 2-wk delay between infection and and infectious periods. We assumed that the background
developmentofprotectiveantibodies.Thisisbasedonananalysis immunityinthepopulation(inferredbythesusceptibilityprofiles)
ofthedynamicsofseroconversionfollowingcasesofA/H1N1pdm results in a reduced probability of infection rather than full
infectionconfirmedbyPCR[26].Wedonotmodelthedynamics protection.
ofantibodyproductionasin[12]asthesemeasurementsaredone Theepidemiologicalmodeldescribingthetransmissiondynam-
for cases following infection rather than vaccination, and vaccine ics of the virus is similar to that used during the 2009 pandemic
trialsusuallymeasurelevelofantibodiesafteralongerperiod.The [25]. The model has a modified SEIR structure. We assume
period of 2 wk to confer protection appears to be a reasonable randommixing(withinanagegroup)betweentheclinicalgroups.
assumption forour purpose. Thesizeofthesegroupsisgivenforeachseasonbydemographic
Combining the vaccination uptake and the vaccination match figuresfromtheOfficeforNationalStatistics(averagefiguresover
resultsinatimevaryingimmunisationraten inagegroupiand the period of the study are presented in Table 1). To allow the
ik
riskgroupk(processc).Therateofimmunisationn isassumedto latentandinfectiousperiodstobegammadistributed(ratherthan
ik
be constant over a monthly period. The total number of persons exponential), we assume that each of the E and I compartments
immunisedineachagegroupbymonthistakenfromJosephetal. aredefinedbytwoclasses(henceSEEIIRstructure),withthesame
[17] and HPA/DH reports. For the purpose of the transmission rate of loss of latency (c ) and infectiousness (c ) in both groups.
1 2
fitting,weassumethatthechangeofstatus(whetherasSVorRV) Hence, the average latent period is 2/c , and the average
1
occurs twoweeksafter vaccination. infectiousperiodis2/c .FollowingFergusonetal.[30],wechose
2
A recent Cochrane review [27] suggested that vaccine efficacy c =2.5andc =1.1,correspondingtoalatentperiodof0.8dand
1 2
was73%inyearsinwhichthevaccinewaswellmatched,and44% an infectious periodof 1.8d.
in years when there was a poor match between the vaccine and Weassumethatattheoutsetoftheinfluenzaepidemicasmall
circulatingstrains.Inaddition,arecentanalysisbyFlemingetal. fraction of individuals in each age class is infectious, and the
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AssessingVaccinationofSeasonalInfluenza
remainderaresusceptible.Thisfractionisobtainedbyscalingthe consult in general practice. Of them, another fraction will be
initialinfectiouspopulationbyafactorl.Preseasonalsusceptibility recordedasILI(othersbeingrecordedashavingotherrespiratory
isnotnecessarilyassumedtobeabsolute,andmayvarybyage.An symptoms),andifPCR-tested,notallofthemwillenduppositive
age-dependent susceptibility profile {s} is assumed, the param- because of the sensitivity of the test. We derive hereafter a
i
etersofwhichareestimatedfromthemodel-fittingprocessforall statistical model to rigorously link syndromic surveillance and
strainsandyears,exceptforH3N2in2003/2004,forwhichapre- influenza infections inthepopulation.
epidemicserologicalprofile wasavailable [19](moredetail about Thereappearanceofinfluenzaintemperatecountriesfromone
the derivation of susceptibility priors for this year is given in year to another is determined by the introduction by people
Section 2.2.3 of Text S1). As susceptibility has to be inferred, we travelling of some of the new variants from strains circulating
chose to limit the model to three age bands to avoid overfitting. globally [32]. Patterns of circulation between the two global
Weconsideredanaveragesusceptibilityforchildren(0–14yold), hemispheres and persistence in some regions appear to be
younger adults (15–64yold), andelderly adults (65+y old). governing the global circulation of influenza. In a country such
Uncertainty in estimates of these quantities reflects the joint as the United Kingdom, this translates into exposure throughout
uncertainty in the parameters from which they are derived. the year to importation from travellers. The H1N1/2009
Therefore, any correlation structures that may be present are pandemic, with its intense testing and tracking of travellers
appropriately propagated. We start our model at week 35 of the acquiring influenza abroad, shed light on the pattern of
epidemiological season (rather than week 40, which is usually introduction of the virus. In-country epidemics of influenza are
consideredasthestartingdateofthefluseason)tomatchthestart characterised by a balance of constant re-introduction from
oftheepidemicwiththereopeningofschools,theperiodatwhich outside and local in-country transmission until a widespread
weconsidered that ILIstarts toincrease. epidemic emerges (for a comparative description of the initial
TheequationsoftheSEIRepidemiologicalmodelaregivenby phase of the epidemic during the 2009 spring in 12 European
Equation 1 in Text S1. The model’s age-group-specific force of countries, see[33]).
infection isgivenby We thus considered that in addition to the main epidemic
modelledbythe(deterministic)equationsdescribedintheprevious
section,eachindividualinthemonitoredpopulationisassociated
l~qs X7 X2 X c (cid:6)I1XzI2X(cid:7) ð4Þ with a weekly risk of being infected outside of the national
i i ij jk jk
j~1k~1X~fN,Vg (deterministic) epidemic that we are modelling. This risk can be
associatedwithtravellingabroad(e.g.,inthesouthernhemisphere
where q is the transmissibility parameter, c is the rate at which during the influenza season in the northern summer) or with a
ij
individualsinagegroupimakecontactwiththoseinagegroupj, local outbreak independent of the national one. This risk is
and s isthesusceptibility of agegroup i. modelled by a probability y that we assume, for simplicity, is
i
The incidence Z (n) of new infections in age group i and risk independent of timeandage.
ik
group kat week nis If,foreaseofexposition,wedescribebyhtheparametersofthe
epidemic model, the incidence among the monitored population
of age group i at week j of new cases arising from the main
7n
Z ðnÞ~ ð c (cid:8)E2VzE2N(cid:9)dt: ð5Þ deterministic epidemic (assumed to be homogeneous across the
ik 1 ik ik country) is
7ðn{1Þ
(cid:10) (cid:10)
Notethatthegeneralpractitioner(GP)consultationandswabbing zh~(cid:10)(cid:10)NimjonX2 Z ðjÞ(cid:10)(cid:10) ð6Þ
dataareonlyavailableinfiveagegroups.Thesevenagegroupsin ij (cid:10)Ntot ik (cid:10)
(cid:10) ij k~1 (cid:10)
the epidemic model are thus collapsed into these five age groups
for the purpose of the observation model, by combining the ,1 withhtheepidemiologicalparameters(q,s,l,andA),Nmon and
i ij
and1–4yagegroupsandthe15–24and25–44yagegroups.(For Ntot the size of, respectively, the monitored and the total
ij
simplicity of notation, we do not explicitly write the step that
population in age group i and week j, and k:::k the function
consistsofcollapsingthesevenagegroupsintofive.Thisleadsus
rounding tothenearest integer.
toaslightabuseofnotation.TheiindexofZ (n)intheepidemic
ik At the same time, the incidence of infection acquired from
modelisvaryingbetween1and7andisthusdifferentfromthei
outsideofthemainepidemicfollowsabinomiallawofprobability
indexofZ (n)intheobservationmodel,whichisvaryingbetween
ik y:
1 and 5. Passing from one to the other is simply done by adding
thesizes ofthepopulations that arebeing grouped.)
(cid:6) (cid:7)
zoutside*Binomial Nmon,y : ð7Þ
ij ij
Observation Model
Thelaststepofthemodelistolinksyndromicsurveillancedata The ascertainment of a case by the surveillance system is
with thenumber of infectionsdue tocirculating influenza viruses dependent on two steps. First, the infected case needs to go to
in the population. Although GP consultations for ILI are often the GP, and the GP needs to record the case as ILI. Second, a
used as a proxy to monitor transmission of influenza in a swab sample has to be taken and confirmed as containing
population,individualsconsultingforILIandindividualsinfected influenza viruses. Because of these two steps, the number of
with one of the circulating strains from the influenza family are ascertained cases is usually much smaller than the number of
typically two different sets. A large proportion of individuals ascertainable cases: not all persons presenting with ILI are tested
recordedashavingILIbytheirGPconsultforsymptomsresulting for influenza. The number of ascertained cases depends on the
frominfectionbypathogensotherthaninfluenza(e.g.,respiratory testing scheme, while the number of ascertainable cases depends
syncytialvirus).Also,duringaninfluenzaepidemic,onlyafraction onthenumberofindividualswithtrueinfluenzainfectionsinthe
ofcasespresentsymptoms[31],amongwhomonlyafractionwill populationthatpresenttotheirGP.Wethusareinterestedinthe
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AssessingVaccinationofSeasonalInfluenza
numberofascertainablecasesandassumethateachindividualin average number of secondary cases following the introduction of
age group i infected by the strain of influenza studied has a an infectious individual in a totally susceptible large population
probability i of being ascertainable, i.e., going to the GP, being [34].Inaheterogeneouspopulation,R willbeafunctionofeach
0
recordedasILI,andhavingadetectableviralload(thenumberof ofthereproductionnumberswithinpopulationsub-groupsandof
ascertainable cases is thus the number of positives that we would the degree of assortativity of these sub-populations. As a result,
getifallthepatientswithILIwerevirologicallytestedforinfluenza similar R values can arise from very different epidemiological
0
in agivenweek). situations (see Section 2.1.4 of Text S1). We thus measured, in
The number of ascertainable cases that get infected outside of addition to the basic reproduction number for the overall
the main epidemic can then be modelled as binomial of population, the specific reproductive numbers for children under
probabilityyE asthenumberofcaseswithinfectionfromoutside 15y and adults (R and R , respectively) and the degree of
i C A
is a binomial of probability y, and the number of ascertained assortativity d of thetwosubpopulations.
R
cases, conditional on the number of cases, is also binomial with
probability Ei: Generating Alternative Vaccination Scenarios
(cid:6) (cid:7) To estimate the impact of potential changes to the current
moijutside*Binomial Nimjon,yEi : ð8Þ vaccinationstrategy,weranforeachofthe14seasonsandeachof
the three strains, 1,000 simulated epidemics with parameters
Asye issmallandNmonisbig,moutsidecanlesscumbersomelybe sampledfromtheposteriorsobtainedusingMCMCtechniques.In
i ij ij
defined by a Poisson distribution ofrate NmonyE: addition to the actual strategy (used in the fitting process), we
ij i
analysed an additional ten strategies. The ten strategies are three
‘‘basic’’ strategies and incremental extensions of them (at 15%,
(cid:6) (cid:7)
moutside*Poisson yENmon : ð9Þ 30%,50%,and70%coverage):
ij i ij
N
Novaccination: Nobody receivesany vaccinedoses.
Thisapproximationisaccurateforallthevaluesconsideredinthis N
paper. Pre-2000:Thepre-2000schemeiskeptthroughoutthe14y,
Among the m individuals reported with ILI at week j among i.e., the risk groups are targeted as they were during these
ij
age group i, we are interested in the mz who have a detectable years; the change to targeting the low-risk 65+-y group that
ij
occurred in 2000 is not implemented. For the seasons 2000/
viral infection for a certain subtype of influenza. We assume that
2001 to 2008/2009, the average coverage from the pre-2000
they are a binomial sample from the total number of infected
(equal to zhzzoutside) with ascertainment probability E, assumed seasonsiskeptforthisgroup(29.34%coverageinthelow-risk
ij ij i 65+-ygroup).
to be constant over time (Figure 1, process e). The virological N
Post-2000: The post-2000 scheme is applied throughout the
testing scheme can be seen as randomly drawing n samples
ij
14y,i.e.,theriskgroupsaretargetedastheywereduringthese
without replacement from the population of the m individuals
ij
consulting for ILI, in which mz have a virologically detectable years; the low-risk 65+-y group is targeted in all seasons. For
infection. The number of positiivje samples nz that are expected the seasons 1995/1996 to 1999/2000, the coverage of 1999/
ij 2000 is applied for this group (70% coverage in the low-risk
can thus be represented using a hypergeometric distribution
65+-ygroup).
(Figure1,processf).Theconsultationandpositivitymodelisthen N
S1:Low-risk0.5–4-y-oldsarevaccinatedat15%,30%,50%,
described bythefollowing systemof equations:
and70% coverage,incremental on thepost-2000scenario.
N
8><mzij * Binomial(cid:6)zhij,Ei(cid:7)zPoisson(cid:6)yEiNimjon(cid:7) San2d:L7o0w%-rcisokve5r0a–g6e4,-iyn-corledmsaenretavlaocncinthaetepdoastt-1250%00,s3c0e%na,r5io0.%,
(cid:6) (cid:7) ð10Þ N
>: nzij * Hypergeometric nij,mzij ,mij : S3: Low-risk 5–16-y-olds are vaccinated at 15%, 30%, 50%,
and70% coverage,incremental on thepost-2000scenario.
N
Arepresentationofthesurveillancesystemintermsofsetsisgiven S4:S1+S2,i.e.,combination of scenarios1 and2.
N
inFigure2.Followingthissetrepresentation,wecanexpressEi as S5:S1+S3,i.e.,combination of scenarios1 and3.
N
a product of elementary epidemiological quantities (derivation in S6:S1+S2+S3,i.e.,combination of scenarios1,2 and3.
TextS1): N
S7:Universal,i.e.,everybodyamongthelow-riskpopulationis
vaccinatedat15%,30%,50%,and70%coverage,incremen-
E&PðEjA\C\DÞPðDjA\CÞPðCjAÞPðBjA\CÞ ð11Þ tal on thepost-2000 scenario.
whereP(E|A>C>D)istheGPrecognitionability,P(D|A>C) To quantify the efficiency of the assessed programmes, we
the propensity to consult among symptomatic influenza cases, measured the reduction in infections and deaths induced by one
P(C|A) the proportion with symptoms among the infected, and dose of vaccine for each of the different strategies. For this, we
P(B|A > C) the sensitivity of the test against clinical influenza used the estimated total reduction in number of infections and
cases. deathsduringtheperiod(removingtheseason2002/2003,where
Using this, we can derive an order of magnitude for E. In virologicalsamplesaretooscarce)anddivideditbythenumbersof
Table 3, we summarise the range of values that could take the doses of vaccines given by the programme over the same period.
elementary epidemiological parameters forming E and obtain For the extension strategies, we took the median over the four
values between 0.006and0.05. consideredcoverages (15%, 30%,50%,and70%).
Reproduction Numbers and Mixing between Groups Estimation of the Number of Deaths due to Influenza
The transmission potential of a pathogen is traditionally Our model provides estimates of the number of influenza
summarised by way of its basic reproduction number R , the infections ( Ninfec) under different vaccination scenarios for the
0
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AssessingVaccinationofSeasonalInfluenza
Figure2.Venndiagramgivingaschematicrepresentationofthedifferentsurveillanceschemesandclinicalstatuses.Therelative
proportionsofthedifferentsetsvaryfromoneweektoanotherandaredifferentforeachagegroup.
doi:10.1371/journal.pmed.1001527.g002
period 1995–2009. In order to compare these scenarios on the Intheory,itwouldbepossibletoextendourcurrentframework
basis of the predicted number of influenza deaths ( Ndeath), we to include some influenza mortality data in order to estimate
need the case fatality ratio (CFR= Ndeath/ Ninfec) of influenza. Ndeath and then deduce CFRs. Unfortunately, in contrast to the
Ideally, because our model provides estimates of the Ninfec by weekly age- and strain-specific data available for influenza
strain (s), age (a), and risk (r) group we would like to use CFRs morbidity,thebestinformationoninfluenzamortalityinEngland
of influenza as a function of these three variables: CFR . consists only in annual, age-specific estimates for the restricted
s,a,r
However, such estimates are currently lacking in the literature, period1999–2009[1].Inthiscontext(i.e.,onlyonedatapointper
mainly because quantifying the magnitude of both infection year for all three strains and only two-thirds of the period
and mortality attributable to influenza is not straightforward considered),itwouldbeillusorytotrytoestimateannualCFR
s,a,r
[1]. with our dynamical model approach. Instead, we propose to
Table3. Orderofmagnitude ofthe ascertainment probability ederived from theelementary probabilities ofmeasurable
underlyingphenomena.
Quantity Notation Range Source
Sensitivityofvirologicaltest P(B|A>C) 0.6–0.9 Assumption
Proportionofclinicalcasesamong P(C|A) 0.3–0.51 [31]
infections
Propensitytoconsultamongclinical P(D|A>C) 0.05–0.12 [39]
cases
SensitivityoftheGPdiagnostic P(E|A>C>D) 0.65–0.9 Assumption
Ascertainmentprobability E 0.006–0.05 Derived
doi:10.1371/journal.pmed.1001527.t003
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AssessingVaccinationofSeasonalInfluenza
combine available estimates of annual Ndeath by age group in E13,E14,E24,G1,G2,G3,G4,G5,G6,G7,G8,G9,N083,O24
England—obtained from a recently published regression analysis P700, P701, P702, C, D37, D38, D39, D4, B20, B21, B22, B23,
by Hardelid et al. [1] (see Table S2 in Text S1)—with our B24, Z94, Z85, D73, Z9621, G960, D561, D578, D571, D570,
estimates of the annual Ninfec in order to construct and fit K900, D70, D71, D72, D76, D80, D81, D82, D83, D84.)
generalised linear models whose coefficients equal the desired Mortalitywasidentifiedbydischargemethod4,andonlymortality
CFRs. within 30d of admission date was considered attributable to the
Moreprecisely,becausetherewasevidenceofoverdispersionin admission(resultsoftheanalysisaregiveninTableS3inTextS1).
the mortality time series of Hardelid et al. [1], we start with the Following this further simplification we obtain a new death
following age-specific negative binomial regression model with model, withonlythree coefficients toestimate:
identity link andno intercept:
8
(mNadðetaÞt~hðtPÞ*3negPBi2nombialðNmain,wfeacÞð,tÞ, ð12Þ <:maðtÞ~NPade3sa~th1ðtbÞs*,a,1nheNgBsin,afi,en1coðtmÞzialRðma|a,wNaÞsin,,af,e2cðtÞi: ð13Þ
a s~1 r~1 s,a,r s,a,r
where the negative binomial distribution is parametrized by its Finally, because the values of Ndeath, Ninfec, and R come with
a a a
mean (ma) and dispersion (wa), the index a denotes the age group confidenceintervals(CIs),weneedtoaccountforthisuncertainty
considered (we fit each age-specific model independently), and t when computing CFRs. For each age group a, we proceed as
runs over the restricted period 1999–2009. Given that Nadeath(t) follows. (1) We generate K=1,000 sample datasets (cid:2)Nadeath,k(t),
(Hardelid et al. data) and Nsin,af,erc(t) (our model outputs) are Nsin,af,erc,k(t),Rkagk~1:::K, where Nadeath,k(t) and Rka are sampled
‘‘known’’ (with uncertainty in both sources), the objective is to
fromanormaldistributionwiththesamemeanand95%CIasin
estimate the coefficients bs,a,r that, given the identity link and the Tables S2 and S3 of Text S1, whereas Ninfec,k(t) values are
absence of intercept, correspondtothedesiredCFR values. s,a,r
s,a,r obtainedbyrunningourmodelparameterssampledfromthejoint
Note that the age groups in the study of Hardelid et al. [1]
posteriordistributionofourMCMCanalysis.(2)Wefitthedeath
(,15, 15–44, 45–74, 75+ y) do not exactly match those of our
model for each replicate k by maximum likelihood using the
model (,1, 1–4, 5–14, 15–24, 25–44, 45–64, 65+ y). We tackle
functionglm.nb ofR2.15.1[35].
thisissueby(1)aggregatingthethree youngestagegroupsinour
We obtain the distribution of the K maximum likelihood
modeland(2)refittingtheHardelidetal.regressionmodelforthe
age groups 45–64 and 65+ y (H. Green, Health Protection estimates bb^ks,a,1~CCdFFRRks,a,1 of Figure S2 in Text S1. These
Agency, personal communication). distributionsareusedtoaccountforuncertaintywhencomputing
In principle, because the severity of a strain is expected to the distribution of the cumulated number of influenza deaths
n o
changefromoneyeartoanother,CFRsshouldalsodependonthe Ndeath,k over the 1995–2009 period predicted under
seasont,thusgreatlyincreasingthenumberofparameters.Here, tot k~1:::K
each vaccinationscenario:
weinsteadassume thattheseverity effectcanbecaptured by the
overdispersionparameterw.Suchasimplificationisrequiredfor
a
tpweroyreeaars,oanns:df,irssetc,owned,htahveeseaesstinimglaete(usnacreerntaoitn)aveastiliambaleteboeffoNreadetahthe Ntdoetath,k~ X14 X4 X3 CCdFFRRks,a,1hNsin,af,e1c,kðtÞzRka|Nsin,af,e2c,kðtÞið14Þ
1999/2000 season [1]. Put another way, we assume that the t~1,t=7a~1s~1
CFR valuesareconstantfrom1999to2009andcanbeapplied
s,a,r
tothe1995–1999 period. wheret=7correspondstothe2002/2003seasonandistherefore
Inaddition,onecanseethateachage-specificmodel(Equation excluded.The95%credibleintervalsofthecumulatednumberof
n o
12) suffers from overparametrization as it intends to estimate six influenzadeaths Ndeath,k arecalculatedforeachscenario
parameters (three strains times two risk groups) from only nine tot k~1:::K
usingthe2.5%and97.5%quantilesoftheposteriordistributions
datapoints(ofthetenseasonsprovidedbythestudyofHardelidet
al. [1], only nine are used since our estimates of Ninfec for the of thequantities ofinterest.
2002/2003seasonarenotreliablebecauseofalackofvirological
Statistical Inference
data during that particular season). To tackle this issue, we
assumedthattheriskratioCFR /CFR dependsonlyonthe The multiple sources of observation give rise to an intractable
s,a,2 s,a,1
age group a and is equal to R: the age-specific risk ratio of the likelihood, which we explore via data augmentation [36]
a
CFRsforacuterespiratoryinfectionamongpatientsnotinahigh- techniques. In order to manage to integrate numerically the
riskgroupversuspatientsinahigh-riskgroup.TheR valueswere likelihood,werewritethelikelihoodbymarginalisingsomeofthe
a
obtainedbyanalysingextractsfromtheHospitalEpisodeStatistics augmented variables. Then, we derive a recursive definition of
database(Health&SocialCareInformationCentre)forEngland, each of the elementary components of the likelihood in order to
for the period April 2000–March 2009. Patients were included minimise the number of computational steps involved in the
whentheyhadanacuterespiratoryICD-10diagnosticcode(J0*, estimation of the likelihood of the model. Finally, we modify the
J1*, J2*, J3*, J40*, J41*, J42*, J43*, J44*, J47*) in any diagnostic summation surface of the likelihood to derive an accurate
fieldsandweredividedintoriskgroup/non-riskgroupbasedona approximation of this likelihood by truncating some of the terms
risk-group-related ICD-10 code. (We used the following ICD-10 with very low probability (see Text S1 for more details of the
codes forrisk groups [where a two-digit code is given, it includes statisticalinference).Thisallowsustoacceleratethecomputation
all ICD-10 codes beginning with that code]: D73, J4, J6, J7, J8, ofthelikelihoodinordertorun11-million-lengthchainsforeach
Q30, Q31,Q32, Q33, Q34,Q35, Q36,Q37, I05,I06, I07,I08, strainandseason(1millionfortheburn-in).Samplesofsize1,000
I09, I11, I12, I13, I20, I21, I22, I25, I27, I28, I3, I40, I41, I42, are obtainedby thinning thechain by10,000.
I43,I44,I45,I47,I48,I49,I5,I6,Q2,N0,N11,N12,N14,N15, Serology data were available for the H3N2-dominated 2003/
N16,N18,N19,N25,Q60,Q61,K7,P788,Q44,E10,E11,E12, 2004 season and facilitated inference for the transmissibility and
PLOSMedicine | www.plosmedicine.org 10 October2013 | Volume 10 | Issue 10 | e1001527