Diggle, PJ

Rowlingson, B

Stanton, M

National Centre for Research Methods: NCRM EPrints Repository

Empirical Modelling of Spatio-temporalVariation in Meningitis IncidenceNiamey, November 2009Peter J Diggle, Barry Rowlingson andMichelle StantonSchool of Health and Medicine, Lancaster, UKSupported by:Ethiopian Ministry of Health,Madeleine Thomson and colleagues, IRI Columbia NY,Mohammed Yassin, Liverpool School of Tropical MedicineWhere did 2009 go?• Key objective: short-term forecasting– spatial scale: district-level– time-scale: weekly– forecast lead-time: 1, 2, ... weeks• Funding applications:– Menigitis Research Foundation: uncuccessful– Medical Researxh Council: pending– ... ?• PhD recruitment: Michelle Stanton, Lydiane AgierOutline• Ethiopian data: weekly time-series at woreda-level,July 2002 – June 2008:– number of incident cases– land-surface temperature– rainfall• Exploratory analyis:– temporal: country-wide incidence– spatial: woreda-level incidence– spatio-temporal: animation• Proposed modelling framework:– multiplicative decomposition of incidence intotemporal and spatio-temporal components– regression adjustments for time-laggedenvironmental variables– stochastic model to mimic short-term spread ofepidemic amongst neighbouring woredasEthiopian data: temporal structureTime series at weekly intervals in each of 567 woredas:• incident counts, July 20002 to June 2008• average land surface temperature (LST)• total rainfall (TR)• LST and TR mapped onto woredas,using the IRI Data LibraryEthiopian data: weekly national incidence0 50 100 150 200 250 3000.00.10.20.30.40.50.6weekincidence/100,000Incidence on log-scale0 50 100 150 200 250 300−14−12−10−8−6−4−20weeklog−incidenceLand surface temperature0 50 100 150 200 250 30046810121416weekLSTTotal rainfall0 50 100 150 200 250 3000.000.050.100.150.200.250.300.35weekTRCross-correlation: incidence vs LST−20 −10 0 10 20−1.0−0.50.00.51.0lagCCFCross-correlation: incidence vs TR−20 −10 0 10 20−1.0−0.50.00.51.0lagCCFRegression model for country-wide incidenceINCIDENCE = SEASONAL × RESIDUAL0 50 100 150 200 250 300−14−12−10−8−6−4−20weeklog−incidenceRegression model for country-wide incidenceINCIDENCE = SEASONAL × RESIDUAL0 50 100 150 200 250 300−14−12−10−8−6−4−20weeklog−incidenceRegression model for country-wide incidenceINCIDENCE = SEASONAL × RAINFALL × RESIDUAL0 50 100 150 200 250 300−14−12−10−8−6−4−20weeklog−incidenceCorrelated residuals0 50 100 150 200 250 300−6−4−20246weekresidualsCorrelated residuals0 10 20 30 40 50−0.50.00.51.0lagACFCorrelated residuals0 10 20 30 40 50−0.50.00.51.0lagACFA dynamic seasonal modelYt = log incidence in week t= At + Bt cos(2πt/52) + Ct sin(2πt/52)residualRegression coefficients modelled stochastically:At = At−1 + ǫAtBt = Bt−1 + ǫBtCt = Ct−1 + ǫCtCan treat environmental variables similarly, but beware of over-elaborationSeasonal variation in black smokeStatic model:1200 1300 1400 1500 160012345WeekLog average black smoke levelFitted values, model 1Seasonal variation in black smokeDynamic model:1200 1300 1400 1500 160012345WeekLog average black smoke levelEthiopian data: spatial structure34 36 38 40 42 44 46246810121416Ethiopian data: spatio-temporal structureAnimation of incident countsEthiopian data: spatio-temporal structureAnimation of incident counts shows familiar epidemicstructure:• long, quiescent periods punctuated by localised outbreaks• local spread over short time-periodsDynamic spatio-temporal seasonal modelRt(x) = risk in week tlog Rt(x) = At(x) + Bt(x) cos(2πt/52) + Ct(x) sin(2πt/52)Regression coefficients modelled as random fields, for example:A0 = A0(x) At(x) =∫At−1(x − u)w(u)du + ǫAt(x)Conditionally independent Poisson counts:Yt(x) =incidence in week tNt(x) = population in woreda xYt(x)|Rt(x) ∼ Poisson{Nt(x)Rt(x)}Take-home messages1. Spatial scale:• analyse at finest available spatial resolution• interpret at policy-relevant scale2. Information synthesis:• environmental covariates:– spatially sparse ground-truth (eg met-stations)– and spatially dense surrogates (eg satellite data)– and physically based models• GIS layers (eg transport routes)• social context (eg major population movements)Take-home messages3. Correlation is your friend:• what is happening here and now• can help to predict what will happen somewhere else4. An honest answer to any prediction problem isa probability distribution• sensitivity (true positive)• specificity (false positive)• timeliness (forecast horizon)5. Open-source software implementationfor access and portabilityExamples: www.lancs.ac.uk/staff/diggle

Empirical modelling of spatio-temporal variation in meningitis incidence

http://eprints.ncrm.ac.uk/1276/1/Empirical_modelling_of_spatio-temporal_variation_in_Meningitis_Incidence_-_P._Diggle%2C_Third_MERIT_workshop%2C_Nigeria_2009.pdf

Empirical modelling of spatio-temporal variation in meningitis incidence

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