Social contact data in endemic-epidemic models and probabilistic forecasting with surveillance Sebastian Meyer Institute of Medical Informatics, Biometry, and Epidemiology Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany 5 July 2017 Joint work with Johannes Bracher and Leonhard Held (University of Zurich)
World Health Organization 2014 Forecasting disease outbreaks is still in its infancy, however, unlike weather forecasting, where substantial progress has been made in recent years. Sebastian Meyer | FAU | hhh4contacts and probabilistic forecasting 5 July 2017 1
World Health Organization 2014 Forecasting disease outbreaks is still in its infancy, however, unlike weather forecasting, where substantial progress has been made in recent years. Key requirements to forecast infectious disease incidence • Multivariate view to predict incidence in different regions and subgroups • Stratified count time series from routine public health surveillance • Useful statistical models to reflect forecast uncertainty • Predictive model assessment Sebastian Meyer | FAU | hhh4contacts and probabilistic forecasting 5 July 2017 1
Infectious disease spread ~ social contacts library ("hhh4contacts") plotC ( contactmatrix (grouping = NULL )) EU-funded POLYMOD study [Mossong et al. 2008] : 70+ 4.0 Average number of contact persons 65−69 • 7 290 participants from eight 60−64 3.5 age group of participant 55−59 European countries recorded 3.0 50−54 45−49 contacts during one day 2.5 40−44 35−39 • Contact characteristics were 2.0 30−34 similar across countries 25−29 1.5 20−24 1.0 • Remarkable mixing patterns 15−19 10−14 0.5 with respect to age 05−09 00−04 0.0 4 9 4 9 4 9 4 9 4 9 4 9 4 9 + 0 0 1 1 2 2 3 3 4 4 5 5 6 6 0 − − − − − − − − − − − − − − 7 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 0 1 1 2 2 3 3 4 4 5 5 6 6 age group of contact Sebastian Meyer | FAU | hhh4contacts and probabilistic forecasting 5 July 2017 2
Infectious disease spread ~ location and distance Tobler’s First Law of Geography: Everything is related to everything else, but near things are more related ● ● than distant things. ● ● ● ● ● Specifically [e.g., Meyer and Held 2017] : ● ● ● ● Spatial interaction decays ● ● ● as a power law. ● ● ● ● ● Regional characteristics may also ● ● affect disease spread, e.g., rural vs. ● ● urban municipalities ● Sebastian Meyer | FAU | hhh4contacts and probabilistic forecasting 5 July 2017 3
Infectious disease spread ~ time susceptible Number of individuals 150 infectious removed 100 • Occasional outbreaks 50 • Limited infectious period 0 0 20 40 60 80 Time [days] 15 Seasonal effect • Seasonality (influenza, 10 measles, norovirus gastroenteritis, . . . ) 5 0 0 10 20 30 40 50 Calendar week Sebastian Meyer | FAU | hhh4contacts and probabilistic forecasting 5 July 2017 4
Case study: norovirus gastroenteritis in Berlin, 2011–2016 noroBEg <- noroBE (by = "agegroups", timeRange = c ("2011-w27", "2016-w26")) 00−04 05−14 15−24 30 20 weekly incidence [per 100 000 inhabitants] 10 25−44 45−64 65+ 30 20 10 2012 2013 2014 2015 2016 2012 2013 2014 2015 2016 2012 2013 2014 2015 2016 Lab-confirmed counts from survstat.rki.de , stratified by 12 city districts and 6 age groups Sebastian Meyer | FAU | hhh4contacts and probabilistic forecasting 5 July 2017 5
An age-stratified, spatio-temporal model Negative binomial likelihood for infectious disease counts Y grt with endemic-epidemic mean decomposition: µ grt = ν grt + φ grt ∑ c g ′ g w r ′ r Y g ′ , r ′ , t − 1 g ′ , r ′ Sebastian Meyer | FAU | hhh4contacts and probabilistic forecasting 5 July 2017 6
An age-stratified, spatio-temporal model Negative binomial likelihood for infectious disease counts Y grt with endemic-epidemic mean decomposition: µ grt = ν grt + φ grt ∑ c g ′ g w r ′ r Y g ′ , r ′ , t − 1 g ′ , r ′ Log-linear predictors ν grt and φ grt • Population offsets • Seasonality • Group-specific susceptibility • Covariates, e.g., vaccination coverage Sebastian Meyer | FAU | hhh4contacts and probabilistic forecasting 5 July 2017 6
An age-stratified, spatio-temporal model Negative binomial likelihood for infectious disease counts Y grt with endemic-epidemic mean decomposition: µ grt = ν grt + φ grt ∑ c g ′ g w r ′ r Y g ′ , r ′ , t − 1 g ′ , r ′ Log-linear predictors Aggregated POLYMOD ν grt and φ grt contactmatrix() ( c g ′ g ) 0.5 • Population 65+ age group of participant 0.4 offsets 45−64 • Seasonality 0.3 25−44 15−24 • Group-specific 0.2 05−14 susceptibility 0.1 00−04 • Covariates, e.g., 0.0 00−04 05−14 15−24 25−44 45−64 65+ vaccination age group of contact coverage Sebastian Meyer | FAU | hhh4contacts and probabilistic forecasting 5 July 2017 6
An age-stratified, spatio-temporal model Negative binomial likelihood for infectious disease counts Y grt with endemic-epidemic mean decomposition: µ grt = ν grt + φ grt ∑ c g ′ g w r ′ r Y g ′ , r ′ , t − 1 g ′ , r ′ Log-linear predictors Aggregated POLYMOD Spatial weights, e.g., power-law decay w r ′ r = ( o r ′ r + 1 ) − ρ ν grt and φ grt contactmatrix() ( c g ′ g ) 0.5 • Population 65+ age group of participant 0.4 offsets 46.8% 45−64 8.4% • Seasonality 0.3 25−44 8.4% 8.4% 3.0% 3.0% 15−24 • Group-specific 8.4% 0.2 3.0% 05−14 susceptibility 0.1 3.0% 3.0% 1.5% 3.0% 00−04 • Covariates, e.g., 0.0 00−04 05−14 15−24 25−44 45−64 65+ vaccination age group of contact coverage Sebastian Meyer | FAU | hhh4contacts and probabilistic forecasting 5 July 2017 6
Power-adjustment of the contact matrix: C κ := E Λ κ E − 1 powerC <- make_powerC ( contactmatrix (), normalize = TRUE) powerC(0) powerC(0.5) 1.0 1.0 65+ 65+ age group of participant 0.8 age group of participant 0.8 45−64 45−64 0.6 0.6 25−44 25−44 15−24 15−24 0.4 0.4 05−14 05−14 0.2 0.2 00−04 00−04 0.0 0.0 00−04 05−14 15−24 25−44 45−64 65+ 00−04 05−14 15−24 25−44 45−64 65+ age group of contact age group of contact powerC(1) powerC(2) 1.0 1.0 65+ 65+ age group of participant 0.8 age group of participant 0.8 45−64 45−64 0.6 0.6 25−44 25−44 15−24 15−24 0.4 0.4 05−14 05−14 0.2 0.2 00−04 00−04 0.0 0.0 00−04 05−14 15−24 25−44 45−64 65+ 00−04 05−14 15−24 25−44 45−64 65+ age group of contact age group of contact Sebastian Meyer | FAU | hhh4contacts and probabilistic forecasting 5 July 2017 7
Model estimation Likelihood inference using surveillance::hhh4() [Meyer, Held, and Höhle 2017] A “simple”, age-stratified, spatio-temporal model 1 : noroBEall <- noroBE (by = "all", flatten = TRUE, # 6 x 12 = 72 columns timeRange = c ("2011-w27", "2016-w26")) fit <- hhh4 (stsObj = noroBEall, control = list ( end = list (f = addSeason2formula (~1), offset = prop.table ( population (noroBEall), 1)), ne = list (f = ~1 + log (pop), weights = W_powerlaw (maxlag = 5, log = TRUE), scale = expandC ( contactmatrix (), 12)), data = list (pop = prop.table ( population (noroBEall), 1)), family = "NegBin1", subset = 2:(4*52))) 1 Full models in demo("hhh4contacts", package = "hhh4contacts") Sebastian Meyer | FAU | hhh4contacts and probabilistic forecasting 5 July 2017 8
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