the R Package sr Sebastian Meyer Epidemic phenomena Examples: - PowerPoint PPT Presentation

Epidemiology, Biostatistics and Prevention Institute Spatio-Temporal Analysis of Epidemic Phenomena Using the R Package s✉r✈❡✐❧❧❛♥❝❡ Sebastian Meyer

Epidemic phenomena Examples: – Earth quakes – Riots / crimes – Infectious diseases Data: Surveillance systems routinely collect – time-stamped – geo-referenced case reports useR! 2015, Spatial Session 1 July 2015 s✉r✈❡✐❧❧❛♥❝❡ : Spatio-Temporal Analysis of Epidemic Phenomena Page 2

Case study I: Invasive meningococcal disease ❧✐❜r❛r②✭✧s✉r✈❡✐❧❧❛♥❝❡✧✮❀ ❞❛t❛✭✧✐♠❞❡♣✐✧✮ ♣❧♦t✭✐♠❞❡♣✐✱ ✧s♣❛❝❡✧✮ ♣❧♦t✭✐♠❞❡♣✐✱ ✧t✐♠❡✧✮ type ● ● ● B ● ● ● C ● ● ● ● ● ● ● ● ● ● ● ● ● ● 20 336 ● ● ● ● ● ● B ● ● ● ● ● ● ● ● ● ● ● ● ● C ● ● ● Cumulative number of cases ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 15 252 ● ● ● ● ● Number of cases ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 10 168 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 5 84 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 0 0 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 1 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 2 ● ● ● ● ● ● ● 2002 2004 2006 2008 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 4 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 8 ● ● ● ● ● ● Time (months) ● ● ● 16 Dot size proportional to the number of Monthly and cumulative number of cases cases (residence postcode) (by date of specimen sampling) useR! 2015, Spatial Session 1 July 2015 s✉r✈❡✐❧❧❛♥❝❡ : Spatio-Temporal Analysis of Epidemic Phenomena Page 3

❛♥✐♠❛t❡✭s✉❜s❡t✭✐♠❞❡♣✐✱ t②♣❡❂❂✧❇✧✮✱ ❛♥✐♠❛t❡✭s✉❜s❡t✭✐♠❞❡♣✐✱ t②♣❡❂❂✧❈✧✮✱ t✐♠❡✳s♣❛❝✐♥❣ ❂ ✼✮ t✐♠❡✳s♣❛❝✐♥❣ ❂ ✼✮ Does the force of infection depend on the bacterial finetype? useR! 2015, Spatial Session 1 July 2015 s✉r✈❡✐❧❧❛♥❝❡ : Spatio-Temporal Analysis of Epidemic Phenomena Page 4

Case study II: Measles ❧✐❜r❛r②✭✧s✉r✈❡✐❧❧❛♥❝❡✧✮❀ ❞❛t❛✭✧♠❡❛s❧❡s❲❡s❡r❊♠s✧✮ Publically available surveillance data: time series of counts of newly reported infections by district ♣❧♦t✭♠❡❛s❧❡s❲❡s❡r❊♠s✱ ♣❧♦t✭♠❡❛s❧❡s❲❡s❡r❊♠s✱ t②♣❡ ❂ ♦❜s❡r✈❡❞ ⑦ ✉♥✐t✮ t②♣❡ ❂ ♦❜s❡r✈❡❞ ⑦ t✐♠❡✮ 2001/1 − 2002/52 60 50 40 No. infected 30 20 10 0 2001 2001 2002 2002 II IV II IV 036 100 196 324 400 484 576 676 time useR! 2015, Spatial Session 1 July 2015 s✉r✈❡✐❧❧❛♥❝❡ : Spatio-Temporal Analysis of Epidemic Phenomena Page 5

❛♥✐♠❛t❡✭♠❡❛s❧❡s❲❡s❡r❊♠s✮ Is local vaccination coverage related to disease dynamics? useR! 2015, Spatial Session 1 July 2015 s✉r✈❡✐❧❧❛♥❝❡ : Spatio-Temporal Analysis of Epidemic Phenomena Page 6

s✉r✈❡✐❧❧❛♥❝❡ Characteristics of epidemic-type data – Low number of cases – Seasonality – Occassional outbreaks (“self-exciting” process) – Dependence between areas, age groups, etc. – Underreporting, reporting delays useR! 2015, Spatial Session 1 July 2015 s✉r✈❡✐❧❧❛♥❝❡ : Spatio-Temporal Analysis of Epidemic Phenomena Page 7

Characteristics of epidemic-type data – Low number of cases – Seasonality – Occassional outbreaks (“self-exciting” process) – Dependence between areas, age groups, etc. – Underreporting, reporting delays Aims of s✉r✈❡✐❧❧❛♥❝❡ Monitoring (prospective): Outbreak prediction and detection ( → “Zombie Preparedness” talk by Michael Höhle) Modelling (retrospective): Quantify epidemicity and effects of external covariates on disease dynamics useR! 2015, Spatial Session 1 July 2015 s✉r✈❡✐❧❧❛♥❝❡ : Spatio-Temporal Analysis of Epidemic Phenomena Page 7

Place in the world of R packages s✉r✈❡✐❧❧❛♥❝❡ is the first and only software package dedicated to the space-time modelling and monitoring of epidemic phenomena Related packages: s♣❛❝❡t✐♠❡ : Basic classes and methods for spatio-temporal data s♣❛tst❛t : THE package for purely spatial point patterns ts❝♦✉♥t , ❊♣✐❊st✐♠ , ♦✉t❜r❡❛❦❡r , ❛♠❡✐ : Several packages dealing with purely temporal epidemic data st♣♣ : Simulation & visualization of space-time point patterns For a more complete picture: → CRAN task view “Handling and Analyzing Spatio-Temporal Data” useR! 2015, Spatial Session 1 July 2015 s✉r✈❡✐❧❧❛♥❝❡ : Spatio-Temporal Analysis of Epidemic Phenomena Page 8

Three modelling frameworks in s✉r✈❡✐❧❧❛♥❝❡ Data Resolution Example Model Function individual events cases of invasive spatio-temporal t✇✐♥st✐♠✭✮ in continuous meningococcal point process space-time disease (IMD) Meyer et al., 2012 event counts week × district multivariate ❤❤❤✹✭✮ aggregated in counts of measles NegBin time space & time Meyer et al., 2014 series individual SIR spread of classi- multivariate t✇✐♥❙■❘✭✮ event history of a cal swine fever temporal point fixed population among domes- process tic pig farms Höhle, 2009 useR! 2015, Spatial Session 1 July 2015 s✉r✈❡✐❧❧❛♥❝❡ : Spatio-Temporal Analysis of Epidemic Phenomena Page 9

Basic modelling concept Stochastic branching process with immigration – Decomposed disease risk: Endemic: seasonality, population, socio-demography, . . . ⊕ Epidemic: force of previously infected individuals – Ebola: R 0 of about 1.5 – 2.5 – Force of infection may depend on age and spatial/temporal distance to infective useR! 2015, Spatial Session 1 July 2015 s✉r✈❡✐❧❧❛♥❝❡ : Spatio-Temporal Analysis of Epidemic Phenomena Page 10

Spatial interaction Tobler’s First Law of Geography: Everything is related to everything else, but near things are more related than distant things. Brockmann et al., 2006 (dollar bill tracking): The distribution of travelling distances decays as a power law. log ( f ( x )) = − 1.6 ⋅ log ( x ) 1.0 3 3 2 3 0.8 f ( x ) = x − 1.6 3 1 2 1 0 0.6 2 1 2 1 5 50 500 3 0.4 Distance x 2 4 3 0.2 4 0 500 1000 2000 3000 Distance x 0.0 o − 1.6 useR! 2015, Spatial Session 1 July 2015 s✉r✈❡✐❧❧❛♥❝❡ : Spatio-Temporal Analysis of Epidemic Phenomena Page 11

♥❧♠✐♥❜✭✮ ♣♦❧②❈✉❜ Case study I: Invasive meningococcal disease Regression framework for the conditional intensity function λ ( s , t ) = ρ [ s ][ t ] ν [ s ][ t ] Endemic component – Piecewise constant on a suitable space-time grid – Explanatory variables in a log-linear predictor ν [ s ][ t ] – Equivalent to Poisson-GLM for aggregated counts useR! 2015, Spatial Session 1 July 2015 s✉r✈❡✐❧❧❛♥❝❡ : Spatio-Temporal Analysis of Epidemic Phenomena Page 12