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Motivation Methods Results Surveillance Discussion References Modelling and surveillance of infectious diseases - or why there is an in SARS ohle 1 , 2 Michael H 1 Department of Statistics, Ludwig-Maximilians-Universit at M unchen,

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Motivation Methods Results Surveillance Discussion References

Modelling and surveillance of infectious diseases

  • or why there is an

in SARS

Michael H¨

  • hle1,2

1Department of Statistics, Ludwig-Maximilians-Universit¨

at M¨ unchen, Germany

2Centre for Mathematical Sciences, Technische Universit¨

at M¨ unchen M¨ unchen, Germany

useR!2008 Kaleidoscope II Session Dortmund, 12 August 2008

Michael H¨

  • hle

Modelling and surveillance of infectious diseases 1/ 20

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Motivation Methods Results Surveillance Discussion References

Motivation

How can R assist in understanding and controlling infectious diseases – be it in human, plant or veterinary epidemiology. Two R packages exist:

1

RLadyBug contains a set of functions for the simulation and parameter estimation in spatially heterogeneous SIR models.

2

surveillance contains algorithms for the detection of aberrations in time series of counts arising from routine public health surveillance

This talk intends to give an overview of using R for especially (1) – deeper mathematical details are suspended to the lunch break

> library("RLadyBug")

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  • hle

Modelling and surveillance of infectious diseases 2/ 20

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Motivation Methods Results Surveillance Discussion References

Applications (1): SARS in Hong Kong 2003

Daily number of new cases of the severe acute respiratory syndrome (SARS) in Hong Kong (Anonymous, 2003) Epidemic curve created with package epitools (Aragon, 2007).

Healthcare worker Community

  • No. cases

20 40 60 80 100 15 21 27 5 11 17 23 29 4 9 15 21 27 3 8 14 20 Feb Feb Mar Mar Mar Mar Apr Apr Apr Apr May May

Michael H¨

  • hle

Modelling and surveillance of infectious diseases 3/ 20

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Motivation Methods Results Surveillance Discussion References

Applications (2): CSF Transmission Experiment

Experiment by Laevens et al. (1999) with classical swine fever (CSF) using S(0) = (5, 5, 6) and E = (0, 1, 0). Event history of each pig with inoculation as origin

5 10 15 20 25 30 35

( 1 , 1 )

11:01 11:03 11:05 5 10 15 20 25 30 35

( 1 , 2 )

12:01 12:03 12:05 5 10 15 20 25 30 35

( 1 , 3 )

13:01 13:03 13:05

> data("laevens") > plot(laevens, type = individual ~ time | position)

Michael H¨

  • hle

Modelling and surveillance of infectious diseases 4/ 20

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Motivation Methods Results Surveillance Discussion References

Applications (3) – CSF surveillance

Classical swine fever (CSF) in Brandenburg (BB) and Mecklenburg-Western Pomerania (MP), Germany Total of 81 infected farms out of 3290 during 1993-2004

CSF in domestic pig farms in MPBB

Quarters

  • No. of cases

1994 1998 2002 2 4 6 8 10

CSF among wild boars in MPBB

Quarters

  • No. of cases

1994 1998 2002 40 80 120

Interest in investigating the connection between the CSF incidence among domestic pigs and wild boars

Michael H¨

  • hle

Modelling and surveillance of infectious diseases 5/ 20

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Motivation Methods Results Surveillance Discussion References

Applications (4) - Spatial incidence of CSF in MPBB

Domestic pigs in MPBB

No case 1 case 2−5 cases More than 5 cases

Wild boars in MPBB

No case 1 case 2−5 cases 6−20 cases More than 20 cases Michael H¨

  • hle

Modelling and surveillance of infectious diseases 6/ 20

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Motivation Methods Results Surveillance Discussion References

Stochastic epidemic models (1)

SEIR model: A closed population of n + m individuals divided into susceptible, exposed, infectious, and recovered S(0) = n, E(0) = m, I(0) = 0 and R(0) = 0 At time t, an individual j meets infectious at rate λj(t|Ht) =

n+m

  • i=1

✶i∈Infectious(t) · f (i, j), where f (·) ≥ 0 is a function of the distance between i and j If a susceptible meets an infected, it becomes exposed

Michael H¨

  • hle

Modelling and surveillance of infectious diseases 7/ 20

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Motivation Methods Results Surveillance Discussion References

Stochastic epidemic models (2) – Distance kernels

1 Homogeneous model: ∀i, j : f (i, j) = β > 0 and hence

λj(t|Ht) = βI(t)

2 Heterogeneous model: The population is made up of k units

arranged on a grid in space. For j in unit uj: λj(t|Ht) = βIuj(t) + βη

  • u∈N(uj)

Iu(t)

3 Heterogeneous model, where individuals have locations in R2

and f (i, j) is a function on the Euclidean distance dist(i, j)

Michael H¨

  • hle

Modelling and surveillance of infectious diseases 8/ 20

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Motivation Methods Results Surveillance Discussion References

SARS in Hong Kong 2003

Assuming a constant incubation time of 6.4 days and a constant recovery time of 34 days as suggested by the mean

  • f the distributions in Donelly et al. (2003) we obtain

> data("hksars") > print(m1 <- seir(hksars, hksars.opts.ml)) Calling LadyBug (monitor ladybug.system.out/err for progress)... ... Parameter Estimations: Parameter: beta 4.3984e-09 ...

Basic reproduction number R0 = R0(m1, hksars) = 1.0012.

Michael H¨

  • hle

Modelling and surveillance of infectious diseases 9/ 20

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Motivation Methods Results Surveillance Discussion References

CSF Transmission Experiment (1)

Exposure times are not observed, instead of imposing we assume TE ∼ Ga(δE, γE) and TI ∼ Ga(δI, γI) A Bayesian setting with MCMC is used for parameter inference

> print(m2 <- seir(laevens, laevens.opts.mcmc)) An object of class LBInferenceMCMC Parameter Estimations (posterior mean from 2500 samples): Parameter: beta betaN gammaE deltaE gammaI deltaI 0.03706 0.02837 56.82000 9.37400 2.16200 0.25640 StandardErrors (posterior std.dev. from 2500 samples): beta betaN gammaE deltaE gammaI deltaI 0.018500 0.009481 45.510000 7.761000 0.738100 0.097760

Michael H¨

  • hle

Modelling and surveillance of infectious diseases 10/ 20

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Motivation Methods Results Surveillance Discussion References

CSF Transmission Experiment (2)

MCMC output can be further analysed by e.g. coda package Posterior density of β/βη and R0

> plot(m2, which = "betabetaN") > quantile(R0(m2, laevens), c(0.025, 0.5, 0.975))

0.02 0.06 0.10 0.01 0.03 0.05 0.07 β βn

1 2 300 400 500 600 700 800 900

2 4 6 8 0.0 0.1 0.2 0.3 0.4 0.5 0.6 β βn Density

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Mean Median 95% HPD

2.5% 50% 97.5% 0.3245 0.6370 1.2426

Michael H¨

  • hle

Modelling and surveillance of infectious diseases 11/ 20

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Motivation Methods Results Surveillance Discussion References

CSF surveillance (1)

CSF surveillance data consists of multiple outbreaks SIR Extension: Risk of infection consists of two components

endemic component: Time to infection from external sources modelled by a Cox model epidemic component: Similar to heterogeneous SIR model with distance weighting of infectives

Rate of infection has the following form λj(t|Ht) = exp

  • h0(t) + zj(t)′α
  • +

n+m

  • i=1

✶i∈Infectious(t) · f (i, j) When using a linear basis expansion of f (i, j) this rate is similar to the conditional intensity of an additive-multiplicative hazard model from survival analysis

Michael H¨

  • hle

Modelling and surveillance of infectious diseases 12/ 20

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Motivation Methods Results Surveillance Discussion References

CSF surveillance (2)

Endemic component: piecewise exponential baseline and time varying covariates boars and vaccination area Epidemic component: f (i, j) = β > 0 Inference using penalized loglikelihood with a model syntax similar to the timereg package (Scheike, 2006)

> m3 <- spatialSIR(Surv(start, stop, event) ~ fconst + + cox(boar) + cox(vacc), data = mpbb.evHist, ...) > coef(m3)[c("fconst", "cox(boar)", "cox(vacc)")] > diag(vcov(m3))[c("fconst", "cox(boar)", "cox(vacc)")] fconst cox(boar) cox(vacc) 3.814e-06 2.108e+00 1.261e+00 fconst cox(boar) cox(vacc) 7.371e-12 9.263e-02 1.729e-01

Michael H¨

  • hle

Modelling and surveillance of infectious diseases 13/ 20

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Motivation Methods Results Surveillance Discussion References

CSF surveillance (3)

Plot of the total intensity n+m

j=1 λj(t|Ht), the log baseline

hazard h0(t) (with a 95% CI) and the epidemic proportion

1000 2000 3000 4000 0.02 0.06 0.10 days total intensity 1000 2000 3000 4000 −15 −13 −11 days log−baseline h0 1000 2000 3000 4000 0.0 0.4 0.8 days epidemic proportion

Michael H¨

  • hle

Modelling and surveillance of infectious diseases 14/ 20

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Motivation Methods Results Surveillance Discussion References

The surveillance package (1)

> library("surveillance") > data("shadar") > control = list(range = 105:295, ret = "cases", alpha = 0, + c.ARL = 5) > plot(algo.glrnb(shadar, control = control))

Analysis of shadar using glrpois: intercept

time

  • No. infected

2003 I 2003 III 2004 I 2004 III 2005 I 2005 III 2006 I 2006 III 5 10 15 20 Infected Upperbound Alarm Outbreak

Michael H¨

  • hle

Modelling and surveillance of infectious diseases 15/ 20

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Motivation Methods Results Surveillance Discussion References

The surveillance package (2)

Surveillance algorithms:

cdc – Stroup et al. (1989) farrington – Farrington et al. (1996) cusum – Rossi et al. (1999) roya – Rogerson and Yamada (2004) (Experimental) lr and glr – H. and Paul (2008)

Comparsion of surveillance algorithms using sensitivity, specificity and its variants in simulations Surveillance time series models:

hhh - Held et al. (2005); Paul et al. (2008) twins - Held et al. (2006) (Experimental)

Michael H¨

  • hle

Modelling and surveillance of infectious diseases 16/ 20

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Motivation Methods Results Surveillance Discussion References

Discussion

First steps towards R functionality for infectious disease

  • modelling. More complex and realistic models imaginable.

Packages contain many additional visualization and simulation procedures (Sellke construction, Ogata’s modified thinning) Combining database, R, Sweave/odfWeave and LaTeX/OpenOffice allows for easy generation of daily bulletins

  • r reports

> motd

Message of the day

Packages are on CRAN. Starting points are H. (2007); H. and Feldmann (2007). Maybe they are of help. If adaptation is needed for your problem let me know.

Michael H¨

  • hle

Modelling and surveillance of infectious diseases 17/ 20

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Motivation Methods Results Surveillance Discussion References

Acknowledgements

Persons: Ulrike Feldmann, Sebastian Meyer and Valentin Wimmer, Ludwig-Maximilians-Universit¨ at M¨ unchen, Germany Michaela Paul and Andrea Riebler, Institute of Social and Preventive Medicine, University of Zurich, Switzerland Christoph Staubach, Federal Research Institute for Animal Health (FLI), Germany Financial Support: Munich Center of Health Sciences

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  • hle

Modelling and surveillance of infectious diseases 18/ 20

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Motivation Methods Results Surveillance Discussion References

Literature I

Anonymous (2003). Sars bulletin. Technical report, Health, Welfare and Food Bureau, Government of the Hong Kong Special Administrative Region. Aragon, T. (2007). epitools: Epidemiology Tools. R package version 0.4-9. Donelly, C. A., Ghani, A. C., Leung, G. M., and 16 more authors (2003). Epidemiological determinants of spread of causal agent of severe acute respiratory syndrome in Hong Kong. The Lancet, 361:1761. Farrington, C., Andrews, N., Beale, A., and Catchpole, M. (1996). A statistical algorithm for the early detection of outbreaks of infectious disease. Journal of the Royal Statistical Society, Series A, 159:547–563. Held, L., Hofmann, M., H¨

  • hle, M., and Schmid, V. (2006). A two component model

for counts of infectious diseases. Biostatistics, 7:422–437. Held, L., H¨

  • hle, M., and Hofmann, M. (2005). A statistical framework for the analysis
  • f multivariate infectious disease surveillance data. Statistical Modelling,

5:187–199. H¨

  • hle, M. (2007). surveillance: An R package for the monitoring of infectious
  • diseases. Computational Statistics, 22(4):571–582.

H¨

  • hle, M. and Feldmann, U. (2007). RLadyBug – an R package for stochastic

epidemic models. Computational Statistics and Data Analysis, Special Issue on Statistical Software, 52(2).

Michael H¨

  • hle

Modelling and surveillance of infectious diseases 19/ 20

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Literature II

H¨

  • hle, M. and Paul, M. (2008). Count data regression charts for the monitoring of

surveillance time series. Computational Statistics and Data Analysis, 52(9):4357–4368. Laevens, H., Koenen, F., Deluyker, H., and de Kruif, A. (1999). Experimental infection of slaughter pigs with classical swine fever virus: transmission of the virus, course of the disease and antibody response. Vet. Rec., 145:243–248. Paul, M., Held, L., and Toschke, A. M. (2008). Multivariate modelling of infectious disease surveillance data. Statistics in Medicine. In review. Rogerson, P. and Yamada, I. (2004). Approaches to syndromic surveillance when data consist of small regional counts. Morbidity and Mortality Weekly Report, 53:79–85. Rossi, G., Lampugnani, L., and Marchi, M. (1999). An approximate CUSUM procedure for surveillance of health events. Statistics in Medicine, 18:2111–2122. Scheike, T. (2006). timereg: Additive Semiparametric Timevarying Regression. R package version 1.0-2. Stroup, D., Williamson, G., Herndon, J., and Karon, J. (1989). Detection of aberrations in the occurrence of notifiable diseases surveillance data. Statistics in Medicine, 8:323–329.

Michael H¨

  • hle

Modelling and surveillance of infectious diseases 20/ 20