poster unab

Spatio-temporal modelling of dengue cases in the city of Bucaramanga, Colombia, forthe period 2008 to 2013Martınez Bello, D.A.1*; Lopez Quılez A.2 ; Torres Prieto, A.3

*[email protected] MV, MSc, doctoral student, Departament d´Estadıstica i Investigacio Operativa, Facultat deCiencies Matematiques, Universitat de Valencia, Spain2 Statistician, PhD, Departament d´Estadıstica i Investigacio Operativa, Facultat de CienciesMatematiques, Universitat de Valencia, Spain3 Odontologo, Especialista en Epidemiologıa, Coordinacion de Epidemiologıa, Secretarıa de Salud delDepartamento de Santander, Colombia

Abstract

Disease mapping is an important tool to understand the disease distribution in space and time, and to evaluate the public health measures impact to counteract the disease burden. HierarchicalBayesian disease mapping is at the core of the geo-spatial representation of the disease. The objective of the study was to apply spatio-temporal hierarchical Bayesian disease mapping models toaggregated dengue cases from the city of Bucaramanga for the period 2008 to 2013, searching for a model which could be used as a representation of the disease spread and dynamics inBucaramanga, and to supply information in the search of a predictive model. Dengue cases in the city of Bucaramanga for the period 2008 to 2013 were geocoded, and allocated to one of 295sections, extracted from the Census 2005 according to the national statistical office (DANE) by epidemiological periods of 4 epidemiological weeks. Spatio-temporal Bayesian hierarchical modelstype I, II, III and IV were fitted to model relative risk of every census section. The full model contained spatial and temporal heterogeneity and clustering effects and interaction random effects.Models were fitted using the software OpenBUGS and the R package R2openBUGS. Model convergence was established using Gelman and Brooks test and Geweke test and line plots, and modelselection was accomplished using the Deviance Information Criteria (DIC). The results showed from several several fitted models, that the interaction type III models exhibited the smallest DIC, andfrom these, the model containing spatial heterogeneity and clustering effect in every epidemiological period was the selected model to produce relative risk maps for Dengue cases in Bucaramanga.

Introduction

Dengue is one of the most important tropical disease for the XXI century.Dengue is endemic in more than hundred countries from Africa, Asia andAmerica. Dengue virus belongs to the Flaviviridae family and Flavivirus genus,and it is conformed by four serotypes denominated DEN1, DEN2, DEN3, DEN4.In Colombia is responsible of 839013 , 71239 and 740 dengue cases, severedengue cases and deaths respectively, in the period 1995 to 2012. World HealthOrganization prioritized in 1999 the strategy to fight against the disease, directingthree main efforts: strengthening of epidemiological surveillance, conceptualstandardization of dengue disease, and clinical guides for disease control and theimplementation of community strategies directed to the modification of individualpractices (Maestre-Serrano, Gomez-Camargo, 2013). An important point to helpthe efforts of the dengue control is the representation of the disease in space andtime . For this representation Bayesian Disease Mapping methods are known inthe statistical and epidemiological sciences to provide a valuable and efficienttechnique of spatial analysis. The Besag, York and Mollie (BYM) model (Besaget al, 1991) is the starting point to provide smoothed estimates of the relativerisk of a disease, and estimates for other effects like the heterogeneity or theclustering effect of a disease, and also to the inclusion of temporal effects, andthe interaction between spatial and temporal effects. Moreover, following theframework established by Knorr-Held (2000), the BYM model can be extended toinclude the interaction model type I (unstructured interaction), type II (temporalinteraction), type III (spatial interaction) and type IV (full spatio - temporalinteraction). The objective of the study was to apply spatio-temporal hierarchicalBayesian disease mapping models to aggregated dengue cases from the city ofBucaramanga for the period 2008 to 2013, searching for a model which could beused as a representation of the disease spread and dynamics in Bucaramanga.

Materials and methods

Dengue cases count for the period 2008 to 2013 from Bucaramanga, Colombia, obtained from the Sistema deVigilancia Epidemiologica SIVIGILA were aggregated by periods of 4 epidemiological weeks, starting at the firstweek of 2008, and by census section according to the Departamento Administrativo Nacional de Estadıstica(DANE), from Census 2005, giving a total of 78 epidemiological periods for the 295 census section. Male andfemale population for five years age groups, for every section were obtained from DANE, following Census 2005.A basal dengue crude rate adjusted by sex and age group was calculated for the 6 year period, and then dividedby the number of study periods (78). The basal dengue crude rate was multiplied by the census sectionpopulation by age and sex, to obtain the expected number of dengue cases by section and period. Followingmodel 1, the observed dengue cases counts Oi in every section were distributed Poisson with parameter θi(relative risk), which depends of the clustering spatial effect ui with intrinsic conditional auto-regressive (CAR)prior, and uniform hyper prior for the CAR variance, and the heterogeneity spatial effect vi with normal prior anduniform hyper prior in equation (3). From Model 1 as the basic model for one period, spatio temporal interactionmodels were built including terms for temporal heterogeneity γ, temporal clustering φ and interaction effect ψ,for the 78 periods.

Oi ∼ Poisson(Eiθi) (1)

Log(θi) = α + vi + ui (2)

ui |u−i ∼ N

∑j∼i

wijuj∑j wij

,σ2u∑j wij

; vi ∼ N(

0, σ2v

);σv ∼ Unif (0, 1);σu ∼ Unif (0, 1) (3)

Hierarchical spatio-temporal models with interaction type I, II, III and IV following Knorr-Held (2000) were fittedto the data with OpenBUGS (Lunn et al 2009) version 3.2.3 rev 1012, using three chains with a burn-in periodof 10000 iterations, a final run of 10000 iterations, a thinning rate of 2, deriving a final sample of 5000 iterationsfor the inference. For every parameter, trace and density plots were done, and Gelman and Geweke test forconvergence were obtained, Model selection was accomplished using Deviance Information Criteria (DIC). Rversion 3.1.2 (R Core Team, 2014) produced the maps and served as interface to OpenBUGS.

Results

Figure 1(a) shows dengue cases byepidemiological period in the years2008 to 2013. Year 2010 had thehighest number of cases, and thecases peak was presented betweenthe periods 3 and 8, with around

500 cases by epidemiologicalperiod. The auto - correlation plot

displays (Figure 1(b)) highauto-correlation for the denguecases between epidemiological

period.

Figure 1: Dengue cases for censussection by epidemiological periodand auto-correlation plot, 2008 to2013

200

400

600

5 10Epidemiologic period

Den

gue

case

s

year

2008

2009

2010

2011

2012

2013

(a) Count

0.0 0.2 0.4 0.6 0.8 1.0

−0.

20.

00.

20.

40.

60.

81.

0

Lag

AC

F

Autocorrelation of Dengue cases by epidemiologic period

(b) Autocorrelation plot

There was 19124 dengue cases inBucaramanga in the study period.

Fifty one percent of the casescorresponds to people under 24

years of age. The highestpercentage of cases was presentedin the 5 to 9 years category (Table

1). Table 2 shows DIC for theinteraction models fitted to the

data, demonstrating that theinteraction type III model,

assuming different hyper prior forclustering and heterogeneity effectfor every period is the model with

the lowest DIC.

Table 1: Total count, row and columnpercentage of dengue cases in the period 2008to 2013

Row % Column %Total F M F M Total

0 to 4 1976 49.2 50.8 10.5 10.2 10.35 to 9 2866 51.1 48.9 15.8 14.3 15.010 to 14 2787 47.6 52.4 14.3 14.9 14.615 to 19 2347 44.1 55.9 11.1 13.3 12.320 to 24 1968 49.0 51.0 10.4 10.2 10.325 to 29 1546 46.2 53.8 7.7 8.5 8.130 to 34 1090 49.1 50.9 5.8 5.6 5.735 to 39 801 48.6 51.4 4.2 4.2 4.240 to 44 748 46.1 53.9 3.7 4.1 3.945 to 49 683 46.9 53.1 3.4 3.7 3.650 to 54 612 51.5 48.5 3.4 3.0 3.255 to 59 481 56.3 43.7 2.9 2.1 2.560 to 64 400 56.0 44.0 2.4 1.8 2.165 to 69 262 56.1 43.9 1.6 1.2 1.470 to 74 238 48.3 51.7 1.2 1.3 1.275 to 79 149 49.0 51.0 0.8 0.8 0.880 or greater 167 49.1 50.9 0.9 0.9 0.9N.A. 3 33.3 66.7 0.0 0.0 0.0Total 19124 48.6 51.4 100 100 100

Table 2: DIC for interaction models type I, II,III and IV. u: spatial clustering, v : spatialheterogeneity, γ: temporal heterogeneity,φ:temporal clustering, ψ:interaction effect. i :spatial index, k : temporal index

Models Dbar Dhat DIC pD

Interaction type I (unstructured)

α + vi + ui + γk + φk + ψik 42600 36240 48960 6360.0α + ui + γk + φk + ψik 42600 35640 49570 6966.0α + vi + ui + φk + ψik 42600 36010 49190 6592.0α + vi + ui + γk + φk 63210 65790 60630 -2583.0α + ui + φk + φk 42610 34980 50230 7625.0

Interaction type II (temporal)

α + vi + ui + γk + φk + ψik 51030 53090 48960 -2067.0α + ui + γk + φk + ψik 51030 52730 49340 -1696.0α + vi + ui + γk + ψik 50980 53250 48720 -2265.0α + vi + ui + γk + φk + ψik 51100 51720 50480 -622.3

Interaction type III (spatial)

α + uik + vik 42630 42290 42960 337.8α + vik + ui 42560 42070 43050 487.0α + vi + ui 42140 40120 44150 2016.0α + vi + uik 42240 41260 43230 981.8

Interaction type IV (spatio - temporal)

α + ui + ψik 41710 38160 45260 3551.0α + ui + vi + ψik 41700 36680 46720 5020.0

Based on the interaction type III model, withdifferent hyper prior, maps of the smoothed

relative risk (logarithm) were built to show theareas with clusters of high risk of dengue cases,

and maps of the spatial clustering effect overthe relative risk by section. Figures 2 and 4

show a sample for the epidemiological periods 1to 6 of the logarithm of the relative risk, for

year 2010 and 2013, and Figures 3 and 5 showin the same periods, maps of the spatial effect

influencing the relative risk.

Figure 2: Relative risk logarithm of dengue cases, year 2010

−73.16 −73.14 −73.12 −73.10

7.08

7.10

7.12

7.14

7.16

7.18

Log. Relative Risk by Epidemiologic period 1

[5.4,6.6)[4.2,5.4)[3.0,4.2)[1.8,3.0)[0.6,1.8)[−0.6,0.6)[−1.8,−0.6)[−3.0,−1.8)[−4.2,−3.0)[−5.4,−4.2)[−6.6,−5.4)

(a) Period 1−73.16 −73.14 −73.12 −73.10

7.08

7.10

7.12

7.14

7.16

7.18


[5.4,6.6)[4.2,5.4)[3.0,4.2)[1.8,3.0)[0.6,1.8)[−0.6,0.6)[−1.8,−0.6)[−3.0,−1.8)[−4.2,−3.0)[−5.4,−4.2)[−6.6,−5.4)

(b) Period 2−73.16 −73.14 −73.12 −73.10

7.08

7.10

7.12

7.14

7.16

7.18


[5.4,6.6)[4.2,5.4)[3.0,4.2)[1.8,3.0)[0.6,1.8)[−0.6,0.6)[−1.8,−0.6)[−3.0,−1.8)[−4.2,−3.0)[−5.4,−4.2)[−6.6,−5.4)

(c) Period 3

−73.16 −73.14 −73.12 −73.10

7.08

7.10

7.12

7.14

7.16

7.18


[5.4,6.6)[4.2,5.4)[3.0,4.2)[1.8,3.0)[0.6,1.8)[−0.6,0.6)[−1.8,−0.6)[−3.0,−1.8)[−4.2,−3.0)[−5.4,−4.2)[−6.6,−5.4)

(d) Period 4−73.16 −73.14 −73.12 −73.10

7.08

7.10

7.12

7.14

7.16

7.18


[5.4,6.6)[4.2,5.4)[3.0,4.2)[1.8,3.0)[0.6,1.8)[−0.6,0.6)[−1.8,−0.6)[−3.0,−1.8)[−4.2,−3.0)[−5.4,−4.2)[−6.6,−5.4)

(e) Period 5−73.16 −73.14 −73.12 −73.10

7.08

7.10

7.12

7.14

7.16

7.18


[5.4,6.6)[4.2,5.4)[3.0,4.2)[1.8,3.0)[0.6,1.8)[−0.6,0.6)[−1.8,−0.6)[−3.0,−1.8)[−4.2,−3.0)[−5.4,−4.2)[−6.6,−5.4)

(f) Period 6

Figure 3: Spatial effect of dengue cases, year 2010

−73.16 −73.14 −73.12 −73.10

7.08

7.10

7.12

7.14

7.16

7.18

Spatial Effect (u)

[2.7,3.3)[2.1,2.7)[1.5,2.1)[0.9,1.5)[0.3,0.9)[−0.3,0.3)[−0.9,−0.3)[−1.5,−0.9)[−2.1,−1.5)[−2.7,−2.1)[−3.3,−2.7)

(a) Period 1−73.16 −73.14 −73.12 −73.10

7.08

7.10

7.12

7.14

7.16

7.18

Spatial Effect (u)

[2.7,3.3)[2.1,2.7)[1.5,2.1)[0.9,1.5)[0.3,0.9)[−0.3,0.3)[−0.9,−0.3)[−1.5,−0.9)[−2.1,−1.5)[−2.7,−2.1)[−3.3,−2.7)

(b) Period 2−73.16 −73.14 −73.12 −73.10

7.08

7.10

7.12

7.14

7.16

7.18

Spatial Effect (u)

[2.7,3.3)[2.1,2.7)[1.5,2.1)[0.9,1.5)[0.3,0.9)[−0.3,0.3)[−0.9,−0.3)[−1.5,−0.9)[−2.1,−1.5)[−2.7,−2.1)[−3.3,−2.7)

(c) Period 3

−73.16 −73.14 −73.12 −73.10

7.08

7.10

7.12

7.14

7.16

7.18

Spatial Effect (u)

[2.7,3.3)[2.1,2.7)[1.5,2.1)[0.9,1.5)[0.3,0.9)[−0.3,0.3)[−0.9,−0.3)[−1.5,−0.9)[−2.1,−1.5)[−2.7,−2.1)[−3.3,−2.7)

(d) Period 4−73.16 −73.14 −73.12 −73.10

7.08

7.10

7.12

7.14

7.16

7.18

Spatial Effect (u)

[2.7,3.3)[2.1,2.7)[1.5,2.1)[0.9,1.5)[0.3,0.9)[−0.3,0.3)[−0.9,−0.3)[−1.5,−0.9)[−2.1,−1.5)[−2.7,−2.1)[−3.3,−2.7)

(e) Period 5−73.16 −73.14 −73.12 −73.10

7.08

7.10

7.12

7.14

7.16

7.18

Spatial Effect (u)

[2.7,3.3)[2.1,2.7)[1.5,2.1)[0.9,1.5)[0.3,0.9)[−0.3,0.3)[−0.9,−0.3)[−1.5,−0.9)[−2.1,−1.5)[−2.7,−2.1)[−3.3,−2.7)

(f) Period 6

Figure 4: Relative risk logarithm of dengue cases, year 2013

−73.16 −73.14 −73.12 −73.10

7.08

7.10

7.12

7.14

7.16

7.18


[5.4,6.6)[4.2,5.4)[3.0,4.2)[1.8,3.0)[0.6,1.8)[−0.6,0.6)[−1.8,−0.6)[−3.0,−1.8)[−4.2,−3.0)[−5.4,−4.2)[−6.6,−5.4)

(a) Period 1−73.16 −73.14 −73.12 −73.10

7.08

7.10

7.12

7.14

7.16

7.18


[5.4,6.6)[4.2,5.4)[3.0,4.2)[1.8,3.0)[0.6,1.8)[−0.6,0.6)[−1.8,−0.6)[−3.0,−1.8)[−4.2,−3.0)[−5.4,−4.2)[−6.6,−5.4)

(b) Period 2−73.16 −73.14 −73.12 −73.10

7.08

7.10

7.12

7.14

7.16

7.18


[5.4,6.6)[4.2,5.4)[3.0,4.2)[1.8,3.0)[0.6,1.8)[−0.6,0.6)[−1.8,−0.6)[−3.0,−1.8)[−4.2,−3.0)[−5.4,−4.2)[−6.6,−5.4)

(c) Period 3

−73.16 −73.14 −73.12 −73.10

7.08

7.10

7.12

7.14

7.16

7.18


[5.4,6.6)[4.2,5.4)[3.0,4.2)[1.8,3.0)[0.6,1.8)[−0.6,0.6)[−1.8,−0.6)[−3.0,−1.8)[−4.2,−3.0)[−5.4,−4.2)[−6.6,−5.4)

(d) Period 4−73.16 −73.14 −73.12 −73.10

7.08

7.10

7.12

7.14

7.16

7.18


[5.4,6.6)[4.2,5.4)[3.0,4.2)[1.8,3.0)[0.6,1.8)[−0.6,0.6)[−1.8,−0.6)[−3.0,−1.8)[−4.2,−3.0)[−5.4,−4.2)[−6.6,−5.4)

(e) Period 5−73.16 −73.14 −73.12 −73.10

7.08

7.10

7.12

7.14

7.16

7.18


[5.4,6.6)[4.2,5.4)[3.0,4.2)[1.8,3.0)[0.6,1.8)[−0.6,0.6)[−1.8,−0.6)[−3.0,−1.8)[−4.2,−3.0)[−5.4,−4.2)[−6.6,−5.4)

(f) Period 6

Figure 5: Spatial effect of dengue cases, year 2013

−73.16 −73.14 −73.12 −73.10

7.08

7.10

7.12

7.14

7.16

7.18

Spatial Effect (u)

[2.7,3.3)[2.1,2.7)[1.5,2.1)[0.9,1.5)[0.3,0.9)[−0.3,0.3)[−0.9,−0.3)[−1.5,−0.9)[−2.1,−1.5)[−2.7,−2.1)[−3.3,−2.7)

(a) Period 1−73.16 −73.14 −73.12 −73.10

7.08

7.10

7.12

7.14

7.16

7.18

Spatial Effect (u)

[2.7,3.3)[2.1,2.7)[1.5,2.1)[0.9,1.5)[0.3,0.9)[−0.3,0.3)[−0.9,−0.3)[−1.5,−0.9)[−2.1,−1.5)[−2.7,−2.1)[−3.3,−2.7)

(b) Period 2−73.16 −73.14 −73.12 −73.10

7.08

7.10

7.12

7.14

7.16

7.18

Spatial Effect (u)

[2.7,3.3)[2.1,2.7)[1.5,2.1)[0.9,1.5)[0.3,0.9)[−0.3,0.3)[−0.9,−0.3)[−1.5,−0.9)[−2.1,−1.5)[−2.7,−2.1)[−3.3,−2.7)

(c) Period 3

−73.16 −73.14 −73.12 −73.10

7.08

7.10

7.12

7.14

7.16

7.18

Spatial Effect (u)

[2.7,3.3)[2.1,2.7)[1.5,2.1)[0.9,1.5)[0.3,0.9)[−0.3,0.3)[−0.9,−0.3)[−1.5,−0.9)[−2.1,−1.5)[−2.7,−2.1)[−3.3,−2.7)

(d) Period 4−73.16 −73.14 −73.12 −73.10

7.08

7.10

7.12

7.14

7.16

7.18

Spatial Effect (u)

[2.7,3.3)[2.1,2.7)[1.5,2.1)[0.9,1.5)[0.3,0.9)[−0.3,0.3)[−0.9,−0.3)[−1.5,−0.9)[−2.1,−1.5)[−2.7,−2.1)[−3.3,−2.7)

(e) Period 5−73.16 −73.14 −73.12 −73.10

7.08

7.10

7.12

7.14

7.16

7.18

Spatial Effect (u)

[2.7,3.3)[2.1,2.7)[1.5,2.1)[0.9,1.5)[0.3,0.9)[−0.3,0.3)[−0.9,−0.3)[−1.5,−0.9)[−2.1,−1.5)[−2.7,−2.1)[−3.3,−2.7)

(f) Period 6

Discusion

Disease mapping using hierarchical Bayesian models is currently well developed and under continuous research. It is applied for many health problems around the world, but there are not manyreports using the technique to show dengue cases in a region in space and time, as we do in the present report. The main difficulty applying the technique is to find actualized information ofpopulation, for the required aggregation level, discriminated by sex, age and socioeconomical status, to provide accurate estimates of the basal risk, but, this is not a problem of the technique,being more a problem for obtaining epidemiological information useful to provide adequate products for the public health decision process, it is an opportunity to make a call to the different actorsof the health system to share information, joining efforts to provide better health services for people.

References

Besag,J., York, J. and Mollie, A. (1991) Bayesian image restoration with two applications in spatial statistics. Annals of the institute of Statistical Mathematics 43, 1 - 59.Departamento Nacional de Estadıstica (DANE). (2013) Censo General 2005. Republica de Colombia. URL: https://www.dane.gov.co/index.php/poblacion-y-demografia/sistema-de-consultaKnorr-Held, Leonhard (2000) Bayesian modelling of inseparable space-time variation in disease risk, Statistics in Medicine,19: 255-2567

Lawson, A., Browne, W.J., Vidal Rodeiro, C. (2003) Disease mapping with WinBUGS and MLwin, John Wiley & Sons, Chichester, England.Lunn, D., Spiegelhalter, D., Thomas, A., Best, N. (2009). The BUGS project: Evolution, critique, and future directions, Statistics in Medicine, 28, 3049-3067.Maestre-Serrano R., Gomez-Camargo D (2013). Dengue: epidemiologıa, polıticas publicas y resistencia de vectores a insecticidas, Revista Ciencias Biomedicas, 4(2), 302-317.R Core Team (2014). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL: http://www.R-project.org/.

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