Ecological analysis of social risk factors for Rotavirus infections in Berlin, Germany, 2007–2009
© Wilking et al.; licensee BioMed Central Ltd. 2012
Received: 1 June 2012
Accepted: 16 August 2012
Published: 28 August 2012
Socioeconomic factors are increasingly recognised as related to health inequalities in Germany and are also identified as important contributing factors for an increased risk of acquiring infections. The aim of the present study was to describe in an ecological analysis the impact of different social factors on the risk of acquiring infectious diseases in an urban setting. The specific outcome of interest was the distribution of Rotavirus infections, which are a leading cause of acute gastroenteritis among infants and also a burden in the elderly in Germany. The results may help to generate more specific hypothesis for infectious disease transmission.
We analysed the spatial distribution of hospitalized patients with Rotavirus infections in Berlin, Germany. The association between the small area incidence and different socio-demographic and economic variables was investigated in order to identify spatial relations and risk factors. Our spatial analysis included 447 neighbourhood areas of similar population size in the city of Berlin. We included all laboratory-confirmed cases of patients hospitalized due to Rotavirus infections and notified between 01/01/2007 and 31/12/2009. We excluded travel-associated and nosocomial infections. A spatial Bayesian Poisson regression model was used for the statistical analysis of incidences at neighbourhood level in relation to socio-demographic variables.
Altogether, 2,370 patients fulfilled the case definition. The disease mapping indicates a number of urban quarters to be highly affected by the disease. In the multivariable spatial regression model, two risk factors were identified for infants (<4 year olds): Rotavirus incidence increased by 4.95% for each additional percent of unemployed inhabitants in the neighbourhood (95% credibility interval (CI): 3.10%-6.74%) and by 0.53% for each additional percent of children attending day care in the neighbourhood (95% CI: 0.00%-1.06%). We found no evidence for an association with the proportion of foreign residents, population density, the residential quality of accommodations and resident changes in the neighbourhood.
Neighbourhoods with a high unemployment rate and high day care attendance rate appear to be particularly affected by Rotavirus in the population of Berlin. Public health promotion programs should be developed for the affected areas. Due to the ecological study-design, risk pathways on an individual patient level remain to be elucidated.
KeywordsRotavirus infection Urban health Disease clustering Social environment Risk factors Bayesian inference
Rotavirus infections can be repeatedly acquired in persons from birth to old age, although infants in their first years are mostly affected. The virus is highly infectious, and it can be assumed that after one year about 2/3 of the children have experienced at least one Rotavirus infection and 1/3 a second Rotavirus infection. After two years almost all children have undergone a Rotavirus infection, 2/3 a second and 1/3 a third Rotavirus infection. The appearance of most of these infections is either asymptomatic or an episode of mild enteric symptoms, which an infected person may not notice. Despite this, a large number of infections lead to severe disease courses with diarrhoea, need for hospitalization and, in rare cases death. There are considerable differences, however, in disease severity between primary and subsequent infections.
On a population-level Rotavirus infections are the leading cause of acute gastroenteritis among infants and young children in Germany, in Europe and worldwide. The global disease burden of Rotavirus infections for the health care systems can be regarded as high in developing countries, as well as in countries with more advanced economies. The overall worldwide annual mortality of Rotavirus infection is estimated approximately 440,000 deaths, mostly in infants. Rotavirus associated deaths occur almost exclusively in developing countries.
Family structures and social facilities such as day care centres for infants as well as nursing homes for the elderly can facilitate the transmission of the virus, and repeatedly lead to Rotavirus outbreaks. The community spread also seems to be influenced by the climate, leading to a characteristic seasonality with peaks in spring-time[8, 9]. In addition, nosocomial Rotavirus infections are also frequent.
In 2006, two Rotavirus vaccines (Rotarix and RotaTeq) were licensed and introduced in Germany[11, 12].Although currently under consideration by the German Standing Committee on Vaccination, the vaccines are not yet integrated in the routine childhood immunization schedule in Germany. Given the potential for a change in community spread due to expected differences in vaccine coverage in the population, there may thus be a prevalence of groups at special risk that are not currently in focus, but should be. Further understanding of risk factors for Rotavirus distribution on a population level is therefore needed in order to guide future decisions.
Social environments and health outcomes
The importance of links between the social environment and infectious diseases has long been of focus in the developing world, since these regions are burdened with issues that increase the burden of infectious diseases, such as poverty and suboptimal living conditions. Although less pronounced, issues like income inequality are important and relevant in Europe as well as in other advanced economic regions. A part of these groups contain individuals from a marginalized and segregated subpopulation that may not be fully integrated into the general population. In Germany, where poverty and poor housing conditions are also important issues, health inequalities are on the rise due to changes in, e.g., economy and migration[14, 15]. Recent position papers have urged the importance of identifying vulnerable groups on an ecological level complementing strictly individual-based epidemiology on risk factors with population-based approaches, where socioeconomic factors are linked to health outcomes on a spatial aggregate level becomes important[17, 18].
Due to its eventful history Berlin is a city with highly diverse communities in distinctive neighbourhoods, which makes it an ideal prototype to study these influences on a spatial level. In the future these neighbourhoods could form a new level of surveillance, mitigation and containment of infectious diseases in Berlin and elsewhere.
While people often seek out their place of residence based on their social and financial (socioeconomic) status, the social characteristics in those places of residence might reflexively influence people’s social status. These two forces – seeking out and being influenced by – socioeconomic status might contribute to the formation of distinct living environments, which reflect the social diversity of societies especially in metropolitan areas. This can have an impact on the transmission of infectious diseases, which was shown for North American cities and which might also be true for European cities.
Spatial regression analysis of surveillance data
There has been some recent work in the literature that uses mathematical modeling to describe the dynamics of rotavirus at the population level. Models are calibrated using time series data at the national or state level. Since the effect of socio-demographic variables is expected to happen at a much more detailed spatial scale, a more spatial oriented analysis approach is needed for such investigation. However, a good spatial resolution of health data is often in conflict with data privacy issues and small scale spatial analysis of infectious disease data is accordingly underdeveloped in practice. Another hindrance is that advanced statistical methodology is needed in order to properly take the spatial nature of such data into account: if one falsely relies on the common statistical assumption of observations being independent and identically distributed, one is overrating the value of information in the data and might obtain wrong conclusions in statistical significance tests. Thus, statistical methodology and corresponding software implementations should go beyond the independence assumption for such data. Spatial Bayesian regression models are the most common analysis tool in such situations. These models have been successfully applied, e.g. for cancer incidence data, mortality data, but also for worldwide malaria incidence, nationwide surveillance data on Shiga toxin-producing Escherichia coli in Germany and tuberculosis in urban setting in Brazil. Recently, the integrated nested Laplace approximation (INLA) approach together with its implementation has provided a new and efficient method to perform statistical inference for spatial regression models including Gaussian random effects. For example, the method has already been successfully applied for infectious disease surveillance data in veterinary medicine in Switzerland[29, 30]. We employ this technique for the analysis of Rotavirus incidence – see methods section for details. Thus, our analysis covers all aspects of small area infectious disease epidemiology while simultaneously employing advanced statistical methods for the analysis.
The objective of this study was to describe the small-area spatial distribution of the incidence of hospitalized Rotavirus cases in Berlin. A further aim was to explain parts of the spatial distribution pattern using socio-economic and socio-demographic variables.
Age distribution of hospitalized Rotavirus cases in Berlin 2007-2009
Number of cases (percent of all cases)
Average yearly incidence [95% CIa] (in 100,000)
Median length of hospitalization [IQRb] (days)
Male gender (%)
Part of an outbreak (%)
1 - <2 years
2 - <3 years
3 - <4 years
4 - <6 years
6 - < 20 years
20 - < 60 years
Estimation results of univariable and multivariable analysis (age group from <1 to <4 years)
Excess risk ratio (95% CI)
Excess risk ratio (95% CI)
3.94 (2.37, 5.49)
4.95 (3.10, 6.74)
0.56 (−0.30, 1.42)
−0.04 (−1.01, 0.93)
0.62 (−0.31, 1.56)
−0.25 (−1.36, 0.88)
0.04 (−0.04, 0.12)
−0.00 (−0.09, 0.08)
Basic residential qualitya
−0.02 (−0.20, 0.15)
−0.14 (−0.32, 0.04)
Day care attendanceb
0.25 (0.26, 0.77)
0.53 (0.00, 1.06)
1 - <2 yearsa
−30.89 (−37.72, -23.60)
−43.74 (−56.04, -29.19)
2 - <3 yearsa
−77.34 (−80.64, -73.74)
−84.10 (−89.65, -76.66)
3 - <4 yearsa
−91.60 (−93.49, -89.46)
−94.50 (−96.84, -91.12)
Estimation results of univariable and multivariable analysis (age group from 60 years and above)
Excess risk ratio (95% CI)
Excess risk ratio (95% CI)
0.87 (−15.15, 18.70)
−2.56 (−20.30, 17.69)
2.00 (−2.65, 6.78)
4.59 (−1.18, 10.56)
1.12 (−1.13, 3.29)
1.86 (−0.93, 4.45)
−0.95 (−3.45, -1.57)
−1.83 (−4.92, 1.27)
−0.25 (−0.49, -0.01)
−0.30 (−0.56, -0.04)
Basic residential qualitya
0.02 (−0.42, 0.45)
−0.01 (−0.49, 0.46)
Analysis of spatial effects
We identified associations between socioeconomic factors as risk factors and the incidence of severe Rotavirus infections leading to hospitalization in an urban setting in Germany. In addition, it is the first time that socio-demographic and socio-economic factors are analysed to explain variations of infectious diseases in Berlin at such a detailed spatial scale. This study suggests that socioeconomic risk factors may affect the distribution of infectious diseases in Berlin, and that spatially detailed information about infectious disease cases can provide more specific information about these effects.
Both the occurrence and perhaps the severity of disease could also be explained by spatial variations in vaccination coverage. WHO recommends that a surveillance system for severe Rotavirus infections should be in place to monitor the effect of universal childhood rotavirus vaccination once implemented. The German surveillance system is recognized as being able to monitor the impact of the vaccines. The expected changes in burden of disease could be monitored more specifically if information on socioeconomic determinants for specific areas and subgroups would be assignable and accessible for analysis. Unfortunately, data on vaccination coverage with the required spatial precision as in our study is not available. In our study, unemployment is identified as a strong risk factor for disease. The investigation of the underlying causality of this socioeconomic factor requires the setup of appropriate analytical strategies involving multiple interrelated variables[17, 18]. These include proximal biologic precursors (e.g. nutrition) and more distal and contextual risk factors like behaviour or unemployment as psychological burden. Unemployment in families is related to child poverty and maybe connected to poor access to medical care (i.e. Rotavirus vaccination is not generally covered by health insurance programs). Alternatively, unemployment could act as a cofactor for educational background or different risk behaviour regarding hygiene and oral rehydration.
Limitations and strength
The interpretation of the results is limited by the ecological design of the study. The statistical association of unemployment can be explained by the influence of the social situation of the neighbourhoods on the frequency and severity of the disease in all children in the neighbourhoods with high levels of unemployment. This would be a true ecological effect. Alternatively, the effect on the frequency and severity of the disease was observed in the underprivileged sub-group only. Furthermore, it is conceivable that the likelihood of hospitalization is increased in children of families burdened by unemployment, due to differential access to hospital services or, in cases of gastroenteritis, to different routines for referral by general practitioners. Although an analysis with non-hospitalized Rotavirus cases included shows similar associations (data not shown). Similarly, the association of day care attendance rate can be explained as an increased risk in all children attending day care of the respective neighbourhood or only fraction attending day care in the respective neighbourhood.
Altogether, the issue of bias remains a major limitation of any ecological analysis such as our. As a consequence, the results of our analysis should be interpreted with care – not only because of possible ecological bias, but also due to possible confounding due to location, i.e. changes in covariate effects due to the addition of a location based structured random variable in the model.
However, despite its limitations ecological analyses remain an important hypothesis generating tool where already readily available registry data can be used to provide first answers to questions of public health importance. A confirmation of the results by an individual-level based analyses, e.g. through a case–control study, would be the natural next step.
Reporting of laboratory-notified Rotavirus infections in Berlin is mandatory with continuous case definition; however, eligibility for testing is not defined and therefore case ascertainment could vary inside the study area. Under the German reimbursement system for hospitalization charges, hospitals receive higher payments for cases of acute gastrointestinal enteritis with a confirmed infectious agent and therefore have a high incentive for the commission of Rotavirus diagnostic. Further steps in quantifying possible consequences of reporting artefacts could be to perform a joint modelling together with another gastrointestinal disease such as, e.g. Norovirus, as done in Held et al.. However, we believe that our analysis restricted to hospitalized cases only provides results that reduce ascertainment bias.
The results of our study emphasize the relevance of spatial regression models including spatially structured effects and unstructured spatial heterogeneity for the detection of risk factors.
Appropriate targeting of public health promotion programs could be achieved by combining the criteria of neighbourhood with the risk groups identified in this study. The influence of the day care attendance rate indicates that high requirements for hygiene in child day-care facilities should be regularly checked and routinely maintained. Due to different policies in Germany, the attendance rates for day care centres of infants are unequal. Since 2008, a federal law supports the expansion of day care centres, and realizes the legal claim of all parents throughout Germany to a place their child in a day care centre in 2013. Thus, this difference is of future relevance for public health services in regions in West-Berlin and Western Germany with expected increase of children attending day care in the next years.
Subsequent small-area studies of Rotavirus or other infectious diseases could provide further insight into spatial effects on disease risk. Individual based risk factors have to be refined and integrated in the future.
Geo-referencing and disease mapping
where y i,a is the observed number of cases of the disease in the age strata a of the i’th neighbourhood and n i,a is the number of residents in the strata a of the i’th neighbourhood. In our case, a denotes the 13 age groups (<1 year, 1- < 2 years, 2- < 3 years, 3- < 4 years, 4- < 6 years, 6- < 10 years, 10- < 20 years, 20- < 30 years, 30- < 40 years, 40- < 50 years, 50- < 60 years, 60- < 70 years, ≥70 years). For the comparison of expected and observed counts we produced values for the absolute disease excess (z i ) in a neighbourhood i as z i = y i -e i , see Figure1. We choose to illustrate absolute excess in this descriptive figure, since absolute excess immediately contains information about the relevance of the differences (as opposite to relative risk), which is favourable when communicating results on a purely descriptive basis. Note that the subsequent modelling happens on a relative risk scale.
Spatial Bayesian Poisson regression model
Summary statistics of variables in 447 neighbourhoods in Berlin
Proportion of unemployed persons in percent of inhabitants between 15 and 65 years of age. Source: Senate of Berlin's Department for Urban Development. The unemployment rate is highly correlated to other job market related variables. Key variable for the economic status of the inhabitants in the respective neighbourhood. Query date: 31 December, 2008
Sum of all moving to and away from the neighbourhood in percent of inhabitants in the year 2008. Key variable for the dynamic and extent of environmental changes in the area (i.e. gentrification). Source: Senate of Berlin's Department for Urban Development. Query date: 31 December, 2008
Proportion of foreign residents to all inhabitants. Source: Senate of Berlin's Department for Urban Development. Query date: 31 December, 2008
Population density defined as number of inhabitants per hectare settlement area of the neighbourhood. This is a possible proxy for the average frequency of social contact in the respective neighbourhood. Source: Senate of Berlin's Department for Urban Development. Query date: 31 December, 2008
Basic residential quality1
Basic residential quality defined as the proportion of the lowest residential quality class on all three quality classes of the Berlin rent index in the year 2007. Source: Senate of Berlin's Department for Health, Environment and Consumer Protection
Proportion of inhabitants < 4 years in relation to all inhabitants in the neighbourhoods in percent.
Day care attendance (<1 year)1
Proportion of children attending day care centres to all children in the age groups: <1 year; 1 - <2 years; 2 - <3 years and 3 - <4 years. Source: Senate of Berlin's Department for Education, Science and Research. Query date: 31 December, 2009
Day care attendance (1 - <2 years)1
Day care attendance (2 - <3 years)1
Day care attendance (3 - <4 years)1
Here, n i,a denotes the population in neighbourhood i in age group a and z i denotes the vector of explanatory variables which contains the age groups as factor variable. The intercept μ was the estimated value when all predictors were zero (continuous covariates) or at their baseline values (discrete covariates), respectively. For the Bayesian inference, we took the integrated nested Laplace approximation (INLA) approach as introduced by and implemented in the R package R-INLA[40, 41]. Altogether, our statistical approach resembles the one used before by Schrödle et al.[29, 30]. Deviance information criterion (DIC) was used as a measure for comparing Bayesian models, since it provides a trade-off between model fit and model complexity. Thus, we searched for the model with the lowest DIC.
Because we assumed different risk profiles for infants and elderly, the regression analysis was performed in two separate models: One for infants, i.e. the <4 year old containing four age groups (<1, 1- < 2, 2- < 3 and 3- < 4 years) and one for elderly, i.e. the ≥60-years-old containing a single age group. In the infant model the age group specific population was included as an offset variable to control for the strong effect of age in the infant model. Following the suggestions in Rothman et al. we decided to start the investigation by performing a univariable spatial modelling of all potential risk factors adjusting only for the strong effect of age using the above model. The actual underlying multiple-inference question of identifying relevant risk factors while adjusting for the joint conglomerate of risk factors was addressed by fitting a single multivariable model containing all potential risk factors. Thus, we abandon any type of step-wise model selection, which is known to have low efficiency and poor power. Based on DIC, a health-district effect was only included in the infant model.
We used Bayesian inference and report the resulting excess risk ratios as point estimate (posterior mean) and 95% credibility intervals as a quantification of parameter uncertainty. Residual relative risk of the combined structured and unstructured spatial effects, i.e. the posterior median of exp(ψ i + υ i ), and of the 12 health districts, i.e. exp(α j(i) ), for the final multivariable regression model of the infants <4 years were mapped. In a sensitivity analysis (not-shown), possible non-linearity of the covariates was investigated; see Natário and Knorr-Held for a discussion of the method and the consequences of ignoring non-linearity. However, our analyses showed that linear effects of the covariates were adequate for our purposes.
All computations and map visualizations were done in R v. 2.15.0.
The authors would like to thank most cordially the staff members of the Infectious Disease Protection and Epidemiology Unit at the State Office for Health and Social Affairs (LAGeSo) for their essential support; the Statistical Bureau Berlin-Brandenburg and the Senate of Berlin's Department for Urban development for the provision of data; and the coordinators of EPIET and PAE for comments on the manuscript.
- Bishop RF: Natural history of human rotavirus infection. ArchVirolSupp. 1996, 12: 119-Google Scholar
- Velázquez FR, Matson DO, Calva JJ, Guerrero ML, Morrow AL, Carter-Campbell S, Glass RI, Estes MK, Pickering LK, Ruiz-Palacios GM: Rotavirus infection in infants as protection against subsequent infections. N Engl J Med. 1996, 335: 1022-1028. 10.1056/NEJM199610033351404.View ArticlePubMedGoogle Scholar
- Parashar UD, Gibson CJ, Bresse JS, Glass RI: Rotavirus and severe childhood diarrhea. Emerg Infect Dis. 2006, 12: 304-306. 10.3201/eid1202.050006.PubMed CentralView ArticlePubMedGoogle Scholar
- Koch J, Wiese-Posselt M: Epidemiology of rotavirus infections in children < 5 years of age, Germany, 2001–2008. Pediatr Infect Dis. 2011, 30: 112-117. 10.1097/INF.0b013e3181f1eb21.View ArticleGoogle Scholar
- Soriano-Gabarro M, Mrukowicz J, Vesikari T, Verstraeten T: Burden of rotavirus disease in European Union countries. Pediatr Infect Dis. 2006, 25: S7-S11. 10.1097/01.inf.0000197622.98559.01.View ArticleGoogle Scholar
- Parashar UD, Bresee JS, Gentsch JR, Glass RI: Rotavirus. Emerg Infect Dis. 1998, 4: 561-570. 10.3201/eid0404.980406.PubMed CentralView ArticlePubMedGoogle Scholar
- Parashar UD, Hummelman EG, Bresee JS, Miller MA, Glass RI: Global illness and deaths caused by rotavirus disease in children. Emerg Infect Dis. 2003, 9: 565-572. 10.3201/eid0905.020562.PubMed CentralView ArticlePubMedGoogle Scholar
- Atchison C, Lopman B, Edmunds WJ: Modelling the seasonality of rotavirus disease and the impact of vaccination in England and Wales. Vaccine. 2010, 28: 3118-3126. 10.1016/j.vaccine.2010.02.060.View ArticlePubMedGoogle Scholar
- Cook SM, Glass RI, LeBaron CW, Ho MS: Global seasonality of rotavirus infections. Bull World Health Organ. 1990, 68: 171-177.PubMed CentralPubMedGoogle Scholar
- Spackova M, Altmann D, Eckmanns T, Koch J, Krause G: High Level of Gastrointestinal Nosocomial Infections in the German Surveillance System, 2002–2008. Infect Control Hosp Epidemiol. 2010, 31: 1273-1278. 10.1086/657133.View ArticlePubMedGoogle Scholar
- European Medicines Agency (EMEA): European public assessment report: Rotarix.http://www.emea.europa.eu/humandocs/Humans/EPAR/rotarix/rotarix.htm,
- European Medicines Agency (EMEA): European public assessment report: Rotateq.http://www.emea.europa.eu/humandocs/Humans/EPAR/rotateq/rotateq.htm,
- Semenza JC, Suk JE, Tsolova S, Gillespie IA, Mook P, Little CL, Grant KA, McLauchlin J, Kafatos G, Randolph SE: Social determinants of infectious diseases: a public health priority. Euro Surveill. 2010, 15: 2-4.PubMedGoogle Scholar
- Kroll LE, Lampert T: Changing health inequalities in Germany from 1994 to 2008 between employed and unemployed adults. Int J Public Health. 2011, 56: 1-11. 10.1007/s00038-010-0218-4.View ArticleGoogle Scholar
- Zeeb H, Razum O: Epidemiological research on migrant health in Germany. An overview In German: Epidemiologische Studien in der Migrationsforschung. Bundesgesundheitsblatt. 2006, 49: 845-852. 10.1007/s00103-006-0017-5.View ArticleGoogle Scholar
- European Centre for Disease Prevention and Control (ECDC): Meeting Report: ECDC Workshop on social determinants and communicable diseases.http://www.ecdc.europa.eu/en/publications/Publications/0903_MER_Social_Determinants_and_Communicable_Diseases.pdf,
- Diez-Roux AV: Estimating neighborhood health effects: the challenges of causal inference in a complex world. Soc Sci Med. 2004, 58: 1953-1960. 10.1016/S0277-9536(03)00414-3.View ArticlePubMedGoogle Scholar
- Galea S: Macrosocial Determinants of Population Health. 2007, New York: SpringerGoogle Scholar
- Galea S, Vlahov D: 2005, Springer: Handbook of Urban Health New York
- Acevedo-Garcia D: Residential segregation and the epidemiology of infectious diseases. Soc Sci Med. 2000, 51: 1143-1161. 10.1016/S0277-9536(00)00016-2.View ArticlePubMedGoogle Scholar
- Pitzer VE, Viboud C, Simonsen L, Steiner C, Panozzo CA, Alonso WJ, Miller MA, Glass RI, Glasser JW, Parashar UD: Demographic variability, vaccination, and the spatiotemporal dynamics of rotavirus epidemics. Science. 2009, 325: 290-294. 10.1126/science.1172330.PubMed CentralView ArticlePubMedGoogle Scholar
- Besag J, York J, Mollié A: Bayesian image restoration, with two applications in spatial statistics. Ann Inst Stat Math. 1991, 43: 1-20. 10.1007/BF00116466.View ArticleGoogle Scholar
- Carsin AE, Sharp L, Comber H: Geographical, urban/rural and socioeconomic variations in nonmelanoma skin cancer incidence: a population based study in Ireland. BJD. 2011, 164: 822-829. 10.1111/j.1365-2133.2011.10238.x.View ArticleGoogle Scholar
- Kazembe LN, Mpeketula PMG: Quantifying Spatial Disparities in Neonatal Mortality Using a Structured Additive Regression Model. PloS one. 2010, 5: e11180-10.1371/journal.pone.0011180.PubMed CentralView ArticlePubMedGoogle Scholar
- Hay SI, Guerra CA, Gething PW, Patil AP, Tatem AJ, Noor AM, Kabaria CW, Manh BH, Elyazar IRF, Brooker S: A world malaria map: Plasmodium falciparum endemicity in 2007. PLoS Medicine. 2009, 6: e1000048-PubMed CentralView ArticlePubMedGoogle Scholar
- Frank C, Kapfhammer S, Werber D, Stark K, Held L: Cattle density and Shiga toxin-producing Escherichia coli infection in Germany: increased risk for most but not all serogroups. Vector Borne Zoonotic Dis. 2008, 8: 635-644. 10.1089/vbz.2007.0237.View ArticlePubMedGoogle Scholar
- Souza WV, Carvalho MS, Albuquerque MFPM, Barcellos CC, Ximenes RAA: Tuberculosis in intra urban settings: a Bayesian approach. Trop Med Int Health. 2007, 12: 323-330. 10.1111/j.1365-3156.2006.01797.x.View ArticlePubMedGoogle Scholar
- Rue H, Martino S, Chopin N: Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. J Royal StatSoc B. 2009, 71: 319-392. 10.1111/j.1467-9868.2008.00700.x.View ArticleGoogle Scholar
- Schrödle B, Held L: A primer on disease mapping and ecological regression using INLA. Computational statistics. 2009, 26: 241-258.View ArticleGoogle Scholar
- Schrödle B, Held L, Riebler A, Danuser J: Using integrated nested Laplace approximations for the evaluation of veterinary surveillance data from Switzerland: a case study. JRoyal StatSocB C (Applied Statistics). 2010, 60: 261-279.View ArticleGoogle Scholar
- World Health Organisation (WHO): World Health Organisation (WHO). Rotavirus vaccines - WHO position paper Weekly epidemiological record. 2007, 82: 285-296.Google Scholar
- Greenland S: Divergent biases in ecologic and individual-level studies. Stat Med. 1992, 11: 1209-1223. 10.1002/sim.4780110907.View ArticlePubMedGoogle Scholar
- Clayton DG, Bernardinelli L, Montomoli C: Spatial correlation in ecological analysis. Int J Epidemiol. 1993, 22: 1193-1202. 10.1093/ije/22.6.1193.View ArticlePubMedGoogle Scholar
- Held L, Graziano G, Frank C, Rue H: Joint spatial analysis of gastrointestinal infectious diseases. Stat Methods Med Res. 2006, 15: 465-480.PubMedGoogle Scholar
- German Childcare Funding Act - Kinderförderungsgesetz (Kifög): Â§ 24 SGB VII in der Fassung des Artikel 1 Nr. 2008, 7 (KiföG). BundesgesetzblattGoogle Scholar
- Faensen D, Krause G: SurvStat@ RKI-a web-based solution to query surveillance data in Germany. Euro Surveill. 2004, 8: 5-7.Google Scholar
- Bömermann H, Jahn S, Nelius K: Lebensweltlich orientierte Räume im Regionalen Bezugssystem. Werkstattbericht zum Projekt Vereinheitlichung von Planungsräumen. Berliner Statistik, Statistische Monatsschrift. 2006, 8: 366-370.Google Scholar
- Senate of Berlin's Department for Urban Development: Lebensweltlich orientierte Räume (LOR) in Berlin.https://www.stadtentwicklung.berlin.de/planen/basisdaten_stadtentwicklung/lor/index.shtml,
- Rue H, Held L: Gaussian Markov random fields: theory and applications. 2005, Chapman & HallView ArticleGoogle Scholar
- Martino S, Rue H: Implementing approximate Bayesian inference using Integrated Nested Laplace Approximation: A manual for the inla program.http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.142.3845,
- R Development Core Team: R: A language and environment for statistical computing. 2011, Vienna, Austria: R Foundation for Statistical ComputingGoogle Scholar
- Spiegelhalter DJ, Best NG, Carlin BP, Van der Linde A: Bayesian measures of model complexity and fit. JRoyal StatSocB. 2002, 64: 583-639.Google Scholar
- Rothman KJ, Greenland S, Lash TL: Fundamentals of Epidemiologic Data Analysis. 2008, In Modern epidemiology 3rd Edition, Lippincott Williams & Wilkins, 237-Google Scholar
- Natário I, Knorr-Held L: Non-Parametric Ecological Regression and Spatial variation Biometrical Journal. 2003, 45: 670-688.Google Scholar
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.