TB incidence is often linked to environmental exposures and person-person interactions. Recent epidemiological studies have investigated the interaction of risk factors based on demography, en- vironment, genetics and other socio-economic factors. Potential spatial risk patterns can be found according to the interaction of these factors in both space and time. This can be useful in public health planning and decision making (Farmer, 1997). Couceiro et al. (2011) conducted a country- wide analysis of TB and developed a sequence of statistical methods to identify risk factors and high risk areas for pulmonary TB for supporting local interventions. This includes a multivariate regres- sion method with variable selection and identification of spatial clusters based on Kulldorff’s scan statistics (Kulldorff, 1997). Some areas were shown to have higher relative risks; Oporto and Lisbon Metropolitan Areas showed the highest incidence.
Spatial scan statistics can be extended to the space-time domain and include both retrospective (Kulldorf et al., 1998) and prospective (Kulldorf, 2001) methods. Instead of using circular windows as in the spatial scan statistic, the space-time method uses a cylindrical window with the circular part of
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the window relating to space. The space-time scan statistic identifies the most significant cluster area under the null hypothesis that the data are from a constant risk Poisson process. Inference is based on the maximum likelihood ratio of a potential cluster with a null assumption of no clustering; Monte Carlo simulation is used to obtain the approximate distribution of the test statistic. The retrospective scan statistic tests the spatio-temporal cluster for a geographical region over a predetermined time whilst the prospective scan statistics only detects the regions which present excess risk in the last time period. These methods described in above papers are available via the SaTScanTM software
(www.satscan.org).
Using scan statistics, Gomez-Barroso et al. (2013) found that there are 28 significant pure spatial clusters and 20 spatio-temporal clusters, with the most likely cluster formed by 7 municipalities within Greater Barcelona Area. The same areas are seen in most spatio-temporal clusters with time intervals between April 2008 and March 2009. The space-time scan statistic with 25km spatial window and 12 month time window was used to detect spatio-temporal clusters. A similar approach of employing the retrospective space-time scan statistic is also seen in (Zhao et al., 2013) where the most likely cluster is seen in southern-central regions of China between 2006 and 2008. Other examples of space-time scan statistics can be found in Onozuka and Hagihara (2007); the authors cite the identified cluster in the north of Fukuoka as a reason to review control measures for TB.
Nunes (2008) further developed Kulldorf’s space-time scan statistic in two directions: using the mean spatial semivariograms to determine window size and format, then employing geostatistical simula- tions for a posterior validation step after cluster identification. The semivariogram showed evidence of clear spatial patterns in TB incidence (60% spatial contribution) within a 143km range.The semivar- iogram was then used to set scan window parameters. Their results showed a significant high rate of incidence in 3 critical regions (Oporto, Set´ubal and Lisbon) between 2000 and 2004 with a temporal cluster over the whole of Portugal in 2002. A more recent analysis of this issue between 2000 and 2010 (Areias et al., 2015) showed that the most likely space-time clusters were still presented by the Lisbon and Oporto regions with more rapid declines compared to the rest of country.
Randremanana et al. (2010) approached spatio-temporal modelling on TB data using Bayesian meth- ods and a generalised linear mixed model (GLMM). They included the following covariates: number of re-treatments, number of failures, number of losses to follow-up, number of households with two or more cases and distance between residence to treatment centre. They assume a Poisson distribution
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for the observed number of cases and produce model inferences using MCMC. Having adjusted for the covariates, spatial and non-spatial random effects, they found that 19.28% of the neighbourhoods in Antananarivo show significantly higher than average TB risk and that those areas are clustered. The number lost to follow-up and the number of households with two or more cases were found to be important in identifying higher risk areas. Leite da Roza et al. (2012) used a similar Bayesian approach to confirm the spatial patterns of TB in Ribeir˜ao Preto Brazil. The covariates in their Poisson GLMM model included income, education and social vulnerability.
Cao et al. (2016) used a spatiotemporal Bayesian negative-binomial to model observed TB rates; they fitted their model using the WinBUGS software. The paper analysed data for TB cases in 31 provinces of mainland China between 2009 and 2013. Alongside a spatio-temporal interaction term, the identified risk factors included average temperature, rainfall, wind speed, and air pressure.
Kipruto et al. (2013) conducted a county-level analysis of TB incidence in Kenya using a Bayesian Poisson GLMM. The model considers a first order time trend together with structured and unstruc- tured spatial effects between 2012 and 2014. Inference was delivered using the INLA software for R. The results indicated that the Nairobi, Mombasa, Isiolo, Homa bay, Kisumu and Siaya regions were at greater risk of severe TB outbreaks. Gender proportion, HIV proportion, the proportion receiving directly observed treatment (DOT) therapy, average weight and average age were found to be significant risk factors.
In summary, a variety of techniques have historically been used to understand the spatial/spatiotemporal variation in risk of tuberculosis in different regions; some models have included a variety of covariates. The most common two methods are the spatial scan statistic approach and the GLMM approach; both having their own advantages and disadvantages. The spatial scan approach detects clusterings and allows flexible choices of window sizes but it does not adjust for relevant risk factors. Also predeterminate of appropriate window sizes maybe challenging in practice. Other methods mostly considered Bayesian GLMM as such model allows free intake of covariates comparing to scan statis- tics. The spatiotemporal patterns are taken into account by including random effect terms; this avoids the choice of window sizes comparing to scan statistics. However, appropriate assumptions modelling distributions for random effects can be hard to decide.
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interactions between space and time. As a follow-up study to TB in Portugal, knowing that it shows space-time behaviours, the present part in thesis follows the modelling approach of Randremanana et al. (2010), Cao et al. (2016) and Kipruto et al. (2013), using a Bayesian GLMM with spatiotemporal interaction terms. This is because they share similar nature of the data (tuberculosis cases with spatial and temporal information) through an overlapping period of time. The models are fit using the R-INLA package Rue et al. (2009) for its ability to provide fast model fits.