Development of Bayesian Geostatistical Models with Applications in Malaria Epidemiology

methods enables model fit. A common assumption in geostatistical modeling of malaria data is the stationarity, that is the spatial correlation is a function of distance between locations and not of the locations themselves. This hypothesis does not always hold, especially when modeling malaria over large areas, hence geostatistical models that take into account non-stationarity need to be assessed. Fitting geostatistical models requires repeated inversions of the variance-covariance matrix modeling geographical dependence. For very large number of data locations matrix inversion is considered infeasible. Methods for optimizing this computation are needed. In addition, the relation between environmental factors and malaria risk is often not linear and parametric functions may not be able to determine the shape of the relationship. Nonparametric geostatistical regression models that allow the data to determine the form of the environment-malaria relation need to be further developed and applied in malaria mapping. The aim of this thesis was to develop appropriate models for non-stationary and large geostatistical data that can be applied in the field of malaria epidemiology to produce accurate maps of malaria distribution. The main contributions of this thesis are the development of methods for: (i) analyzing non-stationary malaria survey data; (ii) modeling the nonlinear relation between malaria risk and environment/climatic conditions; (iii) modeling geostatistical mortality data collected at very large number of locations and (iv) adjusting for seasonality and age in mapping heterogeneous malaria survey data. Chapter 2 assessed the spatial effect of bednets on all-cause child mortality by analyzing data from a large follow-up study in an area of high perennial malaria transmission in Kilombero Valley, southern Tanzania. The results indicated a lack of community effect of bednets density possibly because of the homogeneous characteristic of nets coverage and the small proportion of re-treated nets in the study area. The mortality data of this application were collected over 7, 403 locations. To overcome large matrix inversion a Bayesian geostatistical model was developed. This model estimates the spatial process by a subset of locations and approximates the location-specific random effects by a weighted sum of the subset of location-specific random effects with the weights inversely proportional to the separation distance. In Chapter 3 a Bayesian non-stationary model was developed by partitioning the study region into fixed subregions, assuming a separate stationary spatial process in each tile and taking into account between-tile correlation. This methodology was applied on malaria survey data extracted from the MARA database and produced parasitaemia risk maps in Mali. The predictive ability of the non-stationary model was compared with the stationary analogue and the results showed that the stationarity assumption influenced the significance of environmental predictors as well as the the estimation of the spatial parameters. This indicates that the assumptions about the spatial process play an important role in inference. Model validation showed that the non-stationary model had better predictive ability. In addition, experts opinion suggested that the parasitaemia risk map based on the nonstationary model reflects better the malaria situation in Mali. This work revealed that non-stationarity is an essential characteristic which should be considered when mapping malaria. Chapter 4 employed the above non-stationary model to produce maps of malaria risk in West Africa considering as fixed tiles the four agro-ecological zones that partition the region. Non-linearity in the relation between parasitaemia risk and environmental conditions was assessed and it was addressed via P-splines within a Bayesian geostatistical model formulation. The model allowed a separate malaria-environment relation in each zone. The discontinuities at the borders between the zones were avoided since the spatial correlation was modeled by a mixture of spatial processes over the entire study area, with the weights chosen to be exponential functions of the distance between the locations and the centers of the zones corresponding to each of the spatial processes. The above modeling approach is suitable for mapping malaria over areas with an obvious fixed partitioning (i.e. ecological zones). For areas where this is not possible, a nonstationary model was developed in Chapter 5 by allowing the data to decide on the number and shape of the tiles and thus to determine the different spatial processes. The partitioning of the study area was based on random Voronoi tessellations and model parameters were estimated via reversible jump Markov chain Monte Carlo (RJMCMC) due to the variable dimension of the parameter space. In Chapter 6 the feasibility of using the recently developed mathematical malaria transmission models to adjust for age and seasonality in mapping historical malaria survey data was investigated. In particular, the transmission model was employed to translate age heterogeneous survey data from Mali into a common measure of transmission intensity. A Bayesian geostatistical model was fitted on the transmission intensity estimates using as covariates a number of environmental/climatic variables. Bayesian kriging was employed to produce smooth maps of transmission intensity, which were further converted to age specific parasitaemia risk maps. Model validation on a number of test locations showed that this transmission model gives better predictions than modeling directly the prevalence data. This approach was further validated by analyzing the nationally representative malaria surveys data derived from the Malaria Indicator surveys (MIS) in Zambia. Although MIS data do not have the same limitations with the historical data, the purpose of the analyzes was to compare the maps obtained by modeling 1) directly the raw prevalence data and 2) transmission intensity data derived via the transmission model. Both maps predicted similar patterns of malaria risk, however the map based on the transmission model predicted a slightly higher lever of endemicity. The use of transmission models on malaria mapping enables adjusting for seasonality and age dependence of malaria prevalence and it includes all available historical data collected at different age groups

Spatio-temporal malaria transmission patterns in Navrongo demographic surveillance site, northern Ghana

The relationship between entomological measures of malaria transmission intensity and mortality remains uncertain. This is partly because transmission is heterogeneous even within small geographical areas. Studying this relationship requires high resolution, spatially structured, longitudinal entomological data. Geostatistical models that have been used to analyse the spatio-temporal heterogeneity have not considered the uncertainty in both sporozoite rate (SR) and mosquito density data. This study analysed data from Kassena-Nankana districts in northern Ghana to obtain small area estimates of malaria transmission rates allowing for this uncertainty.; Independent Bayesian geostatistical models for sporozoite rate and mosquito density were fitted to produce explicit entomological inoculation rate (EIR) estimates for small areas and short time periods, controlling for environmental factors.; Mosquitoes were trapped from 2,803 unique locations for three years using mainly CDC light traps. Anopheles gambiae constituted 52%, the rest were Anopheles funestus. Mean biting rates for An. funestus and An. gambiae were 32 and 33 respectively. Most bites occurred in September, the wettest month. The sporozoite rates were higher in the dry periods of the last two years compared with the wet period. The annual EIR varied from 1,132 to 157 infective bites. Monthly EIR varied between zero and 388 infective bites. Spatial correlation for SR was lower than that of mosquito densities.; This study confirms the presence of spatio-temporal heterogeneity in malaria transmission within a small geographical area. Spatial variance was stronger than temporal especially in the SR. The estimated EIR will be used in mortality analysis for the area

Spatially Explicit Burden Estimates of Malaria in Tanzania: Bayesian Geostatistical Modeling of the Malaria Indicator Survey Data

A national HIV/AIDS and malaria parasitological survey was carried out in Tanzania in 2007–2008. In this study the parasitological data were analyzed: i) to identify climatic/environmental, socio-economic and interventions factors associated with child malaria risk and ii) to produce a contemporary, high spatial resolution parasitaemia risk map of the country. Bayesian geostatistical models were fitted to assess the association between parasitaemia risk and its determinants. Bayesian kriging was employed to predict malaria risk at unsampled locations across Tanzania and to obtain the uncertainty associated with the predictions. Markov chain Monte Carlo (MCMC) simulation methods were employed for model fit and prediction. Parasitaemia risk estimates were linked to population data and the number of infected children at province level was calculated. Model validation indicated a high predictive ability of the geostatistical model, with 60.00% of the test locations within the 95% credible interval. The results indicate that older children are significantly more likely to test positive for malaria compared with younger children and living in urban areas and better-off households reduces the risk of infection. However, none of the environmental and climatic proxies or the intervention measures were significantly associated with the risk of parasitaemia. Low levels of malaria prevalence were estimated for Zanzibar island. The population-adjusted prevalence ranges from in Kaskazini province (Zanzibar island) to in Mtwara region. The pattern of predicted malaria risk is similar with the previous maps based on historical data, although the estimates are lower. The predicted maps could be used by decision-makers to allocate resources and target interventions in the regions with highest burden of malaria in order to reduce the disease transmission in the country

Urban agriculture and Anopheles habitats in Dar es Salaam, Tanzania.

A cross-sectional survey of agricultural areas, combined with routinely monitored mosquito larval information, was conducted in urban Dar es Salaam, Tanzania, to investigate how agricultural and geographical features may influence the presence of Anopheles larvae. Data were integrated into a geographical information systems framework, and predictors of the presence of Anopheles larvae in farming areas were assessed using multivariate logistic regression with independent random effects. It was found that more than 5% of the study area (total size 16.8 km2) was used for farming in backyard gardens and larger open spaces. The proportion of habitats containing Anopheles larvae was 1.7 times higher in agricultural areas compared to other areas (95% confidence interval = 1.56-1.92). Significant geographic predictors of the presence of Anopheles larvae in gardens included location in lowland areas, proximity to river, and relatively impermeable soils. Agriculture-related predictors comprised specific seedbed types, mid-sized gardens, irrigation by wells, as well as cultivation of sugar cane or leafy vegetables. Negative predictors included small garden size, irrigation by tap water, rainfed production and cultivation of leguminous crops or fruit trees. Although there was an increased chance of finding Anopheles larvae in agricultural sites, it was found that breeding sites originated by urban agriculture account for less than a fifth of all breeding sites of malaria vectors in Dar es Salaam. It is suggested that strategies comprising an integrated malaria control effort in malaria-endemic African cities include participatory involvement of farmers by planting shade trees near larval habitats

Geographical patterns and predictors of malaria risk in Zambia: Bayesian geostatistical modelling of the 2006 Zambia national malaria indicator survey (ZMIS)

BACKGROUND: The Zambia Malaria Indicator Survey (ZMIS) of 2006 was the first nation-wide malaria survey, which combined parasitological data with other malaria indicators such as net use, indoor residual spraying and household related aspects. The survey was carried out by the Zambian Ministry of Health and partners with the objective of estimating the coverage of interventions and malaria related burden in children less than five years. In this study, the ZMIS data were analysed in order (i) to estimate an empirical high-resolution parasitological risk map in the country and (ii) to assess the relation between malaria interventions and parasitaemia risk after adjusting for environmental and socio-economic confounders. METHODS: The parasitological risk was predicted from Bayesian geostatistical and spatially independent models relating parasitaemia risk and environmental/climatic predictors of malaria. A number of models were fitted to capture the (potential) non-linearity in the malaria-environment relation and to identify the elapsing time between environmental effects and parasitaemia risk. These models included covariates (a) in categorical scales and (b) in penalized and basis splines terms. Different model validation methods were used to identify the best fitting model. Model-based risk predictions at unobserved locations were obtained via Bayesian predictive distributions for the best fitting model. RESULTS: Model validation indicated that linear environmental predictors were able to fit the data as well as or even better than more complex non-linear terms and that the data do not support spatial dependence. Overall the averaged population-adjusted parasitaemia risk was 20.0% in children less than five years with the highest risk predicted in the northern (38.3%) province. The odds of parasitaemia in children living in a household with at least one bed net decreases by 40% (CI: 12%, 61%) compared to those without bed nets. CONCLUSIONS: The map of parasitaemia risk together with the prediction error and the population at risk give an important overview of the malaria situation in Zambia. These maps can assist to achieve better resource allocation, health management and to target additional interventions to reduce the burden of malaria in Zambia significantly. Repeated surveys will enable the evaluation of the effectiveness of on-going intervention

Improvement of cardiometabolic markers after fish oil intervention in young Mexican adults and the role of PPARα L162V and PPARγ2 P12A

Polyunsaturated fatty acids (PUFA) contained in fish oil (FO) are ligands for peroxisome proliferator-activated receptors (PPAR) that may induce changes in cardiometabolic markers. Variation in PPAR genes may influence the beneficial responses linked to FO supplementation in young adults. The study aimed to analyze the effect of FO supplementation on glucose metabolism, circulating lipids and inflammation according to PPARα L162V and PPARγ2 P12A genotypes in young Mexican adults. 191 young, non-smoking subjects between 18 and 40 years were included in a one-arm study. Participants were supplemented with 2.7 g/day of EPA+DHA, during six weeks. Dietary analysis, body composition measurements and indicators for glucose metabolism, circulating lipids, and markers for inflammation were analyzed before and after intervention. An overall decrease in triglycerides (TG) and an increase in HS-ω3 index were observed in all subjects [-4.1 mg/dL, (SD:±51.7), P=.02 and 2.6%, (SD:±1.2), P\u3c.001 respectively]. Mean fasting insulin and glycated hemoglobin (HbA1c%) were significantly decreased in all subjects [-0.547mlU/L, (SD:±10.29), P=.034 and-0.07%, (SD:±0.3), P\u3c.001 respectively], whereas there was no change in body composition, fasting glucose, adiponectin and inflammatory markers. Subjects carrying the minor alleles of PPARα L162V and PPARγ2 P12A had higher responses in reduction of TG and fasting insulin respectively. Interestingly, doses below 2.7 g/day (1.8 g/day) were sufficient to induce a significant reduction in fasting insulin and HbA1c% from baseline (P=.019 and P\u3c.001). The observed responses in triglycerides and fasting insulin in the Mexican population give further evidence of the importance of FO supplementation in young people as an early step towards the prevention of cardiometabolic disease. Trial registration: ClinicalTrials.gov NCT02296385

Spatial effects of mosquito bednets on child mortality

<p>Abstract</p> <p>Background</p> <p>Insecticide treated nets (ITN) have been proven to be an effective tool in reducing the burden of malaria. Few randomized clinical trials examined the spatial effect of ITNs on child mortality at a high coverage level, hence it is essential to better understand these effects in real-life situation with varying levels of coverage. We analyzed for the first time data from a large follow-up study in an area of high perennial malaria transmission in southern Tanzania to describe the spatial effects of bednets on all-cause child mortality.</p> <p>Methods</p> <p>The study was carried out between October 2001 and September 2003 in 25 villages in Kilombero Valley, southern Tanzania. Bayesian geostatistical models were fitted to assess the effect of different bednet density measures on child mortality adjusting for possible confounders.</p> <p>Results</p> <p>In the multivariate model addressing potential confounding, the only measure significantly associated with child mortality was the bed net density at household level; we failed to observe additional community effect benefit from bed net coverage in the community.</p> <p>Conclusion</p> <p>In this multiyear, 25 village assessment, despite substantial known inadequate insecticide-treatment for bed nets, the density of household bed net ownership was significantly associated with all cause child mortality reduction. The absence of community effect of bednets in our study area might be explained by (1) the small proportion of nets which are treated with insecticide, and (2) the relative homogeneity of coverage with nets in the area. To reduce malaria transmission for both users and non-users it is important to increase the ITNs and long-lasting nets coverage to at least the present untreated nets coverage.</p

Spatial distribution of the chromosomal forms of anopheles gambiae in Mali

<p>Abstract</p> <p>Background</p> <p>Maps of the distribution of malaria vectors are useful tools for stratification of malaria risk and for selective vector control strategies. Although the distribution of members of the <it>Anopheles gambiae </it>complex is well documented in Africa, a continuous map of the spatial distribution of the chromosomal forms of <it>An. gambiae s.s. </it>is not yet available at country level to support control efforts.</p> <p>Methods</p> <p>Bayesian geostatistical methods were used to produce continuous maps of the spatial distribution of the chromosomal forms of <it>An. gambiae s.s</it>. (Mopti, Bamako, Savanna and their hybrids/recombinants) based on their relative frequencies in relation to climatic and environmental factors in Mali.</p> <p>Results</p> <p>The maps clearly show that each chromosomal form favours a particular defined eco-climatic zone. The Mopti form prefers the dryer northern Savanna and Sahel and the flooded/irrigated areas of the inner delta of the Niger River. The Savanna form favours the Sudan savanna areas, particularly the South and South-Eastern parts of the country (Kayes and Sikasso regions). The Bamako form has a strong preference for specific environmental conditions and it is confined to the Sudan savanna areas around urban Bamako and the Western part of Sikasso region. The hybrids/recombinants favour the Western part of the country (Kayes region) bordering the Republic of Guinea Conakry.</p> <p>Conclusion</p> <p>The maps provide valuable information for selective vector control in Mali (insecticide resistance management) and may serve as a decision support tool for the basis for future malaria control strategies including genetically manipulated mosquitoes.</p

Nutritional and socio-economic factors associated with Plasmodium falciparum infection in children from Equatorial Guinea: results from a nationally representative survey

<p>Abstract</p> <p>Background</p> <p>Malaria has traditionally been a major endemic disease in Equatorial Guinea. Although parasitaemia prevalence on the insular region has been substantially reduced by vector control in the past few years, the prevalence in the mainland remains over 50% in children younger than five years. The aim of this study is to investigate the risk factors for parasitaemia and treatment seeking behaviour for febrile illness at country level, in order to provide evidence that will reinforce the EG National Malaria Control Programme.</p> <p>Methods</p> <p>The study was a cross-sectional survey of children 0 to 5 years old, using a multistaged, stratified, cluster-selected sample at the national level. It included a socio-demographic, health and dietary questionnaires, anthropometric measurements, and thick and thin blood smears to determine the <it>Plasmodium </it>infection. A multivariate logistic regression model was used to determine risk factors for parasitaemia, taking into account the cluster design.</p> <p>Results</p> <p>The overall prevalence of parasitemia was 50.9%; it was higher in rural (58.8%) compared to urban areas (44.0%, p = 0.06). Age was positively associated with parasitemia (p < 0.0001). In rural areas, risk factors included longer distance to health facilities (p = 0.01) and a low proportion of households with access to protected water in the community (p = 0.02). Having had an episode of cough in the 15 days prior to the survey was inversely related to parasitemia (p = 0.04). In urban areas, the risk factors were stunting (p = 0.005), not having taken colostrum (p = 0.01), and that someone in the household slept under a bed net (p = 0.002); maternal antimalarial medication intake during pregnancy (p = 0.003) and the household socio-economic status (p = 0.0002) were negatively associated with parasitemia. Only 55% of children with fever were taken outside their homes for care, and treatment seeking behaviour differed substantially between rural and urban populations.</p> <p>Conclusion</p> <p>Results suggest that a national programme to fight malaria in Equatorial Guinea should take into account the differences between rural and urban communities in relation to risk factors for parasitaemia and treatment seeking behaviour, integrate nutrition programmes, incorporate campaigns on the importance of early treatment, and target appropriately for bed nets to reach the under-fives.</p

Bayesian modelling of geostatistical malaria risk data

Bayesian geostatistical models applied to malaria risk data quantify the environment-disease relations, identify significant environmental predictors of malaria transmission and provide model-based predictions of malaria risk together with their precision. These models are often based on the stationarity assumption which implies that spatial correlation is a function of distance between locations and independent of location. We relax this assumption and analyse malaria survey data in Mali using a Bayesian non-stationary model. Model fit and predictions are based on Markov chain Monte Carlo simulation methods. Model validation compares the predictive ability of the non-stationary\ud model with the stationary analogue. Results indicate that the stationarity assumption is important because it influences the significance of environmental factors and the corresponding malaria risk maps