Fitting Generalized Linear Mixed Models For Point-Referenced Spatial Data

Non-Gaussian point-referenced spatial data are frequently modeled using generalized linear mixed models (GLMM) with location-specific random effects. Spatial dependence can be introduced in the covariance matrix of the random effects. Maximum likelihood-based or Bayesian estimation implemented via Markov chain Monte Carlo (MCMC) for such models is computationally demanding especially for large sample sizes because of the large number of random effects and the inversion of the covariance matrix involved in the likelihood. We review three fitting procedures, the Penalized Quasi Likelihood method, the MCMC, and the Sampling-Importance-Resampling method. They are assessed in terms of estimation accuracy, ease of implementation, and computational efficiency using a spatially structured dataset on infant mortality from Mali

Bayesian geostatistical modelling of high-resolution NO2 exposure in Europe combining data from monitors, satellites and chemical transport models

Bayesian geostatistical regression (GR) models estimate air pollution exposure at high spatial resolution, quantify the prediction uncertainty and provide probabilistic inference on the exceedance of air quality thresholds. However, due to high computational burden, previous GR models have provided gridded ambient nitrogen dioxide (NO; 2; ) concentrations at smaller areas of investigation. Here, we applied these models to estimate yearly averaged NO; 2; concentrations at 1 km; 2; spatial resolution across 44 European countries, integrating information from in situ monitoring stations, satellites and chemical transport model (CTM) simulations. The tropospheric values of NO; 2; derived from the ozone monitoring instrument (OMI) onboard the National Aeronautics and Space Administration's (NASA's) Aura satellite were converted to near ground NO; 2; concentration proxies using simulations from the 3-D global CTM (GEOS-Chem) at 0.5° × 0.625°spatial resolution and surface-to-column NO; 2; ratios. Simulations from the Ensemble of regional CTMs at spatial resolution of 0.1° × 0.1°were extracted from the Copernicus atmosphere monitoring service (CAMS). The contribution of these covariates to the predictive capability of geostatistical models was for the first time evaluated here through a rigorous model selection procedure along with additional continental high-resolution satellite-derived products, including novel data from the pan-European Copernicus land monitoring service (CLMS). The results have shown that the conversion of columnar NO; 2; values to surface quasi-observations yielded models with slightly better predictive ability and lower uncertainty. Nonetheless, the use of higher resolution CAMS-Ensemble simulations as covariates in GR models granted the most accurate surface NO; 2; estimates, showing that, in 2016, 16.17 (95% C.I. 6.34-29.96) million people in Europe, representing 2.97% (95% C.I. 1.16% - 5.50%) of the total population, were exposed to levels above the EU directive and WHO air quality guidelines threshold for NO; 2; . Our estimates are readily available to policy makers and scientists assessing the burden of disease attributable to NO; 2; in 2016

Relationship Between Child Survival and Malaria Transmission: An Analysis of the Malaria Transmission Intensity and Mortality Burden Across Africa (MTIMBA) Project Data in Rufiji Demographic Surveillance System, Tanzania.

The precise nature of the relationship between malaria mortality and levels of transmission is unclear. Due to methodological limitations, earlier efforts to assess the linkage have lead to inconclusive results. The malaria transmission intensity and mortality burden across Africa (MTIMBA) project initiated by the INDEPTH Network collected longitudinally entomological data within a number of sites in sub-Saharan Africa to study this relationship. This work linked the MTIMBA entomology database with the routinely collected vital events within the Rufiji Demographic Surveillance System to analyse the transmission-mortality relation in the region. Bayesian Bernoulli spatio-temporal Cox proportional hazards models with village clustering, adjusted for age and insecticide-treated nets (ITNs), were fitted to assess the relation between mortality and malaria transmission measured by entomology inoculation rate (EIR). EIR was predicted at household locations using transmission models and it was incorporated in the model as a covariate with measure of uncertainty. Effects of covariates estimated by the model are reported as hazard ratios (HR) with 95% Bayesian confidence interval (BCI) and spatial and temporal parameters are presented. Separate analysis was carried out for neonates, infants and children 1-4 years of age. No significant relation between all-cause mortality and intensity of malaria transmission was indicated at any age in childhood. However, a strong age effect was shown. Comparing effects of ITN and EIR on mortality at different age categories, a decrease in protective efficacy of ITN was observed (i.e. neonates: HR = 0.65; 95% BCI: 0.39-1.05; infants: HR = 0.72; 95% BCI:0.48-1.07; children 1-4 years: HR = 0.88; 95% BCI: 0.62-1.23) and reduction on the effect of malaria transmission exposure was detected (i.e. neonates: HR = 1.15; 95% BCI:0.95-1.36; infants: HR = 1.13; 95% BCI:0.98-1.25; children 1-4 years: HR = 1.04; 95% BCI:0.89-1.18). A very strong spatial correlation was also observed. These results imply that assessing the malaria transmission-mortality relation involves more than the knowledge on the performance of interventions and control measures. This relation depends on the levels of malaria endemicity and transmission intensity, which varies significantly between different settings. Thus, sub-regions analyses are necessary to validate and assess reproducibility of findings

Rise in Malaria Incidence Rates in South Africa: A Small-Area Spatial Analysis of Variation in Time Trends

Using Bayesian statistical models, the authors investigated spatial and temporal variations in small-area malaria incidence rates for the period mid-1986 to mid-1999 for two districts in northern KwaZulu Natal, South Africa. Maps of spatially smoothed incidence rates at different time points and spatially smoothed time trends in incidence gave a visual impression of the highest increase in incidence occurring where incidence rates previously had been lowest. This was confirmed by conditional autoregressive models, which showed that there was a significant negative association between time trends and smoothed baseline incidence before the steady rise in caseloads began. Growth rates also appeared to be higher in the areas close to the Mozambican border. The main findings of this analysis were that: 1) the spatial distribution of the rise in malaria incidence is uneven and strongly suggests a geographic expansion of high-malaria-risk areas; 2) there is evidence of a stabilization of incidence in areas that had the highest rates before the current escalation of rates began; and 3) areas immediately adjoining the Mozambican border appear to have undergone larger increases in incidence, in contrast to the general pattern of low growth in the more northern, high-baseline-incidence areas, but this was not confirmed by modeling. Smoothing of small-area maps of incidence and growth in incidence (trend) is important for interpretation of the spatial distribution of disease incidence and the spatial distribution of rapid changes in disease incidenc

Spatio-temporal statistics : applications in epidemiology, veterinary medicine and ecology

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Relationship between the entomologic inoculation rate and the force of infection for Plasmodium falciparum malaria.

We propose a stochastic model for the relationship between the entomologic inoculation rate (EIR) for Plasmodium falciparum malaria and the force of infection in endemic areas. The model incorporates effects of increased exposure to mosquito bites as a result of the growth in body surface area with the age of the host, naturally acquired pre-erythrocytic immunity, and the reduction in the proportion of entomologically assessed inoculations leading to infection, as the EIR increases. It is fitted to multiple datasets from field studies of the relationship between malaria infection and the EIR. We propose that this model can account for non-monotonic relationships between the age of the host and the parasite prevalence and incidence of disease. It provides a parsimonious explanation for the faster acquisition of natural immunity in adults than in children exposed to high EIRs. This forms one component of a new stochastic model for the entire transmission cycle of P. falciparum that we have derived to estimate the potential epidemiologic impact of malaria vaccines and other malaria control interventions

Bayesian spatio-temporal modeling of mortality in relation to malaria incidence in Western Kenya

The effect of malaria exposure on mortality using health facility incidence data as a measure of transmission has not been well investigated. Health and demographic surveillance systems (HDSS) routinely capture data on mortality, interventions and other household related indicators, offering a unique platform for estimating and monitoring the incidence-mortality relationship in space and time.; Mortality data from the HDSS located in Western Kenya collected from 2007 to 2012 and linked to health facility incidence data were analysed using Bayesian spatio-temporal survival models to investigate the relation between mortality (all-cause/malaria-specific) and malaria incidence across all age groups. The analysis adjusted for insecticide-treated net (ITN) ownership, socio-economic status (SES), distance to health facilities and altitude. The estimates obtained were used to quantify excess mortality due to malaria exposure.; Our models identified a strong positive relationship between slide positivity rate (SPR) and all-cause mortality in young children 1-4 years (HR = 4.29; 95% CI: 2.78-13.29) and all ages combined (HR = 1.55; 1.04-2.80). SPR had a strong positive association with malaria-specific mortality in young children (HR = 9.48; 5.11-37.94), however, in older children (5-14 years), it was associated with a reduction in malaria specific mortality (HR = 0.02; 0.003-0.33).; SPR as a measure of transmission captures well the association between malaria transmission intensity and all-cause/malaria mortality. This offers a quick and efficient way to monitor malaria burden. Excess mortality estimates indicate that small changes in malaria incidence substantially reduce overall and malaria specific mortality

Malaria-anemia comorbidity prevalence as a measure of malaria-related deaths in sub-Saharan Africa

Different methods and data sources have been utilized to determine the relationship between malaria and mortality in endemic countries. Most of these efforts have focused on deaths directly attributed to malaria, while they overlooked causes of mortality that might be indirectly related to the disease, for instance anemia. We estimated the association of malaria parasitaemia, anemia, and malaria-anemia comorbidity with all-cause under-five mortality and evaluated the potential of malaria-anemia comorbidity prevalence to quantify malaria-related deaths in sub-Saharan Africa. We analysed data from Demographic and Health Surveys (DHS) and employed Bayesian geostatistical models. Mortality hazard obtained from malaria-anemia comorbidity prevalence was up to 3·5 times higher compared to the hazard related to Plasmodium parasitaemia only. Malaria parasite prevalence alone could not always capture a statistically important association with under-five mortality. Geographical variation of the malaria-anemia comorbidity effect was observed in most, but not all, countries. We concluded that the malaria burden in sub-Saharan Africa is considerably underestimated when anemia in not taken into account and that the malaria-anemia comorbidity prevalence provides a useful measure of the malaria-related deaths

Risk profiling of hookworm infection and intensity in southern Lao People's Democratic Republic using bayesian models

Among the common soil-transmitted helminth infections, hookworm causes the highest burden. Previous research in the southern part of Lao People's Democratic Republic (Lao PDR) revealed high prevalence rates of hookworm infection. The purpose of this study was to predict the spatial distribution of hookworm infection and intensity, and to investigate risk factors in the Champasack province, southern Lao PDR.; A cross-sectional parasitological and questionnaire survey was conducted in 51 villages. Data on demography, socioeconomic status, water, sanitation, and behavior were combined with remotely sensed environmental data. Bayesian mixed effects logistic and negative binomial models were utilized to investigate risk factors and spatial distribution of hookworm infection and intensity, and to make predictions for non-surveyed locations.; A total of 3,371 individuals were examined with duplicate Kato-Katz thick smears and revealed a hookworm prevalence of 48.8%. Most infections (91.7%) were of light intensity (1-1,999 eggs/g of stool). Lower hookworm infection levels were associated with higher socioeconomic status. The lowest infection levels were found in preschool-aged children. Overall, females were at lower risk of infection, but women aged 50 years and above harbored the heaviest hookworm infection intensities. Hookworm was widespread in Champasack province with little evidence for spatial clustering. Infection risk was somewhat lower in the lowlands, mostly along the western bank of the Mekong River, while infection intensity was homogeneous across the Champasack province.; Hookworm transmission seems to occur within, rather than between villages in Champasack province. We present spatial risk maps of hookworm infection and intensity, which suggest that control efforts should be intensified in the Champasack province, particularly in mountainous areas

Modelling the geographical distribution of soil-transmitted helminth infections in Bolivia

The prevalence of infection with the three common soil-transmitted helminths (i.e. Ascaris lumbricoides, Trichuris trichiura, and hookworm) in Bolivia is among the highest in Latin America. However, the spatial distribution and burden of soil-transmitted helminthiasis are poorly documented.; We analysed historical survey data using Bayesian geostatistical models to identify determinants of the distribution of soil-transmitted helminth infections, predict the geographical distribution of infection risk, and assess treatment needs and costs in the frame of preventive chemotherapy. Rigorous geostatistical variable selection identified the most important predictors of A. lumbricoides, T. trichiura, and hookworm transmission.; Results show that precipitation during the wettest quarter above 400 mm favours the distribution of A. lumbricoides. Altitude has a negative effect on T. trichiura. Hookworm is sensitive to temperature during the coldest month. We estimate that 38.0%, 19.3%, and 11.4% of the Bolivian population is infected with A. lumbricoides, T. trichiura, and hookworm, respectively. Assuming independence of the three infections, 48.4% of the population is infected with any soil-transmitted helminth. Empirical-based estimates, according to treatment recommendations by the World Health Organization, suggest a total of 2.9 million annualised treatments for the control of soil-transmitted helminthiasis in Bolivia.; We provide estimates of soil-transmitted helminth infections in Bolivia based on high-resolution spatial prediction and an innovative variable selection approach. However, the scarcity of the data suggests that a national survey is required for more accurate mapping that will govern spatial targeting of soil-transmitted helminthiasis control