Unstructured Random Effects Research Articles

Bayesian hierarchical spatiotemporal modelling of tuberculosis—Human immunodeficiency virus co-infection in Ethiopia

Understanding the epidemiological patterns of tuberculosis-human immunodeficiency virus (TB-HIV) co-infection over space and time is crucial because it assists in identifying areas with high risks that need special control strategies. This article aimed to determine districts in Ethiopia that are most vulnerable to TB-HIV co-infection by examining the spatiotemporal patterns of the co-infection across four years, from 2015 to 2018. The study’s data came from Ethiopia’s Federal Ministry of Health. The data was analysed by applying the Bayesian hierarchical spatiotemporal modelling. We considered four models with different space–time interaction structures via the Integrated Nested Laplace Approximation (INLA) in the R-INLA package. In addition, we have applied the Deviance Information Criterion to select the most suitable model. The mean raw annual TB-HIV relative risk (RR) continuously decreased from 2015 to 2018, and the raw RRs of co-infection varied over districts and years. The spatiotemporal model, which allows for space–time interaction with independent spatial random effect and dependent temporal random effect, was the preferred model for describing the variations in TB-HIV co-infection across different districts over time. The prior variance for the spatial structured random effect had a smaller precision mode than the spatial unstructured random effect. This difference reveals that the former accounted for more spatial autocorrelation than the latter, indicating an information-borrowing effect amongst districts. Furthermore, the findings exhibit that the relative risk of TB-HIV co-infection had significant spatiotemporal variation and clustering. Through this research, further information was obtained regarding the temporal evolution of the geographical spread of TB and HIV co-infection at the district level in the country. It also made it possible to determine districts that should receive priority for control actions because of their high risk of co-infection.

Model-based disease mapping using primary care registry data

Background:Spatial modeling of disease risk using primary care registry data is promising for public health surveillance. However, it remains unclear to which extent challenges such as spatially disproportionate sampling and practice-specific reporting variation affect statistical inference. Methods:Using lower respiratory tract infection data from the INTEGO registry, modeled with a logistic model incorporating patient characteristics, a spatially structured random effect at municipality level, and an unstructured random effect at practice level, we conducted a case and simulation study to assess the impact of these challenges on spatial trend estimation. Results:Even with spatial imbalance and practice-specific reporting variation, the model performed well. Performance improved with increasing spatial sample balance and decreasing practice-specific variation. Conclusion:Our findings indicate that, with correction for reporting efforts, primary care registries are valuable for spatial trend estimation. The diversity of patient locations within practice populations plays an important role.

A zero‐inflated Poisson spatial model with misreporting for wildfire occurrences in southern Italian municipalities

AbstractWe propose a Poisson model for zero‐inflated spatial counts contaminated by measurement error: we accommodate the excess of zeroes in the counts, consider the possible under/over reporting of the response and account for the neighboring structure of spatial areal units. Bayesian inferences are provided by MCMC implementation through the R package NIMBLE. To evaluate the model performance, a simulation study is carried out under configurations that allow for structured and unstructured spatial random effects. The proposed model is applied to investigate the distribution of the counts of wildfire occurrences in the municipal areas of two neighboring Italian regions for the summer season 2021. Fire counts are obtained by processing MODIS satellite data, while several socio‐economic and environmental‐driven potential risk factors are also considered in the model formulation. Data from multiple sources with different spatial support are processed in order to comply with the municipal units. Results suggest the appropriateness of the approach and provide some insights on the features of wildfire occurrences.

Bayesian spatial modelling of tuberculosis-HIV co-infection in Ethiopia.

An in-depth analysis of the epidemiological patterns of TB/HIV co-infection is essential since it helps to target high-risk areas with effective control measures. The main objective of this study was to assess the spatial clustering of TB/HIV co-infection prevalence in Ethiopia for the year 2018 using district-level aggregated TB and HIV data obtained from the Ethiopian Federal Ministry of Health. The global Moran's index, Getis-Ord [Formula: see text] local statistic, and Bayesian spatial modeling techniques were applied to analyse the data. The result of the study shows that TB among people living with HIV (PLHIV) and HIV among TB patients prevalence were geographically heterogeneous. The highest prevalence of TB among PLHIV in 2018 was reported in the Gambella region (1.44%). The overall prevalence of TB among PLHIV in Ethiopia in the same year was 0.38% while the prevalence of HIV among TB patients was 6.88%. Both district-level prevalences of HIV among TB patients and TB among PLHIV were positively spatially autocorrelated, but the latter was not statistically significant. The local indicators of spatial analysis using the Getis-Ord statistic also identified hot-spots districts for both types of TB/HIV co-infection data. The results of Bayesian spatial logistic regression with spatially structured and unstructured random effects using the Besag, York, and Mollié prior showed that not all the heterogeneities in the prevalence of HIV among TB patients and TB among PLHIV were explained by the spatially structured random effects. This study expanded knowledge about the spatial clustering of TB among PLHIV and HIV among TB patients in Ethiopia at the district level in 2018. The findings provide information to health policymakers in the country to plan geographically targeted and integrated interventions to jointly control TB and HIV.

An Offenders-Offenses Shared Component Spatial Model for Identifying Shared and Specific Hotspots of Offenders and Offenses: A Case Study of Juvenile Delinquents and Violent Crimes in the Greater Toronto Area

ObjectivesWe attempted to apply the Bayesian shared component spatial modeling (SCSM) for the identification of hotspots from two (offenders and offenses) instead of one (offenders or offenses) variables and developed three risk surfaces for (1) common or shared by both offenders and offenses; (2) specific to offenders, and (3) specific to offenses.MethodsWe applied SCSM to examine the joint spatial distributions of juvenile delinquents (offenders) and violent crime (offenses) in the York Region of the Greater Toronto Area at the dissemination area level. The spatial autocorrelation, overdispersion, and latent covariates were adjusted by spatially structured and unstructured random effect terms in the model. We mapped the posterior means of the estimated shared and specific risks for identifying the three risk surfaces and types of hotspots.ResultsResults suggest that about 50% and 25% of the relative risks of juvenile delinquents and violent crimes, respectively, could be explained by the shared component of offenders and offenses. The spatially structured terms attributed to 48% and 24% of total variations of the delinquents and violent crimes, respectively. Contrastingly, the unstructured random covariates influenced 3% of total variations of the juvenile delinquents and 51% for violent crimes.ConclusionsThe Bayesian SCSM presented in this study identifies shared and specific hotspots of juvenile delinquents and violent crime. The method can be applied to other kinds of offenders and offenses and provide new insights into the clusters of high risks that are due to both offenders and offenses or due to offenders or offenses only.

Mapping Geographic Trends in Early Childhood Social, Emotional, and Behavioural Difficulties in Glasgow: 2010-2017.

Measuring variation in childhood mental health supports the development of local early intervention strategies. The methodological approach used to investigate mental health trends (often determined by the availability of individual level data) can affect decision making. We apply two approaches to identify geographic trends in childhood social, emotional, and behavioural difficulties using the Strengths and Difficulties Questionnaire (SDQ). SDQ forms were analysed for 35,171 children aged 4–6 years old across 180 preschools in Glasgow, UK, between 2010 and 2017 as part of routine monitoring. The number of children in each electoral ward and year with a high SDQ total difficulties score (≥15), indicating a high risk of psychopathology, was modelled using a disease mapping model. The total difficulties score for an individual child nested in their preschool and electoral ward was modelled using a multilevel model. For each approach, linear time trends and unstructured spatial random effects were estimated. The disease mapping model estimated a yearly rise in the relative rate (RR) of high scores of 1.5–5.0%. The multilevel model estimated an RR increase of 0.3–1.2% in average total scores across the years, with higher variation between preschools than between electoral wards. Rising temporal trends may indicate worsening social, emotional, and behavioural difficulties over time, with a faster rate for the proportion with high scores than for the average total scores. Preschool and ward variation, although minimal, highlight potential priority areas for local service provision. Both methodological approaches have utility in estimating and predicting children’s difficulties and local areas requiring greater intervention.

Bayesian multiresolution modeling of georeferenced data: An extension of ‘LatticeKrig’

‘LatticeKrig’ (LK) is a spatial model that is often used for modeling multiresolution spatial data with flexible covariance structures. An extension to LK under a Bayesian framework is proposed that uses integrated nested Laplace approximations (INLA). The extension enables the spatial analysis of non-Gaussian responses in latent Gaussian models, joint spatial modeling with structured and unstructured random effects, and native support for multithreaded parallel likelihood computation. The proposed extended LatticeKrig (ELK) model uses a reparameterization of LK so that the parameters and prior selection are intuitive and interpretable. Priors can be used to make inference robust by penalizing more complex models, and integration over model parameters allows for posterior uncertainty estimates that account for uncertainty in covariance parameters. ELK's ability to reliably resolve multiresolution spatial structure for pointwise and areal predictions is demonstrated in both simulation study and two applications with non-Gaussian observations: a set of 188,717 LiDAR forest canopy height observations in Bonanza Creek Experimental Forest in Alaska, and a set of 1,612 clusters containing counts of secondary education completion from the 2014 Kenya demographic health survey. ELK has improved central predictions as well as uncertainty characterization according to the considered scoring rules when compared against a number of other models, particularly in the forest canopy height application, and performed faster than LK in our tests in part due to its support for and use of parallelization.

Multivariate Hierarchical Analysis of Car Crashes Data Considering a Spatial Network Lattice

AbstractRoad traffic casualties represent a hidden global epidemic, demanding evidence-based interventions. This paper demonstrates a network lattice approach for identifying road segments of particular concern, based on a case study of a major city (Leeds, UK), in which 5862 crashes of different severities were recorded over an 8-year period (2011–2018). We consider a family of Bayesian hierarchical models that include spatially structured and unstructured random effects to capture the dependencies between the severity levels. Results highlight roads that are more prone to collisions, relative to estimated traffic volumes, in the north-west and south of city centre. We analyse the modifiable areal unit problem (MAUP), proposing a novel procedure to investigate the presence of MAUP on a network lattice. We conclude that our methods enable a reliable estimation of road safety levels to help identify ‘hotspots’ on the road network and to inform effective local interventions.

Spatiotemporal high-resolution prediction and mapping: methodology and application to dengue disease

Dengue disease has become a major public health problem. Accurate and precise identification, prediction and mapping of high-risk areas are crucial elements of an effective and efficient early warning system in countering the spread of dengue disease. In this paper, we present the fusion area-cell spatiotemporal generalized geoadditive-Gaussian Markov random field (FGG-GMRF) framework for joint estimation of an area-cell model, involving temporally varying coefficients, spatially and temporally structured and unstructured random effects, and spatiotemporal interaction of the random effects. The spatiotemporal Gaussian field is applied to determine the unobserved relative risk at cell level. It is transformed to a Gaussian Markov random field using the finite element method and the linear stochastic partial differential equation approach to solve the “big n” problem. Sub-area relative risk estimates are obtained as block averages of the cell outcomes within each sub-area boundary. The FGG-GMRF model is estimated by applying Bayesian Integrated Nested Laplace Approximation. In the application to Bandung city, Indonesia, we combine low-resolution area level (district) spatiotemporal data on population at risk and incidence and high-resolution cell level data on weather variables to obtain predictions of relative risk at subdistrict level. The predicted dengue relative risk at subdistrict level suggests significant fine-scale heterogeneities which are not apparent when examining the area level. The relative risk varies considerably across subdistricts and time, with the latter showing an increase in the period January–July and a decrease in the period August–December.

COVID-19's intra-urban inequalities and social vulnerability in a medium-sized city.

ABSTRACTBackground: Social conditions are related to the impact of epidemics on human populations. This study aimed to investigate the spatial distribution of cases, hospitalizations, and deaths from COVID-19 and its association with social vulnerability. Methods: An ecological study was conducted in 81 urban regions (UR) of Juiz de Fora from March to November 2020. Exposure was measured using the Health Vulnerability Index (HVI), a synthetic indicator that combines socioeconomic and environmental variables from the Demographic Census 2010. Regression models were estimated for counting data with overdispersion (negative binomial generalized linear model) using Bayesian methods, with observed frequencies as the outcome, expected frequencies as the offset variable, and HVI as the explanatory variable. Unstructured random-effects (to capture the effect of unmeasured factors) and spatially structured effects (to capture the spatial correlation between observations) were included in the models. The models were estimated for the entire period and quarter. Results: There were 30,071 suspected cases, 8,063 confirmed cases, 1,186 hospitalizations, and 376 COVID-19 deaths. In the second quarter of the epidemic, compared to the low vulnerability URs, the high vulnerability URs had a lower risk of confirmed cases (RR=0.61; CI95% 0.49-0.76) and a higher risk of hospitalizations (RR=1.65; CI95% 1.23-2.22) and deaths (RR=1.73; CI95% 1.08-2.75). Conclusions: The lower risk of confirmed cases in the most vulnerable UR probably reflected lower access to confirmatory tests, while the higher risk of hospitalizations and deaths must have been related to the greater severity of the epidemic in the city’s poorest regions.

Modeling the relationship between malaria prevalence and insecticide-treated bed net coverage in Nigeria using a Bayesian spatial generalized linear mixed model with a Leroux prior

OBJECTIVESTo evaluate malaria transmission in relation to insecticide-treated net (ITN) coverage in Nigeria.METHODSWe used an exploratory analysis approach to evaluate variation in malaria transmission in relation to ITN distribution in 1,325 Demographic and Health Survey clusters in Nigeria. A Bayesian spatial generalized linear mixed model with a Leroux conditional autoregressive prior for the random effects was used to model the spatial and contextual variation in malaria prevalence and ITN distribution after adjusting for environmental variables.RESULTSSpatial smoothed maps showed the nationwide distribution of malaria and ITN. The distribution of ITN varied significantly across the 6 geopolitical zones (p<0.05). The North-East had the least ITN distribution (0.196±0.071), while ITN distribution was highest in the South-South (0.309±0.075). ITN coverage was also higher in rural areas (0.281±0.074) than in urban areas (0.240±0.096, p<0.05). The Bayesian hierarchical regression results showed a non-significant negative relationship between malaria prevalence and ITN coverage, but a significant spatial structured random effect and unstructured random effect. The correlates of malaria transmission included rainfall, maximum temperature, and proximity to water.CONCLUSIONSReduction in malaria transmission was not significantly related to ITN coverage, although much could be achieved in attempts to curtail malaria transmission through enhanced ITN coverage. A multifaceted and integrated approach to malaria control is strongly advocated.

Exploring the effects of area-level factors on traffic crash frequency by severity using multivariate space-time models

This study aims to rank high crash risk areas and measure the impacts of accessibility and other spatial and socio-economic factors on county-level crash severities while controlling for spatial and temporal unobserved effects. Among other insights, the results suggest that primary roadway density is positively associated with all crash severities. Contrary, intersection density is negatively associated with injury and no injury crashes. Furthermore, school density and rates of driving under the influence are both positively associated with no injury crashes. Additionally, the mean travel time to the hospital is positively associated, while urbanity is negatively associated with fatal crashes. Unobserved effects due to unstructured random effect terms are significant and contribute to the model’s overall goodness of fit. The within-area correlation among crash severities is positive and non-negligible. From a temporal perspective, both fatal and no injury crashes have decreasing trends. However, no clear pattern for injury crashes is observed across the years. From a spatial perspective, extreme high and low crash risk counties are identified throughout the study area with no clear observed patterns of clustering or dispersion.

An accelerated hierarchical Bayesian crash frequency model with accommodation of spatiotemporal interactions

Although spatial and temporal correlations of crash observations have been well addressed in the literature, the interactions between them are rarely studied. This study proposes a Bayesian spatiotemporal interaction (BSTI) approach for crash frequency modeling with an integrated nested Laplace approximation (INLA) method to greatly expedite the Bayesian estimation process. Manhattan, which is the most densely populated urban area of New York City, is selected as the study area. Hexagons are used as the basic geographic units to capture crash, transportation, land use, and demo-economic data from 2013 to 2019. A series of Bayesian models with various spatiotemporal specifications are developed and compared. The BSTI model with Type II interaction, which assumes that the structured temporal random effect interacts with the unstructured spatial random effect is found to outperform the others in terms of goodness-of-fit and the ability to reduce the dependency of residuals. It is also found that the unobserved heterogeneity is mostly attributed to the spatial effects instead of temporal effects. In addition, the BSTI Type II model also yields the lowest predictive error when the last year’s data are used as the test set. The proposed BSTI approach can potentially advance safety analytics by achieving high prediction accuracy and computational efficiency while maintaining its interpretability on the effects of contributing factors and the unobserved heterogeneity.

Moran eigenvector filtering of multi‐year yield data with application to zone development

AbstractA time‐series of yield monitor data may be used to identify field areas of consistently low or high yield to serve as productivity zones for site‐specific crop management. However, transient factors that affect yield in 1 yr, but not every year, detract from this approach. The objective of this study was to illustrate Moran eigenvector spatial filtering (MESF) with results from analysis of multi‐year crop yield data from two farm fields in the United States. The MESF method accounts for temporal autocorrelation within a common factor map representing the correlation across years and partitions stochastic geographic variation into spatially structured and unstructured components. Crop rotation data were utilized from a dryland field in east‐central South Dakota and an irrigated field in southwestern Georgia. A random effects (RE) model was estimated that utilized eigenfunctions of a geographic connectivity matrix to account for spatially structured random effects (SSRE) and unstructured random effects (SURE) in standardized z scores of multi‐year crop yield. The MESF method was evaluated with conventional averaging of unfiltered yield data as a reference for comparison. In South Dakota, the SSRE accounted for 26% of the yield variance shared across years. Distinct patterns appeared to be related to changes in soil type and landscape position. The Georgia field yielded similar results. The MESF is effective for revealing structured variation in a time series of yield monitor data and may be useful for defining productivity zones within fields.

On the impact of residential history in the spatial analysis of diseases with a long latency period: A study of mesothelioma in Belgium.

Mesothelioma is a rare cancer caused by exposure to asbestos. Belgium has a known long history of asbestos production, resulting in one of the highest mesothelioma mortality rates worldwide. While the production of asbestos has stopped completely, the long latency period of mesothelioma, which can fluctuate between 20 and 40 years after exposure, causes incidences still to be frequent. Mesothelioma's long incubation time affects our assessment of its geographical distribution as well. Since patients' residential locations are likely to change a number of times throughout their lives, the location where the patients develop the disease is often far from the location where they were exposed to asbestos. Using the residential history of patients, we propose the use of a convolution multiple membership model (MMM), which includes both a spatial conditional autoregressive and an unstructured random effect. Pancreatic cancer patients are used as a control population, reflecting the population at risk for mesothelioma. Results show the impact of the residential mobility on the geographical risk estimation, as well as the importance of acknowledging the latency period of a disease. A simulation study was conducted to investigate the properties of the convolution MMM. The robustness of the results for the convolution MMM is assessed via a sensitivity analysis.

Role of nephrology pharmacists in the management of anemia in outpatient dialysis units: A Canadian model .

Hemodialysis patients frequently suffer from anemia. Proper utilization of therapies such as iron and erythropoiesis-stimulating agents (ESAs) is crucial to attain symptom management and established hemoglobin targets. The purpose of this study was to evaluate the clinical and financial impact of nephrology-trained pharmacists on anemia management in these patients. A retrospective study of outpatient hemodialysis patients observed between January 2010 and December 2011. In December 2010, pharmacists were tasked to manage anemia under a medical directive. Primary endpoints were compared across years using a mixed-effects model strategy. An unstructured random effects correlation matrix was utilized to capture patient-level variation in 2010 and 2011, separately. Of 202 patients identified, 163 contributed in both years, 57% were males, aged 65.18 ± 16.3 years. Hemoglobin levels were 10.95 ± 0.95 and 10.83 ± 0.94 g/dL in 2010 vs. 2011, respectively (p = 0.158), while the transfusion rate was 1.3% and 1.8%, respectively (p = 0.196). Ferritin levels of 273.5 ± 22 and 317.1 ± 12 ng/mL (p = 0.0019), iron saturation 0.30 ± 0.11 and 0.30 ± 0.05 (p = 0.838), and parenteral iron dose of 215.4 ± 100.2 and 317.1 ± 123.7 mg, respectively (p = 0.996), were identified. Finally, the average weekly ESA dose in 2010 was higher and trending up as compared to 2011 where it significantly trended down. The amount of intravenous erythropoietin alfa was 12,315.6 ± 76 vs. 11,364.1 ± 52 units/week, respectively (p = 0.0556) with expenditure of 2.8 million Canadian dollars in 2010 vs. 2.3 million Canadian dollars in 2011. The participation of a nephrology pharmacist resulted in favorable outcomes in dose optimization, decreased expenditure, and positive trends in therapeutic goal achievement.

Spatial Modelling of Under-five Mortality in Lesotho with Reference to 2014 Demographic and Health Surveillance Dataset

Background: Lesotho is the country located in the Sub-Saharan region of Africa countries where under-five mortality (U5M) is still a big issue due to some significant social and demographic risk factors. Hence, the investigation of some social and demographic factors that are associated with the U5M, is a critical problem that needs due consideration. Methods: This study used the 2014 Lesotho Demographic and Health Survey (LDHS) that had a sample of over 9000 representative households. Individually, data consisting of a nationally representative sample of 9,543 households in the 2014 Lesotho Demographic and Health Survey were analysed. The Random Walk second-order (RW2) model was adopted for analysis. Maps construction and modelling were done through the spatially structured and unstructured random effects using the Gaussian Markov Random Field and a zero-mean Gaussian process, respectively. The full Bayesian inference was adopted to produce the results using the Integrated Nested Laplace Approximation (INLA) function in R-software. Results: In this study, age at death of an under-five child was found to have a linear association with the U5M in Lesotho. The non-stationary models outperform the stationary models. The low-risk pattern was found in the north of Lesotho, and the highest risk occurs in the centre through the south, east, west, southeast, and northwest. Breastfeeding has contributed significantly to under-five mortality to most of Lesotho districts. Conclusion: This study adopted the newly developed statistical models to model and mapped the U5M in Lesotho. The full Bayesian inference was used to produce the results using R-INLA package. The findings from this study can help introduce new policies that will help reduce disparity in Lesotho.

Bayesian spatial-temporal model for the main and interaction effects of roadway and weather characteristics on freeway crash incidence

This study attempts to examine the main and interaction effects of roadway and weather conditions on crash incidence, using the comprehensive crash, traffic and weather data from the Kaiyang Freeway in China in 2014. The dependent variable is monthly crash count on a roadway segment (with homogeneous horizontal and vertical profiles). A Bayesian spatio-temporal model is proposed to measure the association between crash frequency and possible risk factors including traffic composition, presence of curve and slope, weather conditions, and their interactions. The proposed model can also accommodate the unstructured random effect, and spatio-temporal correlation and interactions. Results of parameter estimation indicate that the interactions between wind speed and slope, between precipitation and curve, and between visibility and slope are significantly correlated to the increase in the freeway crash risk, while the interaction between precipitation and slope is significantly correlated to the reduction in the freeway crash risk, respectively. These findings are indicative of the design and implementation of real-time traffic management and control measures, e.g. variable message sign, that could mitigate the crash risk under the adverse weather conditions.

Bayesian Hierarchical Models as Tools to Evaluate the Association Between Groundwater Quality and the Occurrence of Type 2 Diabetes in Rural Saskatchewan, Canada.

There is growing interest in the role of environmental exposures in the development of diabetes. Previous studies in rural Saskatchewan have raised concerns over drinking water contaminants, including arsenic, which has been identified as a possible risk factor for diabetes. Using administrative health and water-quality surveillance data from rural Saskatchewan, an ecological study design was used to investigate associations between concentrations of arsenic, water health standards and aesthetic objectives, and the incidence and prevalence of diabetes. Mixtures of contaminants measured as health standards or as aesthetic objectives were summarized using principal component (PC) analysis. Associations were modeled using Bayesian hierarchical models incorporating both spatial and unstructured random effects, standardized for age and sex, and adjusted for socioeconomic factors and a surrogate measure for smoking rates. Arsenic was not associated with an increased risk of diabetes. For private wells, having groundwater arsenic concentrations in the highest quintile was associated with decreased cumulative diabetes incidence for 2010-2012 (risk ratio [RR] = 0.854, 95% credible interval [CrI] 0.761-0.958) compared with the lowest quintile, a result inconsistent with other studies. For public water supplies, having a first PC score for health standards (primarily summarized selenium, nitrate, and lead) in the third quintile (RR = 1.101, 95% CrI 1.019-1.188), fourth quintile (RR = 1.088, 95% CrI 1.003-1.180), or fifth quintile (RR = 1.115, 95% CrI 1.026-1.213) was associated with an increase in 2010 diabetes prevalence compared with the first quintile. An increase in the PC scores for the third aesthetic objective in private wells (characterized primarily by iron and manganese) was associated with decreased diabetes incidence, although a meaningful dose-response relationship was not evident. No other associations between PC scores for health standards or aesthetic objectives from public or private water supplies and diabetes were identified.

Estimating multilevel regional variation in excess mortality of cancer patients using integrated nested Laplace approximation

Models of excess mortality with random effects were used to estimate regional variation in relative or net survival of cancer patients. Statistical inference for these models based on the Markov chain Monte Carlo (MCMC) methods is computationally intensive and, therefore, not feasible for routine analyses of cancer register data. This study assessed the performance of the integrated nested Laplace approximation (INLA) in monitoring regional variation in cancer survival. Poisson regression model of excess mortality including both spatially correlated and unstructured random effects was fitted to the data of patients diagnosed with ovarian and breast cancer in Finland during 1955-2014 with follow up from 1960 through 2014 by using the period approach with five-year calendar time windows. We estimated standard deviations associated with variation (i) between hospital districts and (ii) between municipalities within hospital districts. Posterior estimates based on the INLA approach were compared to those based on the MCMC simulation. The estimates of the variation parameters were similar between the two approaches. Variation within hospital districts dominated in the total variation between municipalities. In 2000-2014, the proportion of the average variation within hospital districts was 68% (95% posterior interval: 35%-93%) and 82% (60%-98%) out of the total variation in ovarian and breast cancer, respectively. In the estimation of regional variation, the INLA approach was accurate, fast, and easy to implement by using the R-INLA package.