Body composition and resting energy expenditure in a group of children with achondroplasia

BACKGROUND

Persons with achondroplasia develop early obesity, which is a comorbidity associated with other complications. Currently, there are no validated specific predictive equations to estimate resting energy expenditure in achondroplasia.

METHODS

We analyzed the influence of body composition on this parameter and determined whether predictive models used for children with standard height are adjusted to achondroplasia. In this cross-sectional study, we measured anthropometric parameters in children with achondroplasia. Fat mass was obtained using the Slaughter skinfold-thickness equation and resting energy expenditure was determined with a Fitmate-Cosmed calorimeter and with predictive models validated for children with average height (Schofield, Institute of Medicine, and Tverskaya).

RESULTS

All of the equations yielded a lower mean value than resting energy expenditure with indirect calorimetry (1256±200 kcal/day [mean±SD]) but the closest was the Tverskaya equation (1017 ± 64 kcal/day), although the difference remained statistically significant. We conclude that weight and height have the greatest influence on resting energy expenditure.

CONCLUSION

We recommend studying the relationship between body composition and energy expenditure in achondroplasia in more depth. In the absence of valid predictive models suitable for clinical use to estimate body composition and resting energy expenditure in achondroplasia, it is recommended to use the gold standard methods by taking into account certain anthropometric parameters.

Small area variations in non-affective first-episode psychosis: the role of socioeconomic and environmental factors

BACKGROUND

There is strong evidence supporting the association between environmental factors and increased risk of non-affective psychotic disorders. However, the use of sound statistical methods to account for spatial variations associated with environmental risk factors, such as urbanicity, migration, or deprivation, is scarce in the literature.

METHODS

We studied the geographical distribution of non-affective first-episode psychosis (NA-FEP) in a northern region of Spain (Navarra) during a 54-month period considering area-level socioeconomic indicators as putative explanatory variables. We used several Bayesian hierarchical Poisson models to smooth the standardized incidence ratios (SIR). We included neighborhood-level variables in the spatial models as covariates.

RESULTS

We identified 430 NA-FEP cases over a 54-month period for a population at risk of 365,213 inhabitants per year. NA-FEP incidence risks showed spatial patterning and a significant ecological association with the migrant population, unemployment, and consumption of anxiolytics and antidepressants. The high-risk areas corresponded mostly to peripheral urban regions; very few basic health sectors of rural areas emerged as high-risk areas in the spatial models with covariates.

DISCUSSION

Increased rates of unemployment, the migrant population, and consumption of anxiolytics and antidepressants showed significant associations linked to the spatial-geographic incidence of NA-FEP. These results may allow targeting geographical areas to provide preventive interventions that potentially address modifiable environmental risk factors for NA-FEP. Further investigation is needed to understand the mechanisms underlying the associations between environmental risk factors and the incidence of NA-FEP.

Big problems in spatio-temporal disease mapping: Methods and software

BACKGROUND AND OBJECTIVE

Fitting spatio-temporal models for areal data is crucial in many fields such as cancer epidemiology. However, when data sets are very large, many issues arise. The main objective of this paper is to propose a general procedure to analyze high-dimensional spatio-temporal areal data, with special emphasis on mortality/incidence relative risk estimation.

METHODS

We present a pragmatic and simple idea that permits hierarchical spatio-temporal models to be fitted when the number of small areas is very large. Model fitting is carried out using integrated nested Laplace approximations over a partition of the spatial domain. We also use parallel and distributed strategies to speed up computations in a setting where Bayesian model fitting is generally prohibitively time-consuming or even unfeasible.

RESULTS

Using simulated and real data, we show that our method outperforms classical global models. We implement the methods and algorithms that we develop in the open-source R package bigDM where specific vignettes have been included to facilitate the use of the methodology for non-expert users.

CONCLUSIONS

Our scalable methodology proposal provides reliable risk estimates when fitting Bayesian hierarchical spatio-temporal models for high-dimensional data.

Space-time interactions in Bayesian disease mapping with recent tools: Making things easier for practitioners

Spatio-temporal disease mapping studies the distribution of mortality or incidence risks in space and its evolution in time, and it usually relies on fitting hierarchical Poisson mixed models. These models are complex for practitioners as they generally require adding constraints to correctly identify and interpret the different model terms. However, including constraints may not be straightforward in some recent software packages. This paper focuses on NIMBLE, a library of algorithms that contains among others a configurable system for Markov chain Monte Carlo (MCMC) algorithms. In particular, we show how to fit different spatio-temporal disease mapping models with NIMBLE making emphasis on how to include sum-to-zero constraints to solve identifiability issues when including spatio-temporal interactions. Breast cancer mortality data in Spain during the period 1990-2010 is used for illustration purposes. A simulation study is also conducted to compare NIMBLE with R-INLA in terms of parameter estimates and relative risk estimation. The results are very similar but differences are observed in terms of computing time.

Identifying extreme COVID-19 mortality risks in English small areas: a disease cluster approach

The COVID-19 pandemic is having a huge impact worldwide and has highlighted the extent of health inequalities between countries but also in small areas within a country. Identifying areas with high mortality is important both of public health mitigation in COVID-19 outbreaks, and of longer term efforts to tackle social inequalities in health. In this paper we consider different statistical models and an extension of a recent method to analyze COVID-19 related mortality in English small areas during the first wave of the epidemic in the first half of 2020. We seek to identify hotspots, and where they are most geographically concentrated, taking account of observed area factors as well as spatial correlation and clustering in regression residuals, while also allowing for spatial discontinuities. Results show an excess of COVID-19 mortality cases in small areas surrounding London and in other small areas in North-East and and North-West of England. Models alleviating spatial confounding show ethnic isolation, air quality and area morbidity covariates having a significant and broadly similar impact on COVID-19 mortality, whereas nursing home location seems to be slightly less important.

Estimating LOCP cancer mortality rates in small domains in Spain using its relationship with lung cancer

The distribution of lip, oral cavity, and pharynx (LOCP) cancer mortality rates in small domains (defined as the combination of province, age group, and gender) remains unknown in Spain. As many of the LOCP risk factors are preventable, specific prevention programmes could be implemented but this requires a clear specification of the target population. This paper provides an in-depth description of LOCP mortality rates by province, age group and gender, giving a complete overview of the disease. This study also presents a methodological challenge. As the number of LOCP cancer cases in small domains (province, age groups and gender) is scarce, univariate spatial models do not provide reliable results or are even impossible to fit. In view of the close link between LOCP and lung cancer, we consider analyzing them jointly by using shared component models. These models allow information-borrowing among diseases, ultimately providing the analysis of cancer sites with few cases at a very disaggregated level. Results show that males have higher mortality rates than females and these rates increase with age. Regions located in the north of Spain show the highest LOCP cancer mortality rates.

Induction of Radiata Pine Somatic Embryogenesis at High Temperatures Provokes a Long-Term Decrease in DNA Methylation/Hydroxymethylation and Differential Expression of Stress-Related Genes

Based on the hypothesis that embryo development is a crucial stage for the formation of stable epigenetic marks that could modulate the behaviour of the resulting plants, in this study, radiata pine somatic embryogenesis was induced at high temperatures (23 °C, eight weeks, control; 40 °C, 4 h; 60 °C, 5 min) and the global methylation and hydroxymethylation levels of emerging embryonal masses and somatic plants were analysed using LC-ESI-MS/ MS-MRM. In this context, the expression pattern of six genes previously described as stress-mediators was studied throughout the embryogenic process until plant level to assess whether the observed epigenetic changes could have provoked a sustained alteration of the transcriptome. Results indicated that the highest temperatures led to hypomethylation of both embryonal masses and somatic plants. Moreover, we detected for the first time in a pine species the presence of 5-hydroxymethylcytosine, and revealed its tissue specificity and potential involvement in heat-stress responses. Additionally, a heat shock protein-coding gene showed a down-regulation tendency along the process, with a special emphasis given to embryonal masses at first subculture and ex vitro somatic plants. Likewise, the transcripts of several proteins related with translation, oxidative stress response, and drought resilience were differentially expressed.

Space-time analysis of ovarian cancer mortality rates by age groups in spanish provinces (1989-2015)

BACKGROUND

Ovarian cancer is a silent and largely asymptomatic cancer, leading to late diagnosis and worse prognosis. The late-stage detection and low survival rates, makes the study of the space-time evolution of ovarian cancer particularly relevant. In addition, research of this cancer in small areas (like provinces or counties) is still scarce.

METHODS

The study presented here covers all ovarian cancer deaths for women over 50 years of age in the provinces of Spain during the period 1989-2015. Spatio-temporal models have been fitted to smooth ovarian cancer mortality rates in age groups [50,60), [60,70), [70,80), and [80,+), borrowing information from spatial and temporal neighbours. Model fitting and inference has been carried out using the Integrated Nested Laplace Approximation (INLA) technique.

RESULTS

Large differences in ovarian cancer mortality among the age groups have been found, with higher mortality rates in the older age groups. Striking differences are observed between northern and southern Spain. The global temporal trends (by age group) reveal that the evolution of ovarian cancer over the whole of Spain has remained nearly constant since the early 2000s.

CONCLUSION

Differences in ovarian cancer mortality exist among the Spanish provinces, years, and age groups. As the exact causes of ovarian cancer remain unknown, spatio-temporal analyses by age groups are essential to discover inequalities in ovarian cancer mortality. Women over 60 years of age should be the focus of follow-up studies as the mortality rates remain constant since 2002. High-mortality provinces should also be monitored to look for specific risk factors.

Online relative risks/rates estimation in spatial and spatio-temporal disease mapping

BACKGROUND AND OBJECTIVE

Spatial and spatio-temporal analyses of count data are crucial in epidemiology and other fields to unveil spatial and spatio-temporal patterns of incidence and/or mortality risks. However, fitting spatial and spatio-temporal models is not easy for non-expert users. The objective of this paper is to present an interactive and user-friendly web application (named SSTCDapp) for the analysis of spatial and spatio-temporal mortality or incidence data. Although SSTCDapp is simple to use, the underlying statistical theory is well founded and all key issues such as model identifiability, model selection, and several spatial priors and hyperpriors for sensitivity analyses are properly addressed.

METHODS

The web application is designed to fit an extensive range of fairly complex spatio-temporal models to smooth the very often extremely variable standardized incidence/mortality risks or crude rates. The application is built with the R package shiny and relies on the well founded integrated nested Laplace approximation technique for model fitting and inference.

RESULTS

The use of the web application is shown through the analysis of Spanish spatio-temporal breast cancer data. Different possibilities for the analysis regarding the type of model, model selection criteria, and a range of graphical as well as numerical outputs are provided.

CONCLUSIONS

Unlike other software used in disease mapping, SSTCDapp facilitates the fit of complex statistical models to non-experts users without the need of installing any software in their own computers, since all the analyses and computations are made in a powerful remote server. In addition, a desktop version is also available to run the application locally in those cases in which data confidentiality is a serious issue.

Effect of Thermal Stress on Tissue Ultrastructure and Metabolite Profiles During Initiation of Radiata Pine Somatic Embryogenesis

Climate change will inevitably lead to environmental variations, thus plant drought tolerance will be a determinant factor in the success of plantations and natural forestry recovery. Some metabolites, such as soluble carbohydrates and amino acids, have been described as being the key to both embryogenesis efficiency and abiotic stress response, contributing to phenotypic plasticity and the adaptive capacity of plants. For this reason, our main objectives were to evaluate if the temperature during embryonal mass initiation in radiata pine was critical to the success of somatic embryogenesis, to alter the morphological and ultrastructural organization of embryonal masses at cellular level and to modify the carbohydrate, protein, or amino acid contents. The first SE initiation experiments were carried out at moderate and high temperatures for periods of different durations prior to transfer to the control temperature of 23°C. Cultures initiated at moderate temperatures (30°C, 4 weeks and 40°C, 4 days) showed significantly lower initiation and proliferation rates than those at the control temperature or pulse treatment at high temperatures (50°C, 5 min). No significant differences were observed either for the percentage of embryogenic cell lines that produced somatic embryos, or for the number of somatic embryos per gram of embryonal mass. Based on the results from the first experiments, initiation was carried out at 40°C 4 h; 50°C, 30 min; and a pulse treatment of 60°C, 5 min. No significant differences were found for the initiation or number of established lines or for the maturation of somatic embryos. However, large morphological differences were observed in the mature somatic embryos. At the same time, changes observed at cellular level suggested that strong heat shock treatments may trigger the programmed cell death of embryogenic cells, leading to an early loss of embryogenic potential, and the formation of supernumerary suspensor cells. Finally, among all the differences observed in the metabolic profile, it is worth highlighting the accumulation of tyrosine and isoleucine, both amino acids involved in the synthesis of abiotic stress response-related secondary metabolites.

Two-level resolution of relative risk of dengue disease in a hyperendemic city of Colombia

Risk maps of dengue disease offer to the public health officers a tool to model disease risk in space and time. We analyzed the geographical distribution of relative incidence risk of dengue disease in a high incidence city from Colombia, and its evolution in time during the period January 2009—December 2015, identifying regional effects at different levels of spatial aggregations. Cases of dengue disease were geocoded and spatially allocated to census sectors, and temporally aggregated by epidemiological periods. The census sectors are nested in administrative divisions defined as communes, configuring two levels of spatial aggregation for the dengue cases. Spatio-temporal models including census sector and commune-level spatially structured random effects were fitted to estimate dengue incidence relative risks using the integrated nested Laplace approximation (INLA) technique. The final selected model included two-level spatial random effects, a global structured temporal random effect, and a census sector-level interaction term. Risk maps by epidemiological period and risk profiles by census sector were generated from the modeling process, showing the transmission dynamics of the disease. All the census sectors in the city displayed high risk at some epidemiological period in the outbreak periods. Relative risk estimation of dengue disease using INLA offered a quick and powerful method for parameter estimation and inference.

A two-stage approach to estimate spatial and spatio-temporal disease risks in the presence of local discontinuities and clusters

Disease risk maps for areal unit data are often estimated from Poisson mixed models with local spatial smoothing, for example by incorporating random effects with a conditional autoregressive prior distribution. However, one of the limitations is that local discontinuities in the spatial pattern are not usually modelled, leading to over-smoothing of the risk maps and a masking of clusters of hot/coldspot areas. In this paper, we propose a novel two-stage approach to estimate and map disease risk in the presence of such local discontinuities and clusters. We propose approaches in both spatial and spatio-temporal domains, where for the latter the clusters can either be fixed or allowed to vary over time. In the first stage, we apply an agglomerative hierarchical clustering algorithm to training data to provide sets of potential clusters, and in the second stage, a two-level spatial or spatio-temporal model is applied to each potential cluster configuration. The superiority of the proposed approach with regard to a previous proposal is shown by simulation, and the methodology is applied to two important public health problems in Spain, namely stomach cancer mortality across Spain and brain cancer incidence in the Navarre and Basque Country regions of Spain.

Flexible Bayesian P-splines for smoothing age-specific spatio-temporal mortality patterns

In this paper age-space-time models based on one and two-dimensional P-splines with B-spline bases are proposed for smoothing mortality rates, where both fixed relative scale and scale invariant two-dimensional penalties are examined. Model fitting and inference are carried out using integrated nested Laplace approximations, a recent Bayesian technique that speeds up computations compared to McMC methods. The models will be illustrated with Spanish breast cancer mortality data during the period 1985-2010, where a general decline in breast cancer mortality has been observed in Spanish provinces in the last decades. The results reveal that mortality rates for the oldest age groups do not decrease in all provinces.

Spatial gender-age-period-cohort analysis of pancreatic cancer mortality in Spain (1990-2013)

Recently, the interest in studying pancreatic cancer mortality has increased due to its high lethality. In this work a detailed analysis of pancreatic cancer mortality in Spanish provinces was performed using recent data. A set of multivariate spatial gender-age-period-cohort models was considered to look for potential candidates to analyze pancreatic cancer mortality rates. The selected model combines features of APC (age-period-cohort) models with disease mapping approaches. To ensure model identifiability sum-to-zero constraints were applied. A fully Bayesian approach based on integrated nested Laplace approximations (INLA) was considered for model fitting and inference. Sensitivity analyses were also conducted. In general, estimated average rates by age, cohort, and period are higher in males than in females. The higher differences according to age between males and females correspond to the age groups [65, 70), [70, 75), and [75, 80). Regarding the cohort, the greatest difference between men and women is observed for those born between the forties and the sixties. From there on, the younger the birth cohort is, the smaller the difference becomes. Some cohort differences are also identified by regions and age-groups. The spatial pattern indicates a North-South gradient of pancreatic cancer mortality in Spain, the provinces in the North being the ones with the highest effects on mortality during the studied period. Finally, the space-time evolution shows that the space pattern has changed little over time.

A statistical algorithm showing coenzyme Q10 and citrate synthase as biomarkers for mitochondrial respiratory chain enzyme activities

Laboratory data interpretation for the assessment of complex biological systems remains a great challenge, as occurs in mitochondrial function research studies. The classical biochemical data interpretation of patients versus reference values may be insufficient, and in fact the current classifications of mitochondrial patients are still done on basis of probability criteria. We have developed and applied a mathematic agglomerative algorithm to search for correlations among the different biochemical variables of the mitochondrial respiratory chain in order to identify populations displaying correlation coefficients >0.95. We demonstrated that coenzyme Q10 may be a better biomarker of mitochondrial respiratory chain enzyme activities than the citrate synthase activity. Furthermore, the application of this algorithm may be useful to re-classify mitochondrial patients or to explore associations among other biochemical variables from different biological systems.

Two-level spatially structured models in spatio-temporal disease mapping

This work focuses on extending some classical spatio-temporal models in disease mapping. The objective is to present a family of flexible models to analyze real data naturally organized in two different levels of spatial aggregation like municipalities within health areas or provinces, or counties within states. Model fitting and inference will be carried out using integrated nested Laplace approximations. The performance of the new models compared to models including a single spatial random effect is assessed by simulation. Results show good behavior of the proposed two-level spatially structured models in terms of several criteria. Brain cancer mortality data in the municipalities of two regions in Spain will be analyzed using the new model proposals. It will be shown that a model with two-level spatial random effects overcomes the usual single-level models.

Age-space-time CAR models in Bayesian disease mapping

Mortality counts are usually aggregated over age groups assuming similar effects of both time and region, yet the spatio-temporal evolution of cancer mortality rates may depend on changing age structures. In this paper, mortality rates are analyzed by region, time period and age group, and models including space-time, space-age, and age-time interactions are considered. The integrated nested Laplace approximation method, known as INLA, is adopted for model fitting and inference in order to reduce computing time in comparison with Markov chain Monte Carlo (McMC) methods. The methodology provides full posterior distributions of the quantities of interest while avoiding complex simulation techniques. The proposed models are used to analyze prostate cancer mortality data in 50 Spanish provinces over the period 1986-2010. The results reveal a decline in mortality since the late 1990s, particularly in the age group [65,70), probably because of the inclusion of the PSA (prostate-specific antigen) test and better treatment of early-stage disease. The decline is not clearly observed in the oldest age groups. Copyright © 2016 John Wiley & Sons, Ltd.

Temporal evolution of brain cancer incidence in the municipalities of Navarre and the Basque Country, Spain

BACKGROUND

Brain cancer incidence rates in Spain are below the European's average. However, there are two regions in the north of the country, Navarre and the Basque Country, ranked among the European regions with the highest incidence rates for both males and females. Our objective here was two-fold. Firstly, to describe the temporal evolution of the geographical pattern of brain cancer incidence in Navarre and the Basque Country, and secondly, to look for specific high risk areas (municipalities) within these two regions in the study period (1986-2008).

METHODS

A mixed Poisson model with two levels of spatial effects is used. The model also included two levels of spatial effects (municipalities and local health areas). Model fitting was carried out using penalized quasi-likelihood. High risk regions were detected using upper one-sided confidence intervals.

RESULTS

Results revealed a group of high risk areas surrounding Pamplona, the capital city of Navarre, and a few municipalities with significant high risks in the northern part of the region, specifically in the border between Navarre and the Basque Country (Gipuzkoa). The global temporal trend was found to be increasing. Differences were also observed among specific risk evolutions in certain municipalities.

CONCLUSIONS

Brain cancer incidence in Navarre and the Basque Country (Spain) is still increasing with time. The number of high risk areas within those two regions is also increasing. Our study highlights the need of continuous surveillance of this cancer in the areas of high risk. However, due to the low percentage of cases explained by the known risk factors, primary prevention should be applied as a general recommendation in these populations.

Analyzing the evolution of young people's brain cancer mortality in Spanish provinces

OBJECTIVES

To analyze the spatio-temporal evolution of brain cancer relative mortality risks in young population (under 20 years of age) in Spanish provinces during the period 1986-2010.

METHODS

A new and flexible conditional autoregressive spatio-temporal model with two levels of spatial aggregation was used.

RESULTS

Brain cancer relative mortality risks in young population in Spanish provinces decreased during the last years, although a clear increase was observed during the 1990s. The global geographical pattern emphasized a high relative mortality risk in Navarre and a low relative mortality risk in Madrid. Although there is a specific Autonomous Region-time interaction effect on the relative mortality risks this effect is weak in the final estimates when compared to the global spatial and temporal effects.

CONCLUSIONS

Differences in mortality between regions and over time may be caused by the increase in survival rates, the differences in treatment or the availability of diagnostic tools. The increase in relative risks observed in the 1990s was probably due to improved diagnostics with computerized axial tomography and magnetic resonance imaging techniques.

Age- and sex-specific spatio-temporal patterns of colorectal cancer mortality in Spain (1975-2008)

In this paper, space-time patterns of colorectal cancer (CRC) mortality risks are studied by sex and age group (50-69, ≥70) in Spanish provinces during the period 1975-2008. Space-time conditional autoregressive models are used to perform the statistical analyses. A pronounced increase in mortality risk has been observed in males for both age-groups. For males between 50 and 69 years of age, trends seem to stabilize from 2001 onward. In females, trends reflect a more stable pattern during the period in both age groups. However, for the 50-69 years group, risks take an upward trend in the period 2006-2008 after the slight decline observed in the second half of the period. This study offers interesting information regarding CRC mortality distribution among different Spanish provinces that could be used to improve prevention policies and resource allocation in different regions.

On fitting spatio-temporal disease mapping models using approximate Bayesian inference

Spatio-temporal disease mapping comprises a wide range of models used to describe the distribution of a disease in space and its evolution in time. These models have been commonly formulated within a hierarchical Bayesian framework with two main approaches: an empirical Bayes (EB) and a fully Bayes (FB) approach. The EB approach provides point estimates of the parameters relying on the well-known penalized quasi-likelihood (PQL) technique. The FB approach provides the posterior distribution of the target parameters. These marginal distributions are not usually available in closed form and common estimation procedures are based on Markov chain Monte Carlo (MCMC) methods. However, the spatio-temporal models used in disease mapping are often very complex and MCMC methods may lead to large Monte Carlo errors and a huge computation time if the dimension of the data at hand is large. To circumvent these potential inconveniences, a new technique called integrated nested Laplace approximations (INLA), based on nested Laplace approximations, has been proposed for Bayesian inference in latent Gaussian models. In this paper, we show how to fit different spatio-temporal models for disease mapping with INLA using the Leroux CAR prior for the spatial component, and we compare it with PQL via a simulation study. The spatio-temporal distribution of male brain cancer mortality in Spain during the period 1986-2010 is also analysed.

Projections of cancer mortality risks using spatio-temporal P-spline models

Cancer mortality risk estimates are essential for planning resource allocation and designing and evaluating cancer prevention and management strategies. However, mortality figures generally become available after a few years, making necessary to develop reliable procedures to provide current and near future mortality risks. In this work, a spatio-temporal P-spline model is used to provide predictions of mortality/incidence counts. The model is appropriate to capture smooth temporal trends and to predict cancer mortality/incidence counts in different regions for future years. The prediction mean squared error of the forecast values as well as an appropriate estimator are derived. Spanish prostate cancer mortality data in the period 1975-2008 will be used to illustrate results with a focus on cancer mortality forecasting in 2009-2011.

Modelling risks in disease mapping

In this article, we propose a strategy of analysis of mortality data with the aim of providing a guideline for epidemiologists and public health researchers to choose a reasonable model for estimating mortality (or incidence) risks. Maps displaying the crude mortality rates or ratios are usually misleading because of the instability of the estimators in low populated areas. As an alternative, many smoothing methods have been presented in the literature based on Poisson inference. They account for the extra-Poisson variation (overdispersion), frequently present in the homogeneous Poisson model, by incorporating random effects. Here, we recommend to test for the potential sources of extra-Poisson variation because, depending on them, the models which fit better the data may be different. Overdispersion can be mainly due to spatial autocorrelation, unstructured heterogeneity or to a combination of these two, and also, when studying very rare diseases, it can be due to an excess of zeros in the data. In this article, different situations the analyst may encounter are detailed and appropriate procedures for each case are presented. The alternative models are illustrated using mortality data provided by the Statistical Institute of Navarra, Spain.

The use of mixture models for identifying high risks in disease mapping

Conventional approaches for estimating risks in disease mapping or mortality studies are based on Poisson inference. Frequently, overdispersion is present and this extra variability is modelled by introducing random effects. In this paper we compare two computationally simple approaches for incorporating random effects: one based on a non-parametric mixture model assuming that the population arises from a discrete mixture of Poisson distributions, and the second using a Poisson-normal mixture model which allows for spatial autocorrelation. The comparison is focused on how well each of these methods identify the regions which have high risks. Such identification is important because policy makers may wish to target regions associated with such extreme risks for financial assistance while epidemiologists may wish to target such regions for further study. The Poisson-normal mixture model is presented from both a frequentist, or empirical Bayes, and a fully Bayesian point of view. We compare results obtained with the parametric and non-parametric models specifically in terms of detecting extreme mortality risks, using infant mortality data of British Columbia, Canada, for the period 1981-1985, breast cancer data from Sardinia, for the period 1983-1987, and Scottish lip cancer data for 1975-1980. However, we also investigate the performance of these models in a simulation study. The key finding is that discrete mixture models seem to be able to locate regions which experience high risks; normal mixture models also work well in this regard, and perform substantially better when spatial autocorrelation is present.

Detecting interaction between random region and fixed age effects in disease mapping

The purpose of this article is to draw attention to the possible need for inclusion of interaction effects between regions and age groups in mapping studies. We propose a simple model for including such an interaction in order to develop a test for its significance. The assumption of an absence of such interaction effects is a helpful simplifying one. The measure of relative risk related to a particular region becomes easily and neatly summarized. Indeed, such a test seems warranted because it is anticipated that the simple model, which ignores such interaction, as is in common use, may at times be adequate. The test proposed is a score test and hence only requires fitting the simpler model. We illustrate our approaches using mortality data from British Columbia, Canada, over the 5-year period 1985-1989. For this data, the interaction effect between age groups and regions is quite large and significant.