Mortality Map

Abstract: Plasmodium falciparum malaria is the world’s most important parasitic disease and a major cause of morbidity and mortality in Africa. However figures for the burden of malaria morbidity and mortality are very uncertain, since reliable maps of the distribution of malaria transmission and the numbers of affected individuals are not available for most of the African continent. Accurate statistics on the geographical distribution of different endemicities of malaria, on the populations at risk, and on the implications of given levels of endemicity for morbidity and mortality are important for effective malaria control programs. These estimates can be obtained using appropriate statistical models which relate infection, morbidity, and mortality rates to risk factors, measured at individual level, but also to factors that vary gradually over geographical locations. Statistical models which incorporate geographical or individual heterogeneity are complex and highly parameterized. Limitations in statistical computation have until recently made the implementation of these models impractical for non-normal response data, sampled at large numbers of geographical locations. Modern developments in Markov chain Monte Carlo (MCMC) inference have greatly advanced spatial modelling, however many methodological and theoretical problems still remain. For data collected over a fixed number of locations (point-referenced or geostatistical data) such as malaria morbidity and mortality data used in this study, spatial correlation is best specified by parameterizing the variance-covariance matrix of the outcome of interest in relation to the spatial configuration of the locations (variogram modelling). This has been considered infeasible for a large number of locations because of the repeated inversion of the variance-covariance matrix involved in the likelihood. In addition the spatial correlation in malariological data could be dependent not only on the distance between locations but on the locations themselves. Variogram models need to be further developed to take into account the above property which is known as non-stationarity. This thesis reports research with the objectives of: a) developing Bayesian hierarchical models for the analysis of point-referenced malaria prevalence, malaria transmission and mortality data via variogram modelling for a large number of locations taking into account non-stationarity and misalignment, while present in the data; b) producing country specific and continent-wide maps of malaria transmission and malaria prevalence in Africa, augmented by the use of climatic and environmental data; c) assessing the magnitude of the effects of malaria endemicity on infant and child mortality after adjusting of socio-economic factors and geographical patterns. A comparison of the MCMC and the Sampling-Importance-Resampling approach for Bayesian fitting of variogram models showed that the latter was no easier to implement, did not improve estimation accuracy and did not lead to computationally more efficient estimation. Different approaches were proposed to overcome the inversion of large covariance matrices. Numerical algorithms especially suited within the MCMC framework were implemented to convert large covariance matrices to sparse ones and to accelerate inversion. A tesselation-based model was developed which partition the space into random Voronoi tiles. The model assumes a separate spatial process in each tile and independence between tiles. Model fit was implemented via reversible jump MCMC which takes into account the varying number of parameters arised due to random number of tiles. This approach facilitates inversion by converting the covariance matrix to block diagonal form. In addition, this model is well suited for non-stationary data. An accelerated failure time model was developed for spatially misaligned data to assess malaria endemicity in relation to child mortality. The misalignment arised because the data were extracted from databases which were collected at a different set of locations. The newly developed statistical methodology was implemented to produce smooth maps of malaria transmission in Mali and West- and Central Africa, using malaria survey data from the Mapping Malaria Risk in Africa (MARA) database. The surveys were carried out at arbitrary locations and include non-standardized and overlapping age groups. To achieve comparability between different surveys, the Garki transmission model was applied to convert the heterogeneous age prevalence data to a common scale of a transmission intensity measure. A Bayesian variogram model was fitted to the transmission intensity estimates. The model adjusted for environmental predictors which were extracted from remote sensing. Bayesian kriging was used to obtain smooth maps of the transmission intensity, which were converted to age-specific maps of malaria risk. TheWest- and Central African map was based on a seasonality model we developed for the whole of Africa. Expert opinion suggests that the resulting maps improve previous mapping efforts. Additional surveys are needed to increase the precision of the predictions in zones were there are large disagreement with previous maps and data are sparse. The survival model for misaligned data was implemented to produce a smooth mortality map in Mali and assess the relation between malaria endemicity and child and infant mortality by linking the MARA database with the Demographic and Health Survey (DHS) database. The model was adjusted for socio-economic factors and spatial dependence. The analysis confirmed that mothers education, birth order and preceding birth interval, sex of infant, residence and mothers age at birth have a strong impact on infant and child mortality risk, but no statistically significant effect of P. falciparum prevalence could be demonstrated. This may reflect unmeasured local factors, for instance variations in health provisions or availability of water supply in the dry Sahel region, which could have a stronger influence than malaria risk on mortality patterns.

Abstract: The Italian Atlas of mortality at municipality level is the result of a research project coordinated by the Emilia-Romagna region and supported by the Health Ministry. To the realisation of this project have collaborated the Institute of Medical Statistics of Milano and the CILEA under the supervision of Prof. Cesare Cislaghi. Compared to previous equivalent products, this Atlas contains a number of methodological and content innovations. This was a consequence of the development of new statistical methods and the need of achieving different aims. First of all, the Atlas was aimed at describing the mortality at small area level, which is obtained via Kernel estimates; secondly, the objective was to identify suspect clusters of deaths which may suggest the existence of high risk areas. The Mortality Atlas is formed by 31 tables, one for each of the analysed cause of death; each table has a circular shape of 100 hundred kilometers radius and contains a variable number of municipalities; each municipality may be present in more than one circle. The Atlas is available on magnetic support and for each cause of death are provided several statistical analyses and indicators included in different files. One of these files can be directly used to build high quality maps using the graphical package MAPINFO.

Abstract: The analysis of geographic inequality heavily relies on the use of location-enabled statistical data and quantitative measures to present the spatial patterns of the selected phenomena and analyze their differences. To protect the privacy of individual instance and link to administrative units, point-based datasets are spatially aggregated to area-based statistical datasets, where only the overall status for the selected levels of spatial units is used for decision making. The partition of the spatial units thus has dominant influence on the outcomes of the analyzed results, well known as the Modifiable Areal Unit Problem (MAUP). A new spatial reference framework, the Taiwan Geographical Statistical Classification (TGSC), was recently introduced in Taiwan based on the spatial partition principles of homogeneous consideration of the number of population and households. Comparing to the outcomes of the traditional township units, TGSC provides additional levels of spatial units with finer granularity for presenting spatial phenomena and enables domain experts to select appropriate dissemination level for publishing statistical data. This paper compares the results of respectively using TGSC and township unit on the mortality data and examines the spatial characteristics of their outcomes. For the mortality data between the period of January 1st, 2008 and December 31st, 2010 of the Taitung County, the all-cause age-standardized death rate (ASDR) ranges from 571 to 1757 per 100,000 persons, whereas the 2nd dissemination area (TGSC) shows greater variation, ranged from 0 to 2222 per 100,000. The finer granularity of spatial units of TGSC clearly provides better outcomes for identifying and evaluating the geographic inequality and can be further analyzed with the statistical measures from other perspectives (e.g., population, area, environment.). The management and analysis of the statistical data referring to the TGSC in this research is strongly supported by the use of Geographic Information System (GIS) technology. An integrated workflow that consists of the tasks of the processing of death certificates, the geocoding of street address, the quality assurance of geocoded results, the automatic calculation of statistic measures, the standardized encoding of measures and the geo-visualization of statistical outcomes is developed. This paper also introduces a set of auxiliary measures from a geographic distribution perspective to further examine the hidden spatial characteristics of mortality data and justify the analyzed results. With the common statistical area framework like TGSC, the preliminary results demonstrate promising potential for developing a web-based statistical service that can effectively access domain statistical data and present the analyzed outcomes in meaningful ways to avoid wrong decision making. Keywords—Mortality map, spatial patterns, statistical area, variation. Jung-Hong Hong, Jing-Cen Yang, and Cai-Yu Ou are with the Department of Geomatics, National Cheng Kung University, Tainan, Taiwan (e-mail: junghong@mail.ncku.edu.tw, jingcen1022@gmail.com, pumking23@ gmail.com).