Development of spatial statistical methods for modelling point-referenced spatial data in malaria epidemiology

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.