Bayesian disease mapping with errors in covariates for studying the association between Insulin Dependent Diabetes Mellitus and malaria.

Ecological studies using maps showing relative risks (RR) of a disease in small geo-graphical areas are important for generating aetiological hypotheses and for identifying areas that deserve further investigation. When a disease is rare and non-contagious, a fully Bayesian hierarchial spatial model can be adopted to account for sample variabil-ity caused by scarcity of data as well as for measurement errors of the covariate. A Markov random field prior distribution for the relative risk of the disease can then be specified to incorporate spatial correlation, as neighbouring areas are likely to have similar risks. This smoothens the empirical map and makes the geographical trends and inferences more reliable. Ignoring measurement error in the model would lead to an underestimation of the regression coefficient and of its variance. Bayesian models can be extended to incorporate ecological covariates xi. In practice these covariates are rarely observed directly and the available data z; may either be imperfect measurements of, or proxies for X{. A simple solution to this problem is to estimate the actual covariate xi. and the available data s, independently for each area and to use this estimate as covariate in the ecological regression model. If spatial correlation is expected the Bayesian approach allows spatial smoothing on the covariate. Genetic studies have established the existence of association between Insulin Depen-dent Diabetes Mellitus (IDDM) and the HLA system, which is responsible for immuno-logical functions and is associated with susceptibility towards autoimmune diseases. Sardinia with high incidence of IDDM, a peculiar frequency distribution of HLA alleles and a past history of malaria offers an opportunity for investigating mechanisms under-lying the association between HLA antigens, malaria and IDDM. We carried out a study aimed at establishing the existence of association between genetic selection operated by malaria and the relative risk of IDDM in Sardinia. We estimated the incidence of IDDM in Sardinian residents aged 0-29 between 1987 and 1992 using data from the EURODIAB case register currently running in Sardinia. We used the prevalence of malaria in Sardinian communes in 1938-40 as proxy covariate. We chose a fully Bayesian hierarchial-spalial model to smoothen the random variation in the area-specific raw data as well as to account for measurement errors of the covariate. Since the prevalence of malaria represents the number of cases of malaria at a single point in time and since no information about the long term variability in malaria prevalence was available, this variance was specified a priori as a fixed quantity. The results showed that areas characterised by low past malaria prevalence tend to have higher risks of IDDM than areas with high past malaria prevalence. An analogous result was obtained using a different set of data; the cumulative prevalence of IDDM in army conscripts born in Sardinia between 1936 and 1973 was compared in Sardinian communes. IDDM prevalence steadily increased in both groups of communes at high and low malaria prevalence but it was found to be always lower in communes with high past malaria prevalence. We therefore conclude that the selective pressure operated by malaria could have contributed to the selection of HLA haplotypes associated with resistance to IDDM or genes that are in linkage disequilibrium with these haplotypes.