A Multilevel Regression Model for Geographical Studies in Sets of Non-Adjacent Cities

In recent years, small-area-based ecological regression analyses have been published that study the association between a health outcome and a covariate in several cities. These analyses have usually been performed independently for each city and have therefore yielded unrelated estimates for the cities considered, even though the same process has been studied in all of them. In this study, we propose a joint ecological regression model for multiple cities that accounts for spatial structure both within and between cities and explore the advantages of this model. The proposed model merges both disease mapping and geostatistical ideas. Our proposal is compared with two alternatives, one that models the association for each city as fixed effects and another that treats them as independent and identically distributed random effects. The proposed model allows us to estimate the association (and assess its significance) at locations with no available data. Our proposal is illustrated by an example of the association between unemployment (as a deprivation surrogate) and lung cancer mortality among men in 31 Spanish cities. In this example, the associations found were far more accurate for the proposed model than those from the fixed effects model. Our main conclusion is that ecological regression analyses can be markedly improved by performing joint analyses at several locations that share information among them. This finding should be taken into consideration in the design of future epidemiological studies.