Ecological inference for relative risks, with application to infrequent mental health events

Mental health outcomes may show wide contrasts in incidence or prevalence between ethnic or socio-economic groups, often for relatively infrequent events. To gauge such relativities, one ideally seeks age standardised comparisons, given that ethnic groups may differ in age structure, and that the events themselves often show wide age disparities in risk. It is also advantageous to provide a geographically disaggregated (e.g. neighbourhood) perspective on relative risk differences, with sampling densities (e.g. Poisson) appropriate to possibly infrequent events. Often only total disease counts (with no socio-demographic disaggregation) are available for neighbourhoods, though data on ethnic or social mix (e.g. Census data) are available from other sources. We consider in this paper a novel ecological inference method which can use such information, and which furthermore takes account of the impacts of neighbourhood age structure on health outcomes. We consider a case study to estimate age standardised relative risks for psychosis by neighbourhood and ethnicity. The analysis is for 6856 English neighbourhoods.