Ecological Inference for Relative Risks, with Application to Infrequent Mental Health Events

Abstract Mental health outcomes may show wide contrasts in incidence or prevalence between ethnic groups, often for relatively infrequent events (e.g. suicide). 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 disparities in risk between ages. 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 mix (e.g. Census data) are available. We consider in this paper an ecological inference method, applicable to infrequent events, which can use such information, and which furthermore takes account of the impacts of neighbourhood age structure on the health outcome. We consider two case studies to estimate age standardised relative risks by neighbourhood and ethnicity, one involving suicide, the other concerning psychosis. The analyses are for 6856 neighbourhoods in England.