Using Ecological Propensity Score to Adjust for Missing Confounders in   Small Area Studies
  Small area ecological studies are commonly used in epidemiology to assess the impact of area level risk factors on health outcomes when data are only available in an aggregated form. However the resulting estimates are often biased due to unmeasured confounders, which typically are not available from the standard administrative registries used for these studies. Extra information on confounders can be provided through external datasets such as surveys or cohorts, where the data are available at the individual level rather than at the area level; however such data typically lack the geographical coverage of administrative registries. We develop a framework of analysis which combines ecological and individual level data from different sources to provide an adjusted estimate of area level risk factors which is less biased. Our method (i) summarises all available individual level confounders into an area level scalar variable, which we call ecological propensity score (EPS), (ii) implements a hierarchical structured approach to predict the values of EPS whenever they are missing, (iii) includes the estimated and predicted EPS into the ecological regression linking the risk factors to the health outcome. Through a simulation study we show that integrating individual level data into small area analyses via EPS is a promising method to reduce the bias intrinsic in ecological studies due to unmeasured confounders; we also apply the method to a real case study to evaluate the effect of air pollution on coronary heart disease hospital admissions in Greater London. 
Yingbo Wang, Sylvia Richardson, Anna Hansell, Marta Blangiardo
stat.AP