Using ecological propensity score to adjust for missing confounders in small area studies

Yingbo Wang, Monica Pirani, Anna L. Hansell, Sylvia Richardson, Marta Blangiardo*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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 data sets 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) summarizes 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 impute the values of EPS whenever they are missing, and (iii) includes the estimated and imputed 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.

Original languageEnglish
Pages (from-to)1-16
Number of pages16
Issue number1
Publication statusPublished - 1 Jan 2019
Externally publishedYes

Bibliographical note

Funding Information:
The work of the UK Small Area Health Statistics Unit is funded by Public Health England as part of the MRC-PHE Centre for Environment and Health, funded also by the UK Medical Research Council. This paper does not necessarily reflect the views of Public Health England or the Department of Health. SAHSU holds approvals from the National Research Ethics Service - reference 12/LO/0566 and 12/LO/0567 - and from the Health Research Authority Confidentially Advisory Group (HRA-CAG) for Section 251 support (HRA - 14/CAG/1039). Marta Blangiardo, Monica Pirani, Anna Hansell and Sylvia Richardson acknowledge support from the MRC Methodology grant MR/M025195/1. Sylvia Richardson acknowledges support from the MRC programme grant MC_UP_0801/1.

Publisher Copyright:
© 2017. Published by Oxford University Press.


  • Environmental epidemiology
  • Hierarchical model
  • Missing data
  • Observational study
  • Propensity score
  • Spatial statistics.


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