Small area studies are commonly used in epidemiology to assess the impact of risk factors
on health outcomes when data are available at the aggregated level. However the
estimates are often biased due to unmeasured confounders which cannot be taken into
account. Integrating individual-level information into area-level data in ecological studies
may help reduce bias. To investigate this, I develop an area/ecological level propensity
score (PS) to integrate individual-level data and then synthesise the area-level PS with
routinely available area-level datasets, such as hospital episode statistics (HES) and census
data. This framework comprises three steps:
1. Individual level survey data is used to obtain information on the potential confounders,
which are not measured at the area-level. Using a Bayesian hierarchical
framework I synthesise these variables and calculate PS at the ecological level, taking
into the account the correlation among the potential confounders.
2. The calculated PS is included as a scalar quantity in the regression model linking
environmental exposure/risk factors and health outcome. As PS has no epidemiological
interpretation, I introduce a number of flexible functions to allow for nonlinear
effects, such as fixed-knot splines, reversible jump MCMC (RJ) and random
walk (RW).
3. As real surveys are typically characterized by a limited coverage compared to small
area studies, I impute the ecological PS in the areas with no survey coverage. I propose
two new imputation models: random walk and cluster imputation (including
a) regression tree and b) profile regression ) to relax the assumption of linearity, and
through simulations, both imputation models are proven to produce better results
than the traditional linear imputation model.
I conclude that integrating individual-level data via PS is a promising method to reduce
the bias intrinsic in ecological studies due to unmeasured confounders and I introduce a
real application on small area studies for evaluating the effect of air pollution on CVD
hospital admissions in England.