Abstract
SummarySmall 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.
Highlights
Small area studies are commonly used in epidemiology to investigate the spatial variation of a health condition across the population or to evaluate the geographic patterns of diseases in relation to environmental, demographic and socio-economic factors.These studies are based on administrative registries, which are characterised by good spatial coverage for large populations, but usually only record a very limited set of information and miss important confounders, potentially leading to biased estimates of the effects of risk factors.In this paper, we integrate data from administrative registries with cohorts / surveys, which contain detailed information on participants
Such approach can suffer from lack of “congeniality”: Meng (1994) states that for a model to be congenial the imputation model needs to include the same variables as those of the substantive model, in order to avoid estimates biased toward the null; this might be non trivial for non linear relationships between the outcome and the exposure / risk factors, which is the case when the outcome is available in the form of aggregated counts as in small area studies
In particular (i) we propose an imputation model for areas with a missing propensity score; this accounts for the spatial structure of the data and can accomodate non-linearity in the relationship with other variables; (ii) we include the estimated / imputed propensity score in the analysis model in a flexible way to provide effective confounder adjustment when evaluating the effect of a risk factor on a health outcome; (iii) we discuss and account for the different sources of feedback across the overall modelling framework
Summary
Small area studies are commonly used in epidemiology to investigate the spatial variation of a health condition across the population or to evaluate the geographic patterns of diseases in relation to environmental, demographic and socio-economic factors. In particular (i) we propose an imputation model for areas with a missing propensity score; this accounts for the spatial structure of the data and can accomodate non-linearity in the relationship with other variables; (ii) we include the estimated / imputed propensity score in the analysis model in a flexible way to provide effective confounder adjustment when evaluating the effect of a risk factor on a health outcome; (iii) we discuss and account for the different sources of feedback across the overall modelling framework. The structure of this paper is as follows: Section 2 introduces our proposed ecological propensity score (EPS) framework for small area studies and Section 3 presents an extensive simulation study to evaluate the performance of the developed approach and to compare it with the commonly used MICE for imputing missing data; Section 4 applies this method to assess the link between airborne particle pollution and coronary heart disease hospital admissions in Greater London; we include a discussion and concluding remarks. In the remainder of this section we describe the model in details and discuss the issues around feedback
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