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Biostatistics Advance Access originally published online on November 27, 2008
Biostatistics 2009 10(2):335-351; doi:10.1093/biostatistics/kxn041
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© 2008 The Author(s)
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/2.0/uk/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Bayesian graphical models for regression on multiple data sets with different variables

C. H. Jackson*

MRC Biostatistics Unit, Institute of Public Health, Forvie Site, Robinson Way, Cambridge CB2 0SR, UK chris.jackson{at}mrc-bsu.cam.ac.uk

N. G. Best and S. Richardson

Department of Epidemiology and Public Health, Imperial College London, London, UK

Routinely collected administrative data sets, such as national registers, aim to collect information on a limited number of variables for the whole population. In contrast, survey and cohort studies contain more detailed data from a sample of the population. This paper describes Bayesian graphical models for fitting a common regression model to a combination of data sets with different sets of covariates. The methods are applied to a study of low birth weight and air pollution in England and Wales using a combination of register, survey, and small-area aggregate data. We discuss issues such as multiple imputation of confounding variables missing in one data set, survey selection bias, and appropriate propagation of information between model components. From the register data, there appears to be an association between low birth weight and environmental exposure to NO2, but after adjusting for confounding by ethnicity and maternal smoking by combining the register and survey data under our models, we find there is no significant association. However, NO2 was associated with a small but significant reduction in birth weight, modeled as a continuous variable.

Keywords: Air pollution; Confounding; Data synthesis; Low birth weight; Multiple imputation

* To whom correspondence should be addressed.

Received July 17, 2007; revised July 8, 2008; revised October 7, 2008; accepted for publication October 17, 2008.


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