Using Bayesian graphical models to model biases in observational studies and to combine multiple data sources: Application to low birth-weight and water disinfection by-products

Data in the social, behavioral and health sciences frequently come from observational studies instead of controlled experiments. In addition to random errors, observational data typically contain additional sources of uncertainty such as missing values, unmeasured confounders, and selection biases. Also, due to the complicated nature of the research question, a single data set may not provide sufficient information for valid inference. As a result, multiple data sources are often necessary to identify the biases and inform about different aspects of the research question. Standard analyses of each data source separately may fail to capture uncertainty other than simple random errors, thus may produce misleading results. Therefore it becomes necessary to link together different sub-models for each source in a comprehensive way. Bayesian graphical models provide a coherent way to connect a series of local sub-models, based on different data sets, into a global unified analysis. In this manuscript, we present a unified modeling framework that will account for multiple biases simultaneously and give more accurate parameter estimates than standard approaches. We illustrate our approach by analyzing data from a study of water disinfection by-products and adverse birth outcomes in the U.K.