Bayesian inference for a generalized population attributable fraction: the impact of early vitamin A levels on chronic lung disease in very low birthweight infants.

In this paper, the population attributable fraction is studied using the potential responses framework of Rubin's causal model. This framework facilitates definition of a general measure of population attributable effect which can accommodate many-valued and multivariate exposures as well as many-valued responses. Inferential issues are considered from the Bayesian perspective. Finite population inference is emphasized with inference in the case of a fully observed population given particular attention. The key inferential issue concerns computation of the posterior distribution of unobserved potential responses, given observed responses, exposures and covariates. A dependency on model parameters about which observed data are uninformative is highlighted and this reflects the unobservable nature of causal effects. In an application to a small cohort study of respiratory problems in very low birthweight infants, posterior inferences were found to be insensitive to assumptions concerning the joint distribution of potential response variables but sensitive to the assumption of weak ignorability, a weaker form of the more familiar assumption of no confounding by omitted covariates. In a model-based set-up, the weak ignorability assumption is identified with setting a model parameter to zero, and consequently uncertainty concerning this assumption can, in principle, be handled via the prior distribution for the model parameters. Copyright 2000 John Wiley & Sons, Ltd.