  Epidemiologists often wish to estimate quantities that are easy to
communicate and correspond to the results of realistic public health scenarios.
Methods from causal inference can answer these questions. We adopt the language
of potential outcomes under Rubin's original Bayesian framework and show that
the parametric g-formula is easily amenable to a Bayesian approach. We show
that the frequentist properties of the Bayesian g-formula suggest it improves
the accuracy of estimates of causal effects in small samples or when data may
be sparse. We demonstrate our approach to estimate the effect of environmental
tobacco smoke on body mass index z-scores among children aged 4-9 years who
were enrolled in a longitudinal birth cohort in New York, USA. We give a
general algorithm and supply SAS and Stan code that can be adopted to implement
our computational approach in both time-fixed and longitudinal data.
