  Population attributable risk (PAR) is used in epidemiology to predict the
impact of removing a risk factor from the population. Until recently, no
standard approach for calculating confidence intervals or the variance for PAR
was available in the literature. Pirikahu et al. (2016) outlined a fully
Bayesian approach to provide credible intervals for the PAR from a
cross-sectional study, where the data was presented in the form of a 2 x 2
table. However, extensions to cater for other frequently used study designs
were not provided. In this paper we provide methodology to calculate credible
intervals for the PAR for case-control and cohort studies. Additionally, we
extend the cross-sectional example to allow for the incorporation of
uncertainty that arises when an imperfect diagnostic test is used. In all these
situations the model becomes over-parameterised, or non-identifiable, which can
result in standard "off-the-shelf" Markov chain Monte Carlo updaters taking a
long time to converge or even failing altogether. We adapt an importance
sampling methodology to overcome this problem, and propose some novel MCMC
samplers that take into consideration the shape of the posterior ridge to aid
in the convergence of the Markov chain.
