Statistical inference for population based measures of risk reduction : a thesis presented in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Statistics at Massey University, Palmerston North, New Zealand
Epidemiologists and public health practitioners often wish to determine the population impact
of an intervention to remove or reduce a risk factor. Population attributable type measures, such
as the population attributable risk (PAR) and population attributable fraction (PAF), provide
a means of assessing this impact in a way that is accessible for a non-statistical audience. To
apply these concepts to real-world data, the calculation of estimates and conﬁdence intervals for
these measures should take into account the study design and any sources of uncertainty.
We provide a Bayesian approach for estimating the PAR and its credible interval, from
cross-sectional data resulting in a 2 × 2 table, and assess its Frequentist properties. With the
Bayesian approach proving superior this model is then extended by incorporating uncertainty due
to the use of an imperfect diagnostic test for exposure. The resulting model is under-identiﬁed
which causes convergence problems for common MCMC samplers, such as Gibbs and Metropolis-
Hastings. An alternative importance sampling method performs much better for these under-
identiﬁed models and can be used to explore the limiting posterior distribution. However, this
comes at the cost of needing to identify an appropriate transparent parameterisation, which
can be diﬃcult. We provide an adaptation of the Metropolis-Hastings random walk sampler
which, in comparison to other MCMC samplers, more eﬃciently explores the posterior ridge of
an under-identiﬁed model for large sample sizes.
Often data used to estimate these population attributable measures may include multiple
risk factors in addition to the one being considered for removal. Uncertainty regarding the
distribution of these risk factors in the population aﬀects the inference for PAR and PAF.
To allow for this uncertainty we propose a methodology where the uncertainty in the joint
distribution of the response and the covariate is accommodated.