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. EMBARGOED until 1 September 2023.

Abstract

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.