Bayesian Inference for Population Attributable Measures from Under-identified Models

TL;DR

This paper develops Bayesian methods to accurately estimate confidence intervals for population attributable risk across various epidemiological study designs, addressing issues of model non-identifiability and computational challenges.

Contribution

It extends Bayesian inference for PAR to case-control and cohort studies and introduces importance sampling and novel MCMC techniques for over-parameterized models.

Findings

Provides credible intervals for PAR in multiple study designs.

Introduces importance sampling to handle non-identifiable models.

Develops novel MCMC samplers for better convergence.

Abstract

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.