Bayesian methods of confidence interval construction for the population attributable risk from cross-sectional studies

Population attributable risk measures the public health impact of the removal of a risk factor. To apply this concept to epidemiological data, the calculation of a confidence interval to quantify the uncertainty in the estimate is desirable. However, because perhaps of the confusion surrounding the attributable risk measures, there is no standard confidence interval or variance formula given in the literature. In this paper, we implement a fully Bayesian approach to confidence interval construction of the population attributable risk for cross-sectional studies. We show that, in comparison with a number of standard Frequentist methods for constructing confidence intervals (i.e.delta, jackknife and bootstrap methods), the Bayesian approach is superior in terms of percent coverage in all except a few cases. This paper also explores the effect of the chosen prior on the coverage and provides alternatives for particular situations. Copyright (c) 2016 John Wiley & Sons, Ltd.