Hierarchical Models for International Comparisons: Smoking, Disability, and Social Inequality in 21 European Countries

Background: International comparisons of social inequalities in health outcomes and behaviors are challenging. Due to the level of disaggregation often required, data can be sparse and methods to make adequately powered comparisons are lacking. We aimed to illustrate the value of a hierarchical Bayesian approach that partially pools country-level estimates, reducing the influence of sampling variation and increasing the stability of estimates. We also illustrate a new way of simultaneously displaying the uncertainty of both relative and absolute inequality estimates. Methods: We used the 2014 European Social Survey to estimate smoking prevalence, absolute, and relative inequalities for men and women with and without disabilities in 21 European countries. We simultaneously display smoking prevalence for people without disabilities (x-axis), absolute (y-axis), and relative inequalities (contour lines), capturing the uncertainty of these estimates by plotting a 2-D normal approximation of the posterior distribution from the full probability (Bayesian) analysis. Results: Our study confirms that across Europe smoking prevalence is generally higher for people with disabilities than for those without. Our model shifts more extreme prevalence estimates that are based on fewer observations, toward the European mean. Conclusions: We demonstrate the utility of partial pooling to make adequately powered estimates of inequality, allowing estimates from countries with smaller sample sizes to benefit from the increased precision of the European average. Including uncertainty on our inequality plot provides a useful tool for evaluating both the geographical patterns of variation in, and strength of evidence for, differences in social inequalities in health.