Modeling the relation between socioeconomic status and mortality in a mixture of majority and minority ethnic groups

Ethnic variation in mortality and whether this variation can be explained by socioeconomic status are of substantive interest to social epidemiologists. The authors consider the analysis of mortality data for a mixture of majority and minority ethnic groups. Such data are likely to be coarsely cross-classified by age and socioeconomic status and yet, even then, in some cells of this cross-classification the observed mortality rate will be an imprecise estimate of the underlying rate. The authors illustrate conventional and Bayesian approaches to analysis with data from the 1996 census used by the New Zealand Census-Mortality Study. A conventional approach is exploratory data analysis first followed by Poisson regression. The authors use spline smoothing within a generalized additive model framework as an exploratory data analysis, following a strategy of adding just enough model structure to gain a sensible picture. A Bayesian approach is modeling first and then a description of posterior estimates using exploratory data analysis techniques. The authors use hierarchical Poisson regression and then illustrate their posterior estimates of the mortality rate using the same spline smoothing as before. The advantage of the hierarchical Bayesian approach is that it assesses uncertainty about a Poisson regression model proposed a priori; the conventional approach assumes that the fitted Poisson regression model is correct. All analyses use software that is available at no cost.