On the Use of Age-Adjusted Mortality Rates in Studies of Income Inequality and Population Health

To the editor:

In our recent article published in the June 2001 issue of this journal (Mellor and Milyo 2001b), we demonstrate that the statistical association between either country-level or state-level inequality and population health is not robust to minor and reasonable changes in the model specification or the time period examined. ¹ Two excellent commentaries appear along with our article. James S. House (2001) accepts our evidence and concludes that the income inequality hypothesis has proven a dry well; he urges public health researchers to move on to more promising areas of inquiry within the field of social determinants of health. In contrast, Ichiro Kawachi and Tony A. Blakely make a number of complaints about our study, then call for more research into the relationship between inequality and health. We welcome the opportunity to continue this exchange; in particular, we wish to address a fundamental methodological criticism found in Kawachi and Blakely.

In our JHPPL article, we present the results of several country- and state-level regressions of population health indicators on income inequality as well as regressions of changes in these health indicators on changes in inequality. The central criticism made by Kawachi and Blakely is that in our state-level analysis we account for the differing age composition of state populations through the use of control variables in our multivariate regression analysis. It has been more common in this literature for researchers to first age-adjust mortality rates, then conduct regression analysis. Our failure to do so is, in the eyes of Kawachi and Blakely, a "major threat" to the validity of our analysis.

When comparing mortality rates across geographic areas or other groupings, it is commonplace to adjust these rates for the differing age composition of the groups to be compared. If age is the only determinant of mortality, this is all well and good, but what if mortality rates differ with multiple factors? In such cases, multivariate adjustment is appropriate. Textbook accounts in both econometrics (e.g., Johnston and DiNardo 1997) and epidemiology (e.g., Rothman and Greenland 1998) describe how this can be accomplished in either of two ways: (1) by including independent variables that describe the age distribution of the relevant groups in the regression analysis (our method) or (2) by first age adjusting both the dependent and independent variables, then applying regression analysis to these age-adjusted variables. ²

But Kawachi and Blakely take us to task for failing to take a third way; they prefer that we first age-adjust area mortality rates, then regress these adjusted rates on our unadjusted independent variables. Kawachi and Blakely suggest that this partial adjustment method is standard practice among epidemiologists; we can confirm that it is at least so within the inequality and health literature (e.g., Kawachi and Kennedy 1997). Nevertheless, epidemiologists have long appreciated that direct age adjustment of only the dependent variable in a multivariate regression analysis will in general produce severe bias (Greenland and Morgenstern 1989, 1991; Greenland 1992; Greenland and Robins 1994; Morgenstern 1995). In fact, it is understood by empirical researchers across disciplinary boundaries that one should either directly age adjust all variables in a multivariate regression or none; in the latter case, age variables should be included as controls in the regression analysis (e.g., Rosenbaum and Rubin 1984).

Kawachi and Blakely make a related criticism that is similarly off the mark. They claim that by including variables describing the age and race composition of state populations as independent variables in our state-level regressions we risk aggravating the problem of ecological bias that is inherent in any such analysis. This much is true; in fact, any control variable may exacerbate the problems associated with recovering estimates of individual relationships from aggregate data. Then...