In his commentary on our article,1 Scanlan raises important issues to consider in measurement of health disparities,2 specifically that when measured on the relative scale, disparities are affected by the prevalence of the outcome; that whether disparities are found to be increasing or decreasing depends on whether they are assessed in terms of a favorable outcome or its complementary adverse outcome; and that dependence on prevalence is not only limited to relative measures such as the rate ratio but that the absolute difference also varies with prevalence. These issues were discussed a decade ago in this journal.3-5

The goal of our article was to identify a handful of broad practices in monitoring health disparities, health inequities, and social determinants of health to support the pursuit of health equity in the United States; it was not to describe all of the implications of measurement choices. Furthermore, in our view, Scanlan's commentary supports one of the 5 practices that we set forth: "Provide reasons for methodological choices and clarify their implications"1 and is not relevant to the other 4. The commentary's attention to potential pitfalls of relying solely on particular measures (beyond the pitfalls we had space to highlight in an article of limited length) bolsters the urgency of our call for transparency and, relatedly, for "intensive and systematic training ... for the workforce at the national, state, and local levels."1

Although it presents a compelling case study, the commentary does not resolve measurement conundrums. The commentary proposes that disparities be measured using an "estimated effect size" (EES).2 This is defined as the difference between percentages on the "probit" scale.6 The "probit" transformation finds the quantile of the standard normal distribution that corresponds to any given percentage. The scenarios in Table 1 were selected with EES = 0.5.2

In Table 2, the commentary revisits a study on the effect of school-entry vaccination requirement on racial/ethnic disparities in hepatitis B immunization coverage among students in grades 5 and 9.2 Scanlan reports that, if disparities were measured using EES, a reduction would be observed in both grades after imposition of the requirement (from EES = 0.47 to 0.34 in grade 5 and 0.37 to 0.24 in grade 9). Another effect size measure from the literature, Cohen's h index, is based on the difference between percentages on the "arcsine" scale.7 If disparities had been measured using Cohen's h, a reduction for grade 9 (from h = 0.29 to 0.15) but an increase for grade 5 (from h = 0.23 to 0.27) would have been observed instead. Thus, 2 effect size measures, Cohen's h and EES, can result in diverging conclusions. While it remains unclear which measure is superior as a measure of disparity, selected statistical properties of these, as well as 5 other effect size measures, were examined empirically; the study suggests that EES and the logarithm of the odds ratio (OR) perform equally well on the selected properties.8 Note that the OR concurs with EES in Table 2 of the commentary,2 showing reduction in disparities for both grades (from OR = 2.80 to 1.72 in grade 5 and 1.81 to 1.54 in grade 9).

Furthermore, one can formulate scenarios where EES, like other measures of disparities, is affected by prevalence, contradicting Scanlan's claim that EES is "unaffected by the prevalence of an outcome."2^(p418) Indeed, consider 2 hypothetical percentages 13.9% and 1.7%, with ratio = 8.0, and 72.5% and 48.3%, with ratio = 1.5. Both these scenarios have Cohen's h = 0.5, indicating a "medium" effect size; yet, by Scanlan's interpretation, the "underlying distributions of factors associated with experiencing the outcome"2^(p416) of the 2 groups in the first scenario differ by 1 standard deviation (EES = 1.03), whereas those in the second scenario differ by slightly more than half a standard deviation (EES = 0.64). The difficulty with this interpretation is that, unlike the standard deviation for the difference between 2 normal means, the standard deviation for the difference between binomial proportions depends on the proportions being compared and normality cannot be readily assumed.

We, the authors of the article discussed by Scanlan, agree with the primary issues raised in his commentary and some of us have published on them9; however, we do not see how it casts doubt on our article's content or conclusions about how to handle the complexity inherent in measuring health disparities. We concluded, in part, that "a suite of measures provides the most holistic picture of health disparities."

Our article contributes to the field by setting forth key measurement practices for monitoring national progress toward health equity: (1) assessing differences in health and its determinants that are associated with social position; (2) assessing social and structural determinants of health; (3) providing reasons for methodological choices and clarifying their implications; (4) comparing groups simultaneously classified by multiple social statuses; and (5) considering the needs of stakeholders in choice of measures. The measurement conundrums discussed by Scanlan point to opportunities for future methodological innovation that will complement this set of practices.

-Ana Penman-Aguilar, PhD, MPH

Office of Minority Health and Health Equity

Centers for Disease Control and Prevention

Atlanta, Georgia

[email protected]

-Makram Talih, PhD

National Center for Health Statistics

Hyattsville, Maryland

-Ramal Moonesinghe, PhD, MA, MS

Office of Minority Health and Health Equity

Centers for Disease Control and Prevention

Atlanta, Georgia

-David Huang, PhD, MPH, CPH

National Center for Health Statistics

Hyattsville, Maryland

REFERENCES