Questions about health disparity trends are usually framed in a general form, such as the following: Has disparity increased or decreased? However, this general question obscures the fact that “disparity” is a complex concept (10, 11), and estimating its magnitude may depend heavily on such questions as whether to measure absolute or relative disparity, whether to account for the size (population share) of the groups being compared, and from what reference point differences are measured (4). For example, the question of whether global economic inequality has increased or decreased depends on whether countries are weighted equally or individuals are weighted equally (12, 13). This issue has not been adequately studied with regard to monitoring health disparities and has implications for policy development to reduce disparities. If there is substantial inconsistency among disparity measures, then a deeper understanding of the methodological differences among measures is needed, and a suite of indicators may be warranted.

In this paper, we describe and empirically compare selected summary measures of health disparity. As an example, we analyzed trends in social disparities for lung cancer, which remains the leading cause of US overall cancer death and is among the top three sites of incidence in each race-ethnic group (14). A number of empirical studies have also documented social disparities in lung cancer incidence (15, 16), treatment (17, 18), survival (19), and mortality (20–22).

Rate ratio The rate ratio (RR) is probably the most frequently used measure of health disparity and is calculated as RR = y₁/y_2, where y₁ is the health status of the least healthy group and y₂ is the health status of the most healthy. Although in the context of social group comparisons the rate ratio is typically based on comparing, for example, the least socially advantaged group (e.g., the lowest socioeconomic group) with the most advantaged group, as a summary measure of health disparity as one would a measure of range. That is, at each time point it measures the ratio of the rates of the best and worst group (i.e., the relative range), regardless of their social group status. Thus, the specific groups with the best and worst rates may change over time. If there is no disparity, the rate ratio takes on a value of 1.

Index of disparity The index of disparity (IDisp) summarizes the average difference between several group rates and a reference rate and expresses the summed differences as a proportion of the reference rate (i.e., a ratio). This measure was introduced by Pearcy and Keppel (3) and is calculated as , where y_j indicates the measure of health status in the jth group, and y_ref is the health status indicator in the reference population. Although in principle any reference group may be chosen, typically the best group rate is used as the comparison, because that represents the rate desirable for all groups to achieve (2). We use the best group rate as the reference point and note that the group with the best rate may change over time. If an external rate is used as the reference population (e.g., the total population rate, a target rate), the differences are divided by the total number of groups compared (J) rather than by J − 1. If there is no disparity, the index of disparity takes on a value of 0.

Relative concentration index The relative concentration index (RCI) measures the extent to which health or illness is concentrated among particular social groups. This index may be used only with ordinal social groups (i.e., those that have an inherent ranking), such as income or education. The general formula for the relative concentration index for grouped data is given by Kakwani et al. (23) as , where μ is the population average rate of health, p_j is the group’s population share, y_j is the group’s mean health, and X_j is the relative rank of the jth socioeconomic group, which is defined as X_j = p_γ − 0.5 p_j, where p_γ is the cumulative share of the population up to and including group j, and p_j is the share of the population in group j. X_j indicates the cumulative share of the population up to the midpoint of each group interval. One advantage of the relative concentration index is that it “reflects the socioeconomic dimension to inequalities in health” (8, p. 548). That is, when the outcome is positive (i.e., a measure of “health”), a downward health gradient (where health worsens with increasing social group rank) results in a positive relative concentration index, whereas an upward health gradient results in a negative relative concentration index. The opposite is true when the outcome is negative (i.e., a measure of “illness”). Thus, in our study, a negative relative concentration index indicates that lung cancer incidence is higher among the more disadvantaged groups. When there is no disparity, the relative concentration index is 0. It is worth noting that the relative concentration index has a specific mathematical relation with the more well-known relative index of inequality (8) and will produce similar results (4). To avoid redundancy, we do not include the relative index of inequality.

Theil index and mean log deviation The Theil index (TI) and mean log deviation (MLD) are measures of general disproportionality developed by the economist Henri Theil (24). They summarize the disproportionality between shares of health and shares of population (expressed as a ratio on the natural logarithm scale). For grouped data, they may be written (12) as , where p_j is the proportion of the population in group j, and r_j is the ratio of the prevalence or rate of health in group j relative to the total rate, that is, r_j = y_j/μ, where y_j is the rate of health in group j, and μ is the total population rate. Both measures are population weighted, are more sensitive to health differences further from the average rate (because they use the logarithm of the shares of health), and may be used for both ordinal and nominal social groups. In general, the Theil index will be somewhat more influenced by groups with high incidence ratios, whereas the mean log deviation will be somewhat more influenced by groups with large population shares (12). Both measures take on a value of 0 if there is no disparity.

Rate difference The rate difference (RD) is the absolute disparity between two health status indicators, that is, the simple arithmetic difference. It is calculated as RD = y₁ − y₂, where y₁ and y₂ are indicators of health status in the least healthy and most healthy groups, respectively. As for the rate ratio, the rate difference is often used to compare the health of less advantaged social groups with that of more advantaged groups. However, we use rate difference as a summary measure of the absolute gap between the best rate and the worst rate for a given outcome (i.e., the absolute range across all race-ethnic or socioeconomic groups), regardless of which two social groups are being compared. In this case, the rate difference will be 0 if there is no disparity.

Between-group variance The variance summarizes all squared deviations from a population average. In the case of grouped data, this is the between-group variance (BGV), and it is calculated by squaring the differences in group rates from the population average and weighting by population size: , where p_j is group j’s population size, y_j is group j’s average health status, and μ is the average health status of the population. If there is no disparity, the between-group variance is 0. One way to interpret the between-group variance is as the variance that would exist in the population if each individual had the mean health of his or her social group (i.e., if there were no within-social group variation) (10). The between-group variance may be a useful indicator of absolute disparity for nominal social groups, because it weights by population group size and is sensitive to the magnitude of larger deviations from the population average because it uses a squared deviation (25).

Absolute concentration index The absolute concentration index (ACI) measures the extent to which health or illness is concentrated among particular social groups on the absolute scale. It may only be used with ordinal social groups. It is a measure of the covariance between social rank and health, and it is derived by plotting the cumulative share of the population, ranked by social status, against the cumulative amount of ill health (i.e., the cumulative contribution of each subgroup to the mean level of health in the population). The absolute version of the concentration index is calculated by multiplying the relative concentration index by the mean of the health variable: ACI = μRCI, where RCI is the relative concentration index defined above, and μ is the mean level of health in the population. Thus, if there is no disparity (i.e., if RCI = 0), the ACI is 0.

To generate estimates of precision, we used a resampling or “bootstrap” technique described previously (2, 5). Briefly, for each year, gender, and race-ethnic or socioeconomic subgroup, we used the observed age-adjusted rate and its standard error to reestimate each group’s rate 1,000 times, assuming a random normal distribution. We then calculated each measure of disparity 1,000 times and used the resulting distribution to estimate the standard error (SE) of each index. We estimated the change in each index from the beginning to the end of the period of observation and calculated a 95 percent confidence interval for this change by use of the formula to estimate the standard error of the change (2). Thus, changes in disparity for which the 95 percent confidence interval includes 0 would not be considered statistically significant with conventional criteria. However, because the indices are measured on different scales, we compared the overall change in disparity by calculating the percent change in each index from 1992 to 2004 (for the rate ratio, we calculated the percent change in the excess rate ratio). In order to graphically compare trends in each index, we plotted the percent change in each index since 1992 for each data year.

Our example also showed disagreement about the direction of change for race-ethnic disparities. Measures of absolute disparity declined among males, but some measures of relative disparity increased. Thus, answering the question of whether race-ethnic disparities are improving depends, in part, on whether the absolute or relative scale is used. Yet even among the measures of relative disparity there was disagreement, with the index of disparity suggesting that race-ethnic disparities increased by 36 percent among males but the measures of entropy (Theil index and mean log deviation) suggesting an increase of roughly half that size. Further, despite the similarity in both magnitude and direction of change among females, the index of disparity and measures of entropy went in opposite directions during some intervals between 1992 and 2004. The measures of entropy differ from the index of disparity because they weight by population size, use the total population rate as the reference point, and measure differences using the natural logarithm. In additional analyses, we attempted to minimize these differences by recalculating the index of disparity weighted by population size and using the population average as the reference rate. With these two modifications, the index of disparity still showed a 24.2 percent increase among males (table 3), suggesting that the use of the natural logarithm in the measures of entropy is the likely reason for the difference.

The differences that we observed result from different conceptions of disparity on which these measures are based, and our results suggest that attempts to evaluate trends in health disparities require judgments about which conception of disparity is important for the question at hand. In particular, choices about the appropriate reference point from which to measure disparity, whether disparity should be measured in absolute or relative terms, whether to weight social groups according to the fraction of the population they represent, and whether to place additional weight on particular subgroups of interest (e.g., the poor or the least healthy) should be explicit when assessing health disparity change. These choices may be framed as methodological decisions, but they also reflect value judgments, and this is no different for measuring health inequality than for economic inequality. As Amartya Sen has noted, “In one way or another, usable measures of inequality must combine factual features with normative ones” (10, p. 3). For example, the decision of whether or not to use a population-weighted measure of disparity is a decision about how much value to place on the health of individuals: Population-weighted measures count all individuals equally, while unweighted measures count all groups equally and weight individuals inversely with respect to the size of their social group (12). Population-weighted measures therefore capture changes in the distribution of social groups over time and would serve to complement a view that regards this as an important aspect of health disparity. Alternatively, unweighted measures would complement a view that social groups with normative importance should be weighted equally, regardless of their population size. Either one of these choices may be justifiable, but because this is likely to have consequences for one’s conclusions about the magnitude of disparity, the reasons for choosing one versus another conception of disparity should be made clear at the outset.

We used the example of socioeconomic and race-ethnic trends in lung cancer incidence to compare selected measures of disparity, but our results are likely to apply in assessments of other outcomes or for other social group comparisons. Elsewhere, we have systematically compared this same set of summary measures of disparity across 22 separate analyses of cancer incidence, mortality, and risk factors and found that, in nearly half of all cases, a substantive judgment about disparity trends required a priori decisions about whether disparities should be measured in absolute or relative terms or whether to use population-weighted versus unweighted disparity measures (30).

It is important to reiterate that the methods we evaluated here are not meant as a substitute for a careful analysis of social disparities in health among particular groups or the causes of observed health disparities. Rather, they provide a cautionary note about the importance of carefully thinking through the implications of specific measures of disparity before using them to monitor health disparity trends. Quantifying health disparity requires judgments about what aspects of the distribution of health are important. Making explicit the rationale for choosing particular summary measures of disparity will allow for a more effective understanding of the evidence base used to monitor progress toward health disparity goals and objectives.

This project was carried out under contract with the National Cancer Institute (contract 263-MQ-611198).

The content of this publication does not necessarily reflect the views or policies of the National Cancer Institute.