A system that rewards population health must be able to measure and track health inequalities. Health inequalities have most commonly been measured in a bivariate fashion, as a joint distribution of health and another attribute such as income, education, or race/ethnicity. I argue this practice gives insufficient information to reduce health inequalities and propose a summary measure of health inequalities, which gives information both on overall health inequality and bivariate health inequalities. I introduce 2 approaches to develop a summary measure of health inequalities. The bottom-up approach defines attributes of interest, measures bivariate health inequalities related to these attributes separately, and then combines these bivariate health inequalities into a summary index. The top-down approach measures overall health inequality and then breaks it down into health inequalities related to different attributes. After describing the 2 approaches in terms of building-block measurement properties, aggregation, value, data and sample size requirements, and communication, I recommend that, when data are available, a summary measure should use the top-down approach. In addition, a strong communication strategy is necessary to allow users of the summary measure to understand how it was calculated and what it means.

Developers of any performance reward system must select the performance improvements that deserve rewards and ensure fairness by measuring them appropriately. Measurement is arguably more challenging in pay-for-performance systems that reward population health than those that reward medical care because determinants of population health go beyond medical care. The questions sketched by Kindig (

This article focuses on the second question and calls for development of a summary measure of health inequalities, where health inequalities associated with multiple attributes (such as income, education, and race/ethnicity) are summarized into 1 number. I assume typical measures of population health, such as life years or health-adjusted life years, and population units that have a mandate for the health of their population, such as states. However, the core idea of a summary measure presented here can in principle be applied to other measures of population health and other population units.

Because health inequality is an established field of research and policy making, we might expect that a well-tested template would be available for measuring health inequalities that could be used in a pay-for-population health performance system. However, such guidance has not yet been established. Over the past century, many empirical studies have described health inequalities (

Health inequalities have most commonly been measured in a bivariate fashion, as a joint distribution of health and another attribute, such as income, education, sex, or race/ethnicity (

Around 2000, there was a brief but heated debate about whether we should continue to measure bivariate health inequalities or start measuring univariate health inequality (

A hypothetical presentation of a bivariate health inequality. Measures of bivariate health inequality assess the association of health inequality with another attribute, in this example, income.

A hypothetical presentation of a univariate health inequality. Measures of univariate health inequality assess health inequality across individuals regardless of its association with other attributes.

This debate raised moral and policy questions (

Furthermore, those who support measuring univariate health inequality argued that the choice of which attributes to study is generally driven by the investigator's intuition or interest. Accordingly, we now have numerous empirical descriptions of health inequalities by various attributes, which are not necessarily comparable and do not immediately offer an overall picture of health inequalities. Univariate health inequality, they maintained, can offer an overall picture of health inequality in the population in a way that is comparable across populations. The advocates of measuring bivariate health inequalities, on the other hand, argued that univariate health inequality does not suggest how to tailor interventions or policies to reduce health inequalities.

The result of this debate was an acknowledgment — primarily from supporters of univariate health inequality — that bivariate and univariate health inequalities are complementary (though exactly how they are complementary has not been specified) (

This debate also suggests a strong resistance among health inequality researchers to abandoning bivariate health inequalities. They may be resistant because 1) they view health as not only intrinsically important but also as valuable in terms of its associations with other attributes, and 2) it is useful to know who is sick in order to develop policies. Arguments for measuring univariate health inequality also have merit. Lack of comparability of results and an overall view of health inequalities may be a barrier between numerous descriptions of health inequalities and effective policy making. A lesson from this debate may be that we need to develop a summary measure of health inequalities, which gives an overall picture of health inequalities in the population while maintaining pertinent information on bivariate health inequalities.

Relevant literature suggests 2 approaches to developing a summary measure of health inequalities: the bottom-up and top-down approaches.

The bottom-up approach first defines attributes of interest and measures bivariate health inequalities related to these attributes separately. It then combines these bivariate health inequalities into a summary index. An example is the inequality measure developed for the

Equation 1

Where_{j}_{ref}

The Wisconsin inequality measure calculated the Index of Disparity by using all 14 groups (2 sex groups, 3 education groups, 4 rurality groups, and 5 race/ethnicity groups) and converted the index to a letter grade for ease of communication. All attributes (sex, education, rurality, and race/ethnicity) are considered to be of equal importance. The reference is set as the best health level among all groups (

A simplified example of the Wisconsin health inequality measure. To obtain the overall health inequality, calculate the difference from the reference health level (rich) for each group (poor, low education, high education, male, and female), sum them, and divide by the number of groups minus 1 (6 − 1 = 5).

The top-down approach first measures univariate health inequality, then breaks it down into health inequalities related to different attributes. Unlike the bottom-up approach, there is no known example of a summary measure of health inequalities using this approach. However, this approach comes close to the principal idea underlying WHO's health inequality measurement in the

The top-down approach first attempts to explain the level of health of individual

Equation 2

_{i }_{i}_{i}_{i}_{i}_{i}

Where_{i}

An example of information given by the top-down approach. The top-down approach provides information on univariate health inequality (as overall health inequality) and identifies contributions of the attributes we select (eg, income, education, and race/ethnicity). "Other (residual)" shows univariate health inequality that is not associated with the chosen attributes.

Overall | ||

Income | ||

Education | ||

Race/ethnicity | ||

Other (residual) |

Which approach is better suited to develop a summary measure of health inequalities? To answer this question, I address the following 5 issues: building blocks, aggregation, value, data and sample size requirements, and communication. Building blocks are common to both the bottom-up and top-down approaches. The subsequent 4 issues separate these 2 approaches.

Whichever approach we take, we should carefully choose a bivariate or univariate measure that becomes a building block of a summary measure. The building block for the Wisconsin inequality measure, an example of the bottom-up approach, is the Index of Disparity, and the Gini coefficient (

All measurement properties of the Index of Disparity and the Gini coefficient coincide with the current discussion (

Inequality judgment and subgroup population size. The width of the bars suggests the proportion of poor and rich people in the 2 populations. If we consider the degree of income-related health inequality differs in these populations, an inequality measure should be sensitive to this difference.

The bottom-up and top-down approaches aggregate bivariate inequalities to overall health inequality differently. The bottom-up approach aggregates bivariate inequalities arbitrarily, and the top-down approach decomposes univariate inequality into bivariate inequalities. This difference has 3 implications. First, the top-down approach can identify an independent association between each attribute and health and also interactive associations between attributes and health. Although possible, identifying independent and interactive effects is cumbersome in the bottom-up approach. The bottom-up approach starts by measuring unadjusted bivariate health inequalities, where each attribute of health inequality is measured without consideration for other attributes. We can categorize groups further, for example, from rich and poor (income) and male and female (sex) to rich male, rich female, poor male, and poor female. However, this is a time-consuming way to describe independent and interactive effects of multiple determinants of health.

Second, the difference in aggregation between the 2 approaches leads to a difference in the meaning of an overall picture of health inequalities. An overall health inequality is a composite in the bottom-up approach, but it is univariate health inequality in the top-down approach. The top-down approach has a logical and mathematical hierarchy from bivariate health inequalities to univariate health inequality; the sum of bivariate health inequalities equals univariate health inequality. The bottom-up approach does not have such a hierarchy. Because each individual in the population belongs to multiple groups (eg, an individual is female, rich, educated, and minority), it is unclear exactly what an aggregation of non-mutually exclusive bivariate health inequalities means.

Finally, by decomposing univariate health inequality into bivariate health inequalities, the top-down approach can identify the contribution of each bivariate health inequality to univariate health inequality and thus the relative importance of bivariate health inequalities. For example, Wagstaff and van Doorslaer (

A measure can be descriptive (describing the object) or normative (incorporating our value of the object). Using either the bottom-up or top-down approach, a summary measure of health inequalities is normative in the most fundamental sense; it measures health inequalities that we value. But these approaches differ in terms of how normativity is introduced, and the top-down approach offers a richer framework than the bottom-up approach. The bottom-up approach starts by selecting attributes that we believe to be important in relation to health inequality. The top-down approach, on the other hand, starts by describing health inequalities and moves on to normative assessment of fair and unfair health inequalities (

Furthermore, in either approach we must ask whether a summary measure of health inequalities should incorporate the relative importance of different attributes. According to Wagstaff and van Doorslaer (

Generally, the top-down approach requires more data than the bottom-up approach. The top-down approach works best with individual-level data on health and determinants of health, while the bottom-up approach can be pursued with group-level data. Population health surveys, possibly linked with census data, may offer enough information for the top-down approach, but the sample size of the survey determines how small the population can be for which a summary measure of health inequalities can be calculated. Despite the clear advantage of the top-down approach in terms of aggregation and value, data and sample size requirements may be a critical hindrance to its policy application.

These considerations for data and sample size requirements are typical in any quantitative analysis, but the use of a summary measure of health inequalities for a system of pay-for-population health performance requires at least 2 further considerations. First, how sensitive should a summary measure be to changes? If we agree to reward performance in the short term (eg, in 3-5 years), a summary measure should be sensitive to changes that occur in this time frame, and data should be updated regularly. Second, for which population (eg, state, county, community) does it make the most sense to establish a pay-for-performance system? The smallest population for which data are available may not necessarily be the most appropriate size.

Effective use of a summary measure of health inequalities demands clear communication. Ideally, a measure should be conceptually and methodologically sound and easy to communicate. The bottom-up approach is arguably methodologically simpler than the top-down approach. However, ease of communication does not necessarily equal simplicity in concepts and methods. A complex Concentration Index decomposition, similar to the top-down approach, has been increasingly used in policy-oriented work (

I suggest a summary measure of health inequalities using the top-down approach and a strong communication strategy when data and sample size requirements are surmountable. Compared with the bottom-up approach, it offers a conceptually clearer meaning of overall health inequality and a richer framework for choosing relevant attributes associated with health inequality. In addition, development of a summary measure of health inequalities requires clarification of value questions.

First, a system of pay-for-population health performance should incorporate measurement of health inequalities. Second, measurement of bivariate health inequalities, the most common way to measure health inequalities, may not be the most effective mechanism to reduce health inequalities. A system that rewards population health should seek to develop a summary measure of health inequalities. Third, a summary measure of health inequalities can be developed by adopting the bottom-up or top-down approach. When data are available, a summary measure using the top-down approach should be used, along with a strong communication strategy to help users understand what the measure means and how it was calculated. Finally, clarification of value questions is a high priority for development of a summary measure of health inequalities.

This manuscript was developed as part of the Mobilizing Action Toward Community Health (MATCH) project funded by the Robert Wood Johnson Foundation. The work was also funded by a Canadian Institutes of Health Research New Investigator Award and a Dalhousie Faculty of Medicine Clinical Research Scholar Award. I thank Yoko Yoshida for her assistance during the early stage of this project and anonymous reviewers for providing extensive and constructive comments.

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Questions That Arise in Selecting Health Inequality Measures and Measurement Properties of the Index of Disparity and the Gini Coefficient

Question | Index of Disparity | Gini Coefficient |
---|---|---|

Who is compared against whom or what? Should the comparison be made in terms of health only (univariate) or health and another attribute (bivariate)? | The healthiest group against all other groups | Everyone against everyone |

How are differences aggregated at the population level? For bivariate health inequality measures, should the measures be sensitive to inherent ordering of another attribute (eg, income)? | Unweighted addition of difference and sensitive to inherent ordering of attribute | Weighted addition of health share and unweighted addition of difference |

Should the judgment of inequality be sensitive to the mean level of the population? Absolute measures are translation invariant, meaning that equal absolute difference implies equal degree of inequality, while the equal proportional increase makes inequality larger. Relative measures are scale invariant, meaning that equal proportional difference implies equal degree of inequality, while the equal absolute addition reduces inequality. Intermediate inequality measures consider equal proportional increase makes inequality bigger, while equal absolute addition decreases inequality. | Translation invariant | Scale invariant |

Should the judgment of inequality be sensitive to the total population size? | Insensitive | Insensitive |

Should the judgment of inequality be sensitive to the subpopulation size? How should the overall inequality of a population correspond to inequalities of subgroups in that population? | Insensitive to the group size | Decomposable |