Monitoring changes in health inequalities over time and modeling the impact of potential policies are crucial tasks for successfully combating persistent differences in health across socioeconomic groups. In the article titled A Typology for Charting Socio-Economic Mortality Gradients: “Go South-West,” Blakely et al.^{1} convincingly demonstrate how novel graphical tools can facilitate these tasks. We applaud this initiative!

The questions often asked when monitoring health inequalities are generally as simple as whether these inequalities have increased or decreased over time and whether they are higher or lower in one region than another. However, while these questions seem simple, the answers may be more complex as they can depend on what distribution of health improvements (or losses) one considers to preserve the level of inequality. As an analogy, the answer to whether the temperature is above or below zero degrees can depend on whether we are measuring temperature in Celsius or Fahrenheit.

Similarly, every study on health inequalities that attempts to answer the question of whether inequalities have increased or decreased is based on a set of explicit, or implicit, value judgments of what defines a “zero” change in health inequality. As researchers, we need not only to develop an understanding of these value judgments but also to be equipped to communicate them to a broader audience. Such communication can be facilitated by a set of accessible tools. This is a key issue in said article and one that we discuss in great detail in a previous article published in this outlet.^{2}

A related question is whether we should care about relative or absolute inequalities. That is, do we consider inequality to be unchanged if there was an equal change in everyone’s health (absolute) or if changes were proportional to everyone’s initial level of health (relative)? Thus, when using absolute and relative inequality measures, the change in inequality is simply being measured on a different scale with different “zero” points for each scale. Ideally, it should not be up to us as researchers to decide which scale to use. Our role is rather to make these value judgments explicit and transparently present our results to policymakers, who are the ones who should decide whether the observed distribution of health changes meets their goals. In addition, we should move away from simply telling policymakers whether inequalities have increased or decreased and instead provide more information on the nature of the health changes. For example, it may be useful to illustrate how close the health changes are to being equivalent to a relative versus an absolute change. As these two types of change in the health distribution are easy to conceptualize, they constitute useful benchmarks against which to evaluate the nature of any health changes in terms of their impact on inequality. With this comparison in mind, policymakers are reasonably better equipped to judge to what extent the distribution of health changes should be considered “fair” or to meet policy goals for reducing inequalities.

In this commentary, we will highlight how the graphical tools discussed by Blakely et al.^{1} both increase transparency in the field and facilitate in-depth presentations of changes in inequality. We will also discuss some details of these tools that we consider to be critical to successful communication.

A GRAPHICAL TOOL TO FACILITATE MONITORING OF INEQUALITIES
The main objective of the graphical tools discussed in Blakely et al.^{1} is to present information in an unbiased, transparent, and illustrative way. The two main graphs plot the mean health against either the relative or absolute inequality, demonstrating the other perspective by contours representing different levels of inequality (i.e., the level of inequality is constant along these lines). Thus, as researchers we do not have to make the value-laden decision of whether to apply a relative or an absolute scale. By conveying a lot of information in one graph, these tools also force the audience to think, and be aware, of several aspects simultaneously: in particular the change in average health and the change in inequality on both an absolute and relative scale.^{1} The advantage of these graphical tools, compared with presenting the inequality measures side by side, is that they explicitly, and in a way that is easy to understand, show the strong relationship between these two scales.

By incorporating relative and absolute value judgments with information on how they relate to average health, the graphs usefully demonstrate the consequences of invoking one of the two perspectives, that is, how the choice of an absolute or a relative measure may affect the results. Notably, the impact of this choice is more profound the more the mean of the health outcome varies across populations. This dimension of the graphs also helps illustrate the nature of changes in inequality by clearly demonstrating how close the change in the health of the population is to being similar to an absolute change versus a relative change.

A COMPARISON OF TWO GRAPHS
In Kjellsson et al.,^{2} we present a general graphical representation. Blakely et al.^{1} modifies this graph to better suit their particular data. This modified graph presents the logarithm of the mean of the health variable on the x axis and the log of the relative inequalities on the y axis (Figure 1A ). The absolute inequality is represented by nonlinear contour lines. In the specific application, relative inequalities are measured (using the relative index of inequality) as the ratio between the predicted health of the best and the worst socioeconomic groups.^{3} Given that mortality rates generally are very low, using the logarithm of this specification of relative index of inequality facilitates plotting of populations with varying levels of average health. A greater area of the x –y plane is available for plotting compared with a graph with the absolute inequality on the y axis, in which this area is restricted by the relationship between the absolute inequality and the mean. High levels of absolute inequality are simply impossible for low levels of the mean.

FIGURE 1: Two typology graphs for charting socioeconomic gradients in health. A, The graph advocated by Blakely et al.^{1} : relative inequality (RII; y axis, log scale) and average health in population (x axis, log scale); contour lines represent absolute inequality (SII). B, The graph suggested by Kjellsson et al.^{2} : absolute inequality (SII; y axis) and average health in population (x axis); contour lines represent relative inequality (RII). The grey area indicates impossible combinations of inequality and mean values. For simplicity, this is based on a continuous socioeconomic ranking variable with no ties. However, the general idea translates to any socioeconomic variable. Further note the level of relative inequality cannot be expressed as RII (as defined by Mackenbach & Kunst^{3} ) for combinations of absolute inequality and the mean represented in the space above the “RII-max contour.” Other expressions for relative inequality are still possible in this space.

The graph in Kjellsson et al.^{2} places the mean of the health variable on the x axis and the absolute inequality on the y axis (both in levels). Linear contours starting in the origin represent the relative inequality measures. This representation explicitly illustrates the relationship between mean health and absolute inequality (Figure 1B ). For saliency, the area of impossible combinations of inequality and mean values (given health is not less than 0) is marked grey. Indeed, the area below the maximum value of the relative inequality funnels to the origin. Whereas this may be seen as a practical concern, it also provides an accurate description of the situation and illustrates the value judgments that the absolute and relative measures imply. For example, it clearly explains why relative inequality in mortality (and morbidity) tends to be higher when average mortality (and morbidity) is lower: reducing relative inequalities is more demanding than reducing absolute inequalities as one reduces the mean of the outcome variable.^{4} ^{,} ^{5} For a number of reasons, the linear contours also may make it easier for the reader to compare the nature of health changes to the relative and absolute benchmarks. First, it is straight forward to imagine the additional contours representing levels of inequality not drawn if these contours are linear. Second, it avoids misinterpretations possible in Figure 1A , where a straight line joining two consecutive observations with the same level of absolute inequality (but different means) will cross contours representing higher levels of absolute inequality. Choosing between the two graphs thus implies a trade-off between the practical concern raised by Blakely et al.^{1} and providing an intuitive illustration of the relationship between the relative and absolute value judgments.

An alternative solution to the practical concern is to present an additional graph, zooming in on the (lower left) corner where the development of inequalities may be particularly difficult to see. Figure 2 presents an example reusing data reported in Blakely et al.^{1}

FIGURE 2: Another solution to the practical concern. Age-specific all-cause mortality inequality by household income for New Zealand 1981–1984 to 2006–2011. The direction of the arrows denotes the time dimension. The graph in B zooms in on the lower left corner of the main graph A. (Reproduction of Figure 4 in Blakely et al.^{1} using a Kjellsson et al.^{2} graph.)

EXPRESSING OUTCOMES IN NEGATIVE OR POSITIVE TERMS
Related to the question of applying absolute or relative value judgments is the choice of expressing outcomes in positive or negative terms. That is, for a health variable that ranges between clearly defined minimum and maximum values, we can choose to measure inequality in attainments or shortfalls (e.g., mortality/survival and health/ill-health). Although it is standard in the literature to measure inequality in mortality rates, these could also be expressed instead as mortality risks which could in turn be expressed as survival risks. It is not unusual in the broader inequality literature to measure inequality in attainments. This choice is important as the relative inequality measures of attainments and shortfalls imply very different “zero” points. For example, reducing mortality risks proportionally to every social group’s initial mortality level (shortfall-relative) is not equivalent to increasing survival risks proportionally to every social group’s survival level (attainment-relative). In Kjellsson et al.,^{2} we illustrate how these two relative value judgments—jointly with the absolute—constitute informative benchmarks for this type of variable. Presenting only one of the two relative measures may deprive the audience of an informative perspective or may even bias their view on whether the distribution of health changes was fair.

For the specific data presented by Blakely et al.,^{1} this issue may be less serious as survival-relative contours would practically coincide with the absolute ones due to the extremely low mean mortality rates. Incorporating an additional value judgment into the graphical tool may then only add confusion. However, as this issue is generally of greater importance, a graphical tool flexible enough to include both perspectives is desirable. Such a flexible graph would be more transparent and would also be useful as a tool to educate the audience of the complex relationship between these underlying value judgments.

The entities on, and the scales of, the axes in Figure 1A makes it difficult to incorporate the additional complexity of this type of health variable. By contrast, the graphs in Figures 1B and 2 are easily extended to box diagrams that include this dimension (Figure 3 ). The direct relationship between the mean of attainment and the mean of shortfall implies that these entities can be graphed on the x axis: one from the left to the right and the other from the right to the left. Adding linear contours, starting in each of the two origins and representing the attainment- and shortfall-relative inequality measures, yields a graphical tool that provides a clear illustration of the relationship between the changes of five entities simultaneously: changes in attainment (survival risk), shortfall (mortality risk), and changes in absolute, shortfall-relative, and attainment-relative inequalities.

FIGURE 3: A general typology graph incorporating attainment- and shortfall-relative measures: absolute inequality (SII; y axis) and average health in population (x axis)—as attainments from left to right and as shortfalls from right to left. Contour lines represent attainment- and shortfall-relative inequalities. The grey area indicates impossible combinations of inequality and mean values. For simplicity, this is based on a continuous socioeconomic ranking variable with no ties. However, the general idea translates to any socioeconomic variable.

The upper and lower bounds of the health variable further restrict the values that the inequality measures (both absolute and relative) can attain for a given level of the mean, for example, increasing everyone’s health (proportionally or by equal additions) is only possible until some groups reach the maximum level. Wagstaff^{6} pointed out this issue specifically for the concentration index, but it is also relevant for other measures. By marking the area of values that the inequality measures cannot attain, Figure 3 further demonstrates the area available where points may lie.

CONCLUSIONS
To conclude, we believe that these graphical tools can help teach a nonexpert audience about the underlying value judgments of inequality measures, and also help researchers avoid biasing a policymaker’s view by leaving out measures. Choosing a graph comes down to what the audience finds easiest to understand, but without biasing their view in a particular direction. This task is even more challenging when the health variable can be expressed as both a positive and a negative outcome. We advocate for using a graph similar to Figure 3 , at least to educate the audience. This graph may be of less beauty in some cases, but we believe it is more flexible and more aligned with transparent communication. For an audience informed of the possible perspectives and their relationships, leaving out some perspective may then simplify the graph, and make it more beautiful. Some points raised in this commentary may seem nitpicky, but as a tool to communicate a clear—and transparent—message, the beauty of these graphs really lies in these details.

ABOUT THE AUTHORS
GUSTAV KJELLSSON is an Assistant Professor at the Department of Economics and Centre for Health Economics at the University of Gothenburg. His research focuses on the measurement and causes of socioeconomic health inequality. DENNIS PETRIE is an Associate Professor at the Centre for Health Economics at Monash University. His research focuses on the dynamics of socioeconomic health inequalities and the economic evaluation of health policies and interventions which reduce health disparities.

ACKNOWLEDGMENTS
Kjellsson acknowledges Monash University, and the Partner programme at the University of Gothenburg School of Business, Economics, and Law, for supporting a research visit at Monash. Petrie acknowledges support from the Australian Research Council through grant DE150100309.

REFERENCES
1. Blakely T, Disney G, Atkinson J, McDonald A, Mackenbach JP. A typology for charting socio-economic mortality gradients: “Go south-west”. Epidemiology. 2017.

2. Kjellsson G, Gerdtham UG, Petrie D. Lies, damned lies, and health inequality measurements: understanding the value judgments. Epidemiology. 2015;26:673–680.

3. Mackenbach JP, Kunst AE. Measuring the magnitude of socio-economic inequalities in health: an overview of available measures illustrated with two examples from Europe. Soc Sci Med. 1997;44:757–771.

4. Wagstaff A. Commentary: value judgments in health inequality measurement. Epidemiology. 2015;26:670–672.

5. Mackenbach JP. The persistence of health inequalities in modern welfare states: the explanation of a paradox. Soc Sci Med. 2012;75:761–769.

6. Wagstaff A. The concentration index of a binary outcome revisited. Health Econ. 2011;20:1155–1160.