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Refining Population Health Comparisons: A Multidimensional First Order Dominance Approach

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Abstract

How to determine if a population group has better overall (multidimensional) health status than another is a central question in the health and social sciences. We apply a multidimensional first order dominance concept that does not rely on assumptions about the relative importance of each dimension. In particular, we show how one can explore the “depth” of dominance relations by gradually refining the health dimensions to see which dominance relations persist. We analyze a Danish health survey with many health indicators. These are initially collapsed into a single composite health dimension and then refined to four, seven, and ten health dimensions, each representing an (increasingly refined) area of health. Overall we find that younger age groups dominate older age groups in up to four dimensions, but no dominance relations are present with a more refined view of health. Comparing education groups, we often see dominance relations in four and seven dimensions, but the depth of the dominance vary considerably. We also compare groups based on gender, marital status, region, and ethnicity, where we generally find less dominance relations. Our empirical illustration shows that it is possible to operationalize and meaningfully apply the multidimensional first order dominance concept with gradual refinements of health status in up to ten health dimensions.

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Notes

  1. That is, we do not make other assumptions on an underlying population health evaluation function than the (trivial structural) assumption that better individual health yields better population health.

  2. More indicators have been created from these data (see Koch et al. 2012). For example a number of indicators have been constructed referring to occupational health, which is obviously not relevant for all. We focus in our empirical section on a selection of indicators that is suitable for general population health comparisons.

  3. According to the author, the stability test was conducted by changing weights for one sub-discipline at a time, so a complete robustness check with simultaneous change of weights was not conducted.

  4. The concept of multidimensional first order dominance (FOD) applied in this paper is also known simply as dominance, or the usual (stochastic) order (e.g. Lehmann 1955; Levhari et al. 1975). See Østerdal (2010) for a synthesis of equivalent definitions. Note that FOD is more demanding, and less easy to check, than the multidimensional dominance concepts applied by Atkinson and Bourguignon (1982) and subsequent work referenced in the Introduction. For a general treatment of stochastic dominance concepts, we refer to Shaked and Shanthikumar (2007).

  5. This characterization of FOD does not rely on our assumption of binary indicators.

  6. A numerical illustration of the method in the two dimensional case is also found in Arndt et al. (2012, Table 1), and see Permanyer and Hussain (2014, Fig. 1) for the three dimensional case.

  7. The sample remains representative in important demographic dimensions. The representativeness was tested by dividing individuals in the full and reduced samples by five regions, male/female and three ethnicities, e.g. 30 different groups. Applying a Chi-square test, we cannot reject equal distributions across the thirty categories in the full and reduced samples (P = 0.72).

  8. The left-out items include individual behavior and use of health services, social relations, and working environment—the last item is only relevant for employed individuals.

  9. The correlation between the actual and bootstrap data FOD is 0.89.

  10. The dominance relations in the 1-dimensional case are easily extractable from Table 2 since it is merely a matter of ranking a uni-variate series of prevalence.

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Acknowledgments

We are grateful to Mette Bjerrum Koch for providing the data. We also thank participants at the workshop New Trends in Health Equity Research, SDU, 2014, and two anonymous referees, for helpful comments and suggestions.

Author information

Authors and Affiliations

  1. Department of Society and Globalisation, Roskilde University, Roskilde, Denmark

    M. Azhar Hussain

  2. John F. Kennedy School of Government, Harvard University, Cambridge, MA, USA

    Mette Møller Jørgensen

  3. Department of Business and Economics, and Centre of Health Economics Research (COHERE), University of Southern Denmark, Odense M, Denmark

    Lars Peter Østerdal

Authors
  1. M. Azhar Hussain
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  2. Mette Møller Jørgensen
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  3. Lars Peter Østerdal
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Corresponding author

Correspondence to Lars Peter Østerdal.

Appendix

Appendix

1.1 Appendix 1: FOD for Ethnicity, Marital Status, and Region

We present the 4-dimensional FOD (and the single 7-dimensional FOD also occurring) for ethnicity, marital status, and region in Table 4. Gender is not included in the table since that does not have any FOD beyond the 1-dimensional case.Footnote 10 From Table 4 we see that non-Western immigrants are dominated by both Danes (16–24 years) and other Westerners (45–64 years), but not in all age groups. Thus, we cannot generally conclude that Danes have better health than immigrants when we take a refined multidimensional view, but we can say that when there is domination, it only goes in one direction. Note that although ethnicity had the largest prevalence disparity (in Table 2), it is one of the characteristics with fewest dominance relations. Most dominance relations, next to education, are found for marital status. Particularly for the 45–64 year age group a lot of dominance relations are found. Generally, we see that married and cohabiting individuals tend to have better multi-dimensional health than individuals living without a partner. We also generally observe that unmarried individuals are more often dominated by other groups. The only 7-dimensional FOD is found for the marital status characteristic; married individuals dominate unmarried individuals for the 45–64 year age group. The results for regions are mixed, but we can say that Northern Jutland is the frequent one to dominate others (the Capital Area and the rest of Zealand for the 65+ age group). Middle Jutland together with the rest of Zealand are the only regions who are only dominated and do not dominate others. Southern Denmark is the only region which is neither dominated nor dominates other regions.

Table 4 FOD for ethnicity, marital status, and region in the 4-dimensional case, Denmark
Full size table

1.2 Appendix 2: Bootstrap

See Table 5.

Table 5 Static and bootstrap FOD in the 4-dimensional case
Full size table

1.3 Appendix 3: Total Number of Dominance Relations

See Fig. 5.

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Hussain, M.A., Jørgensen, M.M. & Østerdal, L.P. Refining Population Health Comparisons: A Multidimensional First Order Dominance Approach. Soc Indic Res 129, 739–759 (2016). https://doi.org/10.1007/s11205-015-1115-2

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