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• Life expectancy record holders have about average life disparity levels at each life expectancy level
  Alyson A. van Raalte
  Published on: 23 November 2015
• Life expectancy record holders not most equal if compared within life expectancy levels
  Jeroen Smits
  Published on: 23 November 2015

• Published on: 23 November 2015

  Life expectancy record holders have about average life disparity levels at each life expectancy level

  • Alyson A. van Raalte

  Alyson A. van Raalte, James W. Vaupel, Zhen Zhang

  Monden and Smits raise a valid point that "the countries that reached a certain e(0) first are not the most equal countries at that level of e(0)" [1]. We do not dispute this. In fact, we performed a similar analysis in the supporting material (Figure S4) [2]. At each e(0) level, our figure compared the life disparity level of e(0) leaders to the average life...

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  Alyson A. van Raalte, James W. Vaupel, Zhen Zhang

  Monden and Smits raise a valid point that "the countries that reached a certain e(0) first are not the most equal countries at that level of e(0)" [1]. We do not dispute this. In fact, we performed a similar analysis in the supporting material (Figure S4) [2]. At each e(0) level, our figure compared the life disparity level of e(0) leaders to the average life disparity level of all other countries in the HMD, separately for men and women. For some e(0) levels, the life disparity of the e(0) leader was higher than average, for other levels it was lower. Overall, there was no clear trend. Thus we concluded: "While leaders are the first to reduce premature mortality, thereby reducing life disparity, laggards on average follow with similar reductions in life disparity alongside life expectancy increases."

  While we find no clear difference between the life expectancy leaders and the laggards, the Figure 1 of M&S indicates that leaders have higher lifespan inequality on average at each life expectancy level. These differences are likely stemming from differences in datasets. M&S use a mixture of life tables from various sources including published papers, the WHO life table database, the HLTD and the HMD [3]. Some of these life tables are abridged, while others are full. Some would have been exposed to data smoothing, others not. Our life tables are drawn entirely from the Human Mortality Database [4]. This database has high data quality inclusion criteria and follows strict protocols to ensure a good level of comparability. Thus it could be that when more countries are included into the analysis, instead of laggards having similar life disparity levels to leaders, they in fact have lower levels of life disparity. Or this simply could be a data artefact.

  Nevertheless, neither result would dispute our main finding, which is that life expectancy leaders have low life disparity levels in any given year. This is because the life expectancy leaders are at the frontier of reducing premature mortality, which also reduces life disparity. As we concluded: "It is not a question of either long life or low disparity: countries can achieve both by averting premature deaths". We fully agree with M&S that further research should explore the paths that life expectancy laggards can take to reduce inequality to levels even lower than those achieved earlier by the leaders. There is no reason to think that this is not possible.

  References:

  [1] Monden C, Smits J. Life expectancy record holders not most equal if compared within life expectancy levels. BMJOpen eLetter 7 Sept 2012: http://bmjopen.bmj.com/content/1/1/e000128.full/reply#bmjopen_el_6407

  [2] Vaupel JW, Zhang Z, Van Raalte A.A. Life expectancy and disparity: an international comparison of life table data. BMJ Open 2011;1:e000128 doi:10.1136/bmjopen-2011-000128. [See supplementary material: http://bmjopen.bmj.com/content/suppl/2011/08/03/bmjopen-2011- 000128.DC1/SupplementaryMaterial.pdf]

  [3] The full list of data sources can be found at www.lengthoflife.org.

  [4] Human Mortality Database. University of California, Berkeley (USA), and Max Planck Institute for Demographic Research (Germany). http://www.mortality.org.

  Conflict of Interest:

  None declared

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  Conflict of Interest:
  None declared.

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• Published on: 23 November 2015

  Life expectancy record holders not most equal if compared within life expectancy levels

  • Jeroen Smits, Associate Professor
  • Other Contributors:
    • Christiaan Monden

  Christiaan Monden, lecturer (1), Jeroen Smits, associate professor (2)

  1. University of Oxford, 2. Radboud University Nijmegen

  Vaupel, Zhang and Van Raalte (VZ&V) have made an interesting contribution to the study of variation in length of life (or life disparity as they call it) on the basis of life table data [1]. A fascinating aspect of this literature is that the inequality measures that are...

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  Christiaan Monden, lecturer (1), Jeroen Smits, associate professor (2)

  1. University of Oxford, 2. Radboud University Nijmegen

  Vaupel, Zhang and Van Raalte (VZ&V) have made an interesting contribution to the study of variation in length of life (or life disparity as they call it) on the basis of life table data [1]. A fascinating aspect of this literature is that the inequality measures that are used - such as the Gini coefficient, Standard Deviation, Coefficient of Variation, Interquartile Range, and also the e+ used by VZ&V - are highly correlated, not only amongst themselves, but also with life expectancy[2-4]. In fact, the correlation between life expectancy (LE) and life inequality (LI) is so high (often over -0.9[4]), that one might expect an increase in life expectancy to be almost always associated with lower inequality.

  VZ&V also observe this in their data: the country with the highest e(0) in a given year often had the lowest inequality (e+) in that particular year. From this finding, VZ&V seem to conclude that countries that are leaders in life expectancy are also the most equal ones. However, they base this conclusion on a comparison of differences between countries within a specific year, which in our vision is not the most informative approach in this context.

  This can be seen in Figure 1 -- an adapted version of a figure presented in our 2009 paper[4] --, in which e(0) is plotted against LI (measured by the GINI coefficient) for 4,690 life tables. The data are for males in 194 countries and include besides all the life tables used by VZ&V many additional life tables we collected from other sources[5]. The figures are for all ages (instead of 15+ as in our 2009 paper) to make them better comparable with VZ&V. We show outcomes of tables with an e(0) of over 40, because that range includes all life expectancy leaders of VZ&V.

  Figure 1 can be viewed here - http://dx.doi.org/10.6084/m9.figshare.95456

  Figure 1 contains three kinds of points. The light-colored background points show the association between LI and LE for all 4,690 country-year combinations. The black and green points reveal the positions of the life expectancy leaders from VZ&Vs paper (Table S4 of VZ&V; 169 leaders for each year from 1840-2008). The black points represent the 59 leaders who were true record breakers; they reached an e(0) level that had not been observed before (e.g. Sweden in 1898). The green points represent follow- up leaders; they were VZ&Vs best performers in a particular year, but at a level of e(0) that had already been reached in the past (e.g. Norway 1899- 1901).

  Figure 1 makes clear that the countries that reached a certain e(0) first are not the most equal countries at that level of e(0). On the contrary, in almost all years the life expectancy leaders are found in the middle or upper part of the inequality distribution. In other words, compared to countries that reached a certain level of life expectancy later, the life expectancy leaders seem to perform only average (or worse) in terms of inequality.

  One might observe that at a high level of life expectancy (say an e(0) of over 75) in Figure 1, the life expectancy leaders have relatively low inequality. Note however that the picture at those levels is not yet complete, as the mass of other countries has not yet arrived. Based on what we see at the lower e(0) levels in Figure 1, it seems likely that when the lagging countries reach e(0) of over 75, many of them will do so at a lower level of inequality compared to VZ&Vs leaders.

  Reducing premature mortality generally leads to higher life expectancy and lower inequality in life spans. However, Figure 1 makes clear that reaching a high life expectancy earlier than other countries does not result in the lowest possible inequality at that life expectancy level. An interesting question that thus remains is why many countries that reach a certain level of life expectancy later can do so with lower inequality.

  References

  1. Vaupel JW, Zhang Z, Van Raalte A. Life expectancy and disparity: an international comparison of life table data. BMJ Open 2011;1:e000128 doi:10.1136/bmjopen-2011-000128.

  2. Wilmoth JR, Horiuchi S. Rectangularization revisited: variability of age at death within human populations. Demography 1999;36:475-95.

  3. Shkolnikov V, Andreev E, Begun AZ. Gini coefficient as a life table function. Computation from discrete data, decomposition of differences and empirical examples. Demogr Res 2003;8:305-58.

  4. Smits J, Monden C. Length of life inequality around the globe. Soc SciMed 2009;68:1114-1123.

  5. The data used for Table 1 are available at www.lengthoflife.org.

  Conflict of Interest:

  None declared

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  Conflict of Interest:
  None declared.

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