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Relative survival: a useful tool to assess generalisability in longitudinal studies of health in older persons

Richard Hockey*, Leigh Tooth and Annette Dobson

Emerging Themes in Epidemiology 2011, 8:3  doi:10.1186/1742-7622-8-3

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Understanding contrasting patterns of relative differences in survival and relative differences in mortality

James Scanlan   (2012-01-12 20:11)  James P. Scanlan, Attorney at Law email

Hockey et al.[1] state that the lack of convergence over time between the survival rates of the Australian Longitudinal Study of Women��s Health (ALSWH) cohort and the Australian female population was unexpected given prior research finding convergence over time of mortality rates of sample and unsampled populations. This observation overlooks the pattern by which the rarer an outcome the greater tends to be the relative difference in experiencing it and the smaller tends to be the relative difference in avoiding it.[2-4] For reasons related to the shapes of the underlying risk distributions, as populations age and survival generally declines, relative differences between the survival rates of healthier and less healthy groups tend to increase while relative differences in mortality rates of the two groups tend to decrease.

The pattern is evident in the cumulative survival and mortality ratios, as shown in Table A to this comment.[5] Consistently, as cumulative survival decreases over time, relative differences in survival tend to increase while relative differences in mortality tend to decrease. Very likely, the underlying data would also show that the increasing relative differences in cumulative survival by age shown in Hockey Table 2 are accompanied by decreasing relative differences in mortality.

In theory, the same distributional forces should be at work with regard to the interval-specific relative differences, as discussed in the Cohort Considerations sub-page of the Measuring Health Disparities page of jpscanlan.com .[6] Table 1 of Hockey et al. merely shows that relative differences in interval-specific survival fail to get smaller, not that they get larger. The pattern could reflect random variation, given the small number of ALSWH cohort deaths in each interval, and could reflect the combination of the distributional forces (tending to increase the survival differences) and a meaningful reduction in the difference between the mean health of the ASLWH cohort and the Australian female population at large (tending to reduce the relative survival difference). In any case, as shown in the referenced Table A, while there is no consistent pattern for changes in interval-specific relative mortality differences from interval to interval, interval-specific relative differences in mortality are generally smaller in the later intervals. See the Life Table Illustrations sub-page of the Scanlan��s Rule page of jpscanlan.com [7] and the Life Table Information document [8] for patterns of relative differences in survival and relative differences in mortality based on life tables of healthier and less health populations in the United States.

Hockey et al. note that relative survival was originally used with regard to cancer survival. Relative survival is often discussed in cancer journals. Generally, however, such discussion fails to recognize the contrasting patterns by which relative survival and relative mortality tend to be affected by the overall prevalence of an outcome. Thus sometimes demographic differences in survival and mortality are discussed interchangeably without recognizing that as cancer survival rates increase, relative differences in survival and relative differences in mortality tend to change in opposite directions. See the Mortality and Survival page of jpscanlan.com.[9]

It is not clear just how these patterns might affect interpretations of the generalisability of a patterns observed in ALSWH cohort to the population at large. But one should recognize that general improvements in health will tend to reduce the relative difference in survival but increase the relative difference in mortality between the cohort and the larger population.

References:

1. Hockey R, Tooth l, Dobson A. Relative survival: a useful tool to assess generalisability in longitudinal studies of health in older persons. Emerging Themes in Epidemiology 2011, 8,3: http://www.ete-online.com/content/8/1/3.

2. Scanlan JP. Can we actually measure health disparities? Chance 2006:19(2):47-51:
http://www.jpscanlan.com/images/Can_We_Actually_Measure_Health_Disparities.pdf

3. Scanlan JP. Race and mortality. Society 2000;37(2):19-35: http://www.jpscanlan.com/images/Race_and_Mortality.pdf

4. Scanlan JP. Divining difference. Chance 1994;7(4):38-9,48: http://jpscanlan.com/images/Divining_Difference.pdf

5. http://jpscanlan.com/images/Table_A_to_Comment_on_Hockey_et_al.pdf

6. http://jpscanlan.com/measuringhealthdisp/cohortconsiderations.html

7. http://jpscanlan.com/scanlansrule/lifetableillustrations.html

8. http://jpscanlan.com/images/LIFE_TABLE_INFORMATION.pdf

Competing interests

None declared

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