Study of differences in rates of dying above median age at death raises a number of statistical issues - Part I
The study by Barr et al.[1] endeavored to determine the extent of any
changes in the effects of gender and socioeconomic status on survival from
cystic fibrosis between 1959 and 2008, a period when the median age of
survival increased from 6 months to 27 years. The authors found that the
magnitude of the effects did not appear to have declined substantially
over time. But the study's method raises a number of statistical issues.
A general problem with appraisals of changes in health inequalities
over time (or even with determinations that a particular inequality should
be deemed large or small) is the failure to recognize the way that, solely
for reasons related to the shapes of the comparison groups' underlying
risk distributions, standard measures of differences between the rates at
which advantaged and disadvantaged group experience or avoid an outcome
tend to be affected by the overall prevalence of the outcome. Most
notably, 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.[2-6] Thus, when mortality generally declines,
relative differences in mortality tend to increase while relative
differences in survival tend to decrease. Hence, researchers who examine
relative differences in mortality will tend to find increasing
inequalities and those who examine relative differences in survival will
tend to find decreasing inequalities.
The Barr study's appraisal of relative inequalities differs from more
common analyses in two respects. First, it examined survival/mortality in
terms of proportions of deaths in each group that occurred at ages above
the overall median age of dying. Second, it measured differences in these
proportions in terms of odds ratios.
Taking the latter matter first, it warrants note that the magnitude
of an inequality in terms of odds ratios is unaffected by whether one
examines mortality or survival, since the odds ratio for mortality is the
reciprocal of the odds ratio for survival. However, like other standard
measures of differences between outcome rates, odds ratios tend to be
affected by the overall prevalence of an outcome. Assuming normality of
the underlying distributions, when both comparison groups' rates of
experiencing an outcome are below 50%, overall increases in outcome rates
tend to decrease differences between rates measured in odds ratios. When
both groups' rates are above 50%, increases in outcome rates tend to
increase differences measured by odds ratios. When the rate is greater
than 50% for one group and less the 50% for the other group, the
distributionally-driven patterns are difficult to predict even when the
distributions are perfectly normal. See the introductory material in
reference 6 keeping in mind that the described patterns of changes in
absolute differences between rates are the opposite of the patterns of
changes in differences measured by odds ratios.
When one examines the proportions of two groups of decedents who died
at an age above the median age of death for the entire group, invariably
(assuming that there is some difference between the two groups) the
proportion of the advantaged group that died above the overall median age
will be greater than 50% and the proportion of the disadvantaged group
that died above the overall median age will be below 50%. Thus, in such
an analysis, the way the distributional forces will tend to affect odds
ratios is generally unknown, and hence it will likely be impossible to
determine whether observed patterns are consistent with distributionally-
driven patterns or suggest something meaningful.
Further, an analysis of the proportion of decedents from two groups
who died at an age above the median age does not seem to be examining two
entire populations, but only the parts of the two populations that died.
While it is difficult to conceptualize precisely what the larger universes
are, it should be recognized that, even if the underlying risk
distributions of two larger universes are perfectly normal, the
distribution of the truncated populations will not be normal. This
creates further problems for divining the distributionally-driven patterns
of odds ratios as the overall prevalence of an outcome changes over time
(as illustrated in Figures 8 and 10 of reference 7).
That an analysis is actually of a truncated population also creates a
difficulty for appraising the size of inequalities at different points in
time by deriving from pairs of rates at each point in time the difference
between the underlying means, which approach is discussed in references 5,
7 and 8. That approach assumes that the underlying distributions are
normal and hence is problematic in the analysis of truncated
populations.[8-10]
(Continued)
References:
1. Barr HL, Britton J, Smyth AR, Fogarty AW. Association between
socioeconomic status, sex, and age at death from cystic fibrosis in
England and Wales (1959 to 2008): Cross sectional study. BMJ
2011:343:d4662 doi:10.1136/bmj.d4662.
4. Scanlan JP. The Misinterpretation of Health
Inequalities in the United Kingdom, presented at the British Society for
Populations Studies Conference 2006, Southampton, England, Sept. 18-20,
2006: http://www.jpscanlan.com/images/BSPS_2006_Complete_Paper.pdf.
5. Scanlan JP. Measuring Health Inequalities by an Approach
Unaffected by the Overall Prevalence of the Outcomes at Issue, presented
at the Royal Statistical Society Conference 2009, Edinburgh, Scotland,
Sept. 7-11, 2009: http://www.jpscanlan.com/images/Scanlan_RSS_2009_Presentation.ppt.
7. Scanlan JP. Can We Actually Measure Health Disparities?, presented
at the 7th International Conference on Health Policy Statistics,
Philadelphia, PA, Jan. 17-18, 2008: http://www.jpscanlan.com/images/2008_ICHPS.ppt
10. Scanlan JP. Comparing the size of inequalities in dichotomous
measures in light of the standard correlations between such measures and
the prevalence of an outcome. Journal Review Jan. 14, 2008 (responding to
Bostr?m G, Ros?n M. Measuring social inequalities in health - politics or
science? Scan J Public Health 2003;31:211-
215):http://journalreview.org/v2/articles/view/12850975.html
Competing interests:
No competing interests
07 September 2011
James P. Scanlan
Attorney
James P. Scanlan, Attorney at Law, Washington, DC, USA
Rapid Response:
Study of differences in rates of dying above median age at death raises a number of statistical issues - Part I
The study by Barr et al.[1] endeavored to determine the extent of any
changes in the effects of gender and socioeconomic status on survival from
cystic fibrosis between 1959 and 2008, a period when the median age of
survival increased from 6 months to 27 years. The authors found that the
magnitude of the effects did not appear to have declined substantially
over time. But the study's method raises a number of statistical issues.
A general problem with appraisals of changes in health inequalities
over time (or even with determinations that a particular inequality should
be deemed large or small) is the failure to recognize the way that, solely
for reasons related to the shapes of the comparison groups' underlying
risk distributions, standard measures of differences between the rates at
which advantaged and disadvantaged group experience or avoid an outcome
tend to be affected by the overall prevalence of the outcome. Most
notably, 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.[2-6] Thus, when mortality generally declines,
relative differences in mortality tend to increase while relative
differences in survival tend to decrease. Hence, researchers who examine
relative differences in mortality will tend to find increasing
inequalities and those who examine relative differences in survival will
tend to find decreasing inequalities.
The Barr study's appraisal of relative inequalities differs from more
common analyses in two respects. First, it examined survival/mortality in
terms of proportions of deaths in each group that occurred at ages above
the overall median age of dying. Second, it measured differences in these
proportions in terms of odds ratios.
Taking the latter matter first, it warrants note that the magnitude
of an inequality in terms of odds ratios is unaffected by whether one
examines mortality or survival, since the odds ratio for mortality is the
reciprocal of the odds ratio for survival. However, like other standard
measures of differences between outcome rates, odds ratios tend to be
affected by the overall prevalence of an outcome. Assuming normality of
the underlying distributions, when both comparison groups' rates of
experiencing an outcome are below 50%, overall increases in outcome rates
tend to decrease differences between rates measured in odds ratios. When
both groups' rates are above 50%, increases in outcome rates tend to
increase differences measured by odds ratios. When the rate is greater
than 50% for one group and less the 50% for the other group, the
distributionally-driven patterns are difficult to predict even when the
distributions are perfectly normal. See the introductory material in
reference 6 keeping in mind that the described patterns of changes in
absolute differences between rates are the opposite of the patterns of
changes in differences measured by odds ratios.
When one examines the proportions of two groups of decedents who died
at an age above the median age of death for the entire group, invariably
(assuming that there is some difference between the two groups) the
proportion of the advantaged group that died above the overall median age
will be greater than 50% and the proportion of the disadvantaged group
that died above the overall median age will be below 50%. Thus, in such
an analysis, the way the distributional forces will tend to affect odds
ratios is generally unknown, and hence it will likely be impossible to
determine whether observed patterns are consistent with distributionally-
driven patterns or suggest something meaningful.
Further, an analysis of the proportion of decedents from two groups
who died at an age above the median age does not seem to be examining two
entire populations, but only the parts of the two populations that died.
While it is difficult to conceptualize precisely what the larger universes
are, it should be recognized that, even if the underlying risk
distributions of two larger universes are perfectly normal, the
distribution of the truncated populations will not be normal. This
creates further problems for divining the distributionally-driven patterns
of odds ratios as the overall prevalence of an outcome changes over time
(as illustrated in Figures 8 and 10 of reference 7).
That an analysis is actually of a truncated population also creates a
difficulty for appraising the size of inequalities at different points in
time by deriving from pairs of rates at each point in time the difference
between the underlying means, which approach is discussed in references 5,
7 and 8. That approach assumes that the underlying distributions are
normal and hence is problematic in the analysis of truncated
populations.[8-10]
(Continued)
References:
1. Barr HL, Britton J, Smyth AR, Fogarty AW. Association between
socioeconomic status, sex, and age at death from cystic fibrosis in
England and Wales (1959 to 2008): Cross sectional study. BMJ
2011:343:d4662 doi:10.1136/bmj.d4662.
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_Dispariti...
3. Scanlan JP. Race and mortality. Society 2000;37(2):19-35:
http://www.jpscanlan.com/images/Race_and_Mortality.pdf
4. Scanlan JP. The Misinterpretation of Health
Inequalities in the United Kingdom, presented at the British Society for
Populations Studies Conference 2006, Southampton, England, Sept. 18-20,
2006: http://www.jpscanlan.com/images/BSPS_2006_Complete_Paper.pdf.
5. Scanlan JP. Measuring Health Inequalities by an Approach
Unaffected by the Overall Prevalence of the Outcomes at Issue, presented
at the Royal Statistical Society Conference 2009, Edinburgh, Scotland,
Sept. 7-11, 2009:
http://www.jpscanlan.com/images/Scanlan_RSS_2009_Presentation.ppt.
6. Scanlan's Rule page of jpscanlan.com:
http://jpscanlan.com/scanlansrule.html
7. Scanlan JP. Can We Actually Measure Health Disparities?, presented
at the 7th International Conference on Health Policy Statistics,
Philadelphia, PA, Jan. 17-18, 2008:
http://www.jpscanlan.com/images/2008_ICHPS.ppt
8. Solutions sub-page of Measuring Health Disparities page of
jpscanlan.com: http://www.jpscanlan.com/measuringhealthdisp/solutions.html
9. Truncation Issues sub-page of Scanlan's Rule page of
jpscanlan.com: http://jpscanlan.com/scanlansrule/truncationissues.html
10. Scanlan JP. Comparing the size of inequalities in dichotomous
measures in light of the standard correlations between such measures and
the prevalence of an outcome. Journal Review Jan. 14, 2008 (responding to
Bostr?m G, Ros?n M. Measuring social inequalities in health - politics or
science? Scan J Public Health 2003;31:211-
215):http://journalreview.org/v2/articles/view/12850975.html
Competing interests: No competing interests