# 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 doi: https://doi.org/10.1136/bmj.d4662 (Published 23 August 2011) Cite this as: BMJ 2011;343:d4662## All rapid responses

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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

## Study of differences in rates of dying above median age at death raises a number of statistical issues - Part II

(Continued from Part I)

A further problem with analyzing changes over time by examining for

different time periods proportions of decedents in advantaged and

disadvantaged groups who died at an age above the median age of death for

the entire population lies in the fact that during the earlier time

periods members of the advantaged group tended to live longer than members

of the disadvantaged group. Thus, living persons suffering from cystic

fibrosis in the advantaged group tend to be older than living persons in

the disadvantaged group. While arguments are sometimes made about the way

greater mortality at younger ages among disadvantaged groups will tend to

improve such groups' comparative health at older ages, if for every age

group the mortality rates of the advantaged and disadvantaged groups are

exactly the same, most would regard such situation as reflecting an

absence of inequality. But in such case, simply because the proportion of

living members of the advantaged group that is in the older age ranges is

larger than the proportion of living members of the disadvantaged group

that is in the older age ranges, one would still observe that a higher

proportion of decedents from the disadvantage group died at an age above

the overall median age of death than of the decedents from the

disadvantaged group.

(The above point is different from the point Barr et al. make at the

conclusion of the Limitations section of their article concerning time

lags between the implementation of healthcare improvements and the effects

of those improvements. That point, which seems valid, involves reasons to

expect continuing differences between the mortality rates of advantaged

and disadvantaged groups within each age group, while the point in the

paragraph above involves reasons to expect continuing differences between

the proportions of decedents from each group who die above the overall

median age of death even if the mortality rates within age groups are the

same.)

Another difficulty in evaluating changes in socioeconomic effects

over time using the methodologies employed by Barr et al. involves the

fact that the relative sizes of the demographic groups are changing over

time, which is a common problem in appraisals of socioeconomic

inequalities over extended periods of time. Even in the context of more

standard (though also problematic) measures such as ratios of mortality

rates, that the proportion different socioeconomic groups make up of the

total population changes over time creates an interpretation problem.

Generally, the proportion of the population in the manual laboring classes

has been shrinking.[11,12] Thus, in analyses that compare the highest

with the lowest socioeconomic categories, at one point one may be

comparing the least advantaged 20% of the population with the most

advantaged 20% of the population, while at another point one may be

comparing the least advantaged 10% of the population with the most

advantaged 30% of the population; or, in an analysis that dichotomizes the

entire population, at one point one may be comparing the least advantaged

50% of the population with the most advantaged 50% of the population while

at another point one may be comparing the least advantaged 40% of the

population with the most advantaged 60% of the population. It is not

clear how that factor will affect results since the described changes

cause both the advantaged and disadvantaged groups to have somewhat lower

average quantities of the factors associated with experiencing a favorable

outcome. But it still needs to be recognized that the comparisons are not

the same at the different points in time.

Moreover, this problem would seem especially serious when a reference

point such as median age is used, as in the Barr study (and as would also

be the case in a study that analyzes inequalities in terms of standardized

mortality ratios). For the proportions the groups comprise of the total

population will affect the overall median as well as the proportions of

the groups that may be above that median. For example, where the

advantaged group comprises 50% or less of the total population analyzed,

100% of the group could experience the favorable outcome of in some manner

being above an overall median. But as the proportion the advantaged group

comprises of the total population increases, the smaller is the

proportion of that group that can experience the favorable outcome of

being above the overall median. Further - though possibly it is the same

point - the larger the proportion a group comprises of the total

population the more that group's median will influence the overall median,

hence presumably reducing the extent to which the proportion of the group

that will experience a favorable outcome of being above the overall median

will exceed 50%. This problem, however, ought not to affect the gender

analysis, assuming that the two genders each comprise approximately 50% of

the persons who died in a particular year.

In sum, a number of statistical issues make the interpretation of the

findings in the Barr study quite difficult. Such difficulties suggest

that it is useful to present as much of the underlying data as possible.

References:

11. Heller RF, McElduff P, Edwards R. Impact of upward mobility on

population mortality: analysis with routine data. BMJ

2002;325:134:10.1136/bmj.7356.134

12. Bostr?m G, Ros?n M. Measuring social inequalities in health -

politics or science? Scan J Public Health. 2003:31:211-215.

Competing interests:No competing interests07 September 2011