Interpreting effects on referral inequalities of policies that increase overall referral rates
McBride et al.[1] hypothesized that socioeconomic inequalities in
referrals to secondary care are more likely to occur in the absence of
explicit guidance and potentially life-threatening conditions and found
their hypothesis to be borne out by the data they examined. In
particular, they found socioeconomic inequalities in referrals to
secondary care for hip pain, where there is little guidance as to whom to
refer, but not for referral for postmenopausal bleeding, where guidelines
strongly urge referral. In the case of dyspepsia, where referral is more
strongly urged for patients over 55 than patients under 55, the authors
found evidence of a socioeconomic gradient for patients under 55 but not
for patients over 55.
The authors' hypothesis seems entirely sound. But in analyzing the
statistical support for the hypothesis, the authors overlook the patterns
whereby, solely for reasons related to the shapes of the underlying
distributions of factors associated with likelihood of experiencing an
outcome, standard measures of differences between outcome rates tend to be
affected by the overall prevalence of an outcome. Stronger referral
recommendations generally lead to higher overall referral rates. In such
circumstances, the referenced distributional factors tend to cause
relative differences in referral rates to decrease but relative
differences in rates of failure to be referred to increase.[2-6] Absolute
differences between rates and odds ratios tend also to be affected by the
overall prevalence of an outcome, though in a more complicated way.
Roughly, where an outcome is uncommon (less than 50% for all groups being
compared) increases in the outcome tend to increase absolute differences
between rates; where an outcome is already common (more than 50% for all
groups being compared) further increases in the outcome tend to reduce
absolute differences between rates. Differences measured by odds ratios
tend to change in the opposite direction of absolute differences between
rates.[2,5,6] One can best determine the comparative size of difference
between outcome rates by deriving from each pair of rates the differences
between means of the hypothesized underlying distributions.[5,7]
In the case of a comparison of the socioeconomic inequalities in
referral for postmenopausal bleeding and hip pain, overall referral rates
are much higher for the former (61.4%) than for the latter (17.4). (I
leave person-years out of the matter.) Thus, the distributional factors
would tend to cause smaller relative differences between the rates of the
most and least deprived groups for postmenopausal bleeding than for hip
pain regardless of any meaningful difference in the size of the
inequalities. While the observed pattern of relative differences is
consistent with the distributionally-driven patterns, it is nevertheless
clear that, regardless of how one might appraise the comparative size of
the differences between rates of the most and least deprived groups, the
difference is much smaller for postmenopausal bleeding (61.6% versus
62.4%) than for hip pain (14.2% versus 19.6%). Still, it is worth noting
that the former pair of rates translates into a difference between means
of .021 standard deviations, while the latter pair of rates translates
into a difference between means of .215 standard deviations. The .021
figure indicates that between 50% and 51% of the most deprived group falls
below the mean for the least deprived group, while the .215 figure
indicates that about 58% of the most deprived group falls below the mean
of the least deprived group.
But whether, consistent with the authors' hypothesis, the inequality
in referrals for dyspepsia is larger for patients under 55 than patients
over 55 is not clear. The authors rely on relative differences between
rates of the most and least deprived groups within each age group. The
rate ratio is .76 for the younger group (in which the overall referral
rate is 11.7%) and a nonsignificant .91 for the older group (in which the
overall referral rate is 17.4%). But, putting statistical significance
issues aside, the smaller relative difference for the older group is to be
expected simply because referral is more common in that group. The
authors do not present referral rates for each deprivation group within
the two age groups. Thus, one cannot determine whether the relative
difference in failing to be referred or the absolute difference between
referral rates is larger in the older group, both of which patterns
commonly occur as a result of the shapes of the distributions. More
important, one cannot derive the difference between the underlying means.
Thus, from the data presented, it is not possible to know whether
socioeconomic inequality is in fact lower among older patients than among
younger patients.
These same issues exists in the appraisal of how pay-for-performance
(P4P) programs (which tend to increase overall procedure and appropriate
care rates) affect healthcare inequalities. See the Pay for Performance
sub-page of the Measuring Health Disparities page of jpscanlan.com,[8]
which discusses, inter alia, that reliance on absolute differences between
rates as a measure of healthcare inequalities has led to perceptions in
the United States that P4P will tend to increase healthcare inequalities
and perceptions in the United Kingdom that P4P will tend to reduce
healthcare inequalities. See also the Mortality and Survival page [9] of
jpscanlan.com and the Immunization Disparities sub-page of the Measuring
Health Disparities page of jpscanlan.com [10] regarding varying
perceptions of the comparative size of health and healthcare inequalities
depending on whether inequalities are measured in terms of the relative
difference in the favorable outcome or the relative difference in the
adverse outcome.
References:
1. McBride D, Hardoon S, Walters K, et al.. Explaining variation in
referral from primary to secondary care: Cohort study. BMJ
2010;341:c6267.
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
Rapid Response:
Interpreting effects on referral inequalities of policies that increase overall referral rates
McBride et al.[1] hypothesized that socioeconomic inequalities in
referrals to secondary care are more likely to occur in the absence of
explicit guidance and potentially life-threatening conditions and found
their hypothesis to be borne out by the data they examined. In
particular, they found socioeconomic inequalities in referrals to
secondary care for hip pain, where there is little guidance as to whom to
refer, but not for referral for postmenopausal bleeding, where guidelines
strongly urge referral. In the case of dyspepsia, where referral is more
strongly urged for patients over 55 than patients under 55, the authors
found evidence of a socioeconomic gradient for patients under 55 but not
for patients over 55.
The authors' hypothesis seems entirely sound. But in analyzing the
statistical support for the hypothesis, the authors overlook the patterns
whereby, solely for reasons related to the shapes of the underlying
distributions of factors associated with likelihood of experiencing an
outcome, standard measures of differences between outcome rates tend to be
affected by the overall prevalence of an outcome. Stronger referral
recommendations generally lead to higher overall referral rates. In such
circumstances, the referenced distributional factors tend to cause
relative differences in referral rates to decrease but relative
differences in rates of failure to be referred to increase.[2-6] Absolute
differences between rates and odds ratios tend also to be affected by the
overall prevalence of an outcome, though in a more complicated way.
Roughly, where an outcome is uncommon (less than 50% for all groups being
compared) increases in the outcome tend to increase absolute differences
between rates; where an outcome is already common (more than 50% for all
groups being compared) further increases in the outcome tend to reduce
absolute differences between rates. Differences measured by odds ratios
tend to change in the opposite direction of absolute differences between
rates.[2,5,6] One can best determine the comparative size of difference
between outcome rates by deriving from each pair of rates the differences
between means of the hypothesized underlying distributions.[5,7]
In the case of a comparison of the socioeconomic inequalities in
referral for postmenopausal bleeding and hip pain, overall referral rates
are much higher for the former (61.4%) than for the latter (17.4). (I
leave person-years out of the matter.) Thus, the distributional factors
would tend to cause smaller relative differences between the rates of the
most and least deprived groups for postmenopausal bleeding than for hip
pain regardless of any meaningful difference in the size of the
inequalities. While the observed pattern of relative differences is
consistent with the distributionally-driven patterns, it is nevertheless
clear that, regardless of how one might appraise the comparative size of
the differences between rates of the most and least deprived groups, the
difference is much smaller for postmenopausal bleeding (61.6% versus
62.4%) than for hip pain (14.2% versus 19.6%). Still, it is worth noting
that the former pair of rates translates into a difference between means
of .021 standard deviations, while the latter pair of rates translates
into a difference between means of .215 standard deviations. The .021
figure indicates that between 50% and 51% of the most deprived group falls
below the mean for the least deprived group, while the .215 figure
indicates that about 58% of the most deprived group falls below the mean
of the least deprived group.
But whether, consistent with the authors' hypothesis, the inequality
in referrals for dyspepsia is larger for patients under 55 than patients
over 55 is not clear. The authors rely on relative differences between
rates of the most and least deprived groups within each age group. The
rate ratio is .76 for the younger group (in which the overall referral
rate is 11.7%) and a nonsignificant .91 for the older group (in which the
overall referral rate is 17.4%). But, putting statistical significance
issues aside, the smaller relative difference for the older group is to be
expected simply because referral is more common in that group. The
authors do not present referral rates for each deprivation group within
the two age groups. Thus, one cannot determine whether the relative
difference in failing to be referred or the absolute difference between
referral rates is larger in the older group, both of which patterns
commonly occur as a result of the shapes of the distributions. More
important, one cannot derive the difference between the underlying means.
Thus, from the data presented, it is not possible to know whether
socioeconomic inequality is in fact lower among older patients than among
younger patients.
These same issues exists in the appraisal of how pay-for-performance
(P4P) programs (which tend to increase overall procedure and appropriate
care rates) affect healthcare inequalities. See the Pay for Performance
sub-page of the Measuring Health Disparities page of jpscanlan.com,[8]
which discusses, inter alia, that reliance on absolute differences between
rates as a measure of healthcare inequalities has led to perceptions in
the United States that P4P will tend to increase healthcare inequalities
and perceptions in the United Kingdom that P4P will tend to reduce
healthcare inequalities. See also the Mortality and Survival page [9] of
jpscanlan.com and the Immunization Disparities sub-page of the Measuring
Health Disparities page of jpscanlan.com [10] regarding varying
perceptions of the comparative size of health and healthcare inequalities
depending on whether inequalities are measured in terms of the relative
difference in the favorable outcome or the relative difference in the
adverse outcome.
References:
1. McBride D, Hardoon S, Walters K, et al.. Explaining variation in
referral from primary to secondary care: Cohort study. BMJ
2010;341:c6267.
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. Measurement Problems in the National Healthcare
Disparities Report, presented at American Public Health Association 135th
Annual Meeting & Exposition, Washington, DC, Nov. 3-7, 2007;
http://www.jpscanlan.com/images/ORAL_ANNOTATED.pdf (oral);
http://www.jpscanlan.com/images/Addendum.pdf (addendum);
http://www.jpscanlan.com/images/APHA_2007_Presentation.ppt (PowerPoint
Presentation)
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. Solutions sub-page of Measuring Health Disparities page of
jpscanlan.com: http://www.jpscanlan.com/measuringhealthdisp/solutions.html
8. http://www.jpscanlan.com/measuringhealthdisp/payforperformance.
9. http://jpscanlan.com/mortalityandsurvival2.html
10. http://jpscanlan.com/scanlansrule/immunizationdisparities.html
Competing interests: No competing interests