1. James P. Scanlan Attorney at Law Washington, DC, USA jps@jpscanlan.com
British Society for Population Studies, Annual Conference University of Manchester September An Approach to Measuring Differences between Rates that is not Affected by the Overall Prevalence of an Outcome
James P. Scanlan
Attorney at Law
Washington, DC, USA

2. Subjects
1. The problem with standard binary measures of differences between rates (relative differences, absolute differences, odds ratios): that all exhibit patterns of correlation with overall prevalence (i.e., among other things, they tend to change as overall prevalence changes) (BSPS 2006, 2007)
2. A plausible alternative approach that avoids the problem with standard measures: a measure that does not change as overall prevalence changes

3. References
Measuring Health Disparities page (especially the Solutions tab) and Scanlan’s Rule page on jpscanlan.com
Can We Actually Measure Health Disparities? (Chance 2006) (A12)
Race and Mortality (Society 2000) (A10)
The Misinterpretation of Health Inequalities in the United Kingdom (BSPS 2006) (B6)
BSPS 2007 (B11)

4. Patterns by Which Binary Measures Tend to Change as the Overall Prevalence of an Outcome Changes – Scanlan’s Rules
SR1: The rarer an outcome, the greater tends to be the relative difference in rates of experiencing it and the smaller tends to be the relative difference in rates of avoiding it (IR1 in BSPS 2006; see Bauld, Day, Judge, 2008)
SR2: As an outcome changes in overall prevalence, the odds ratio tends to change in the same direction of the larger of the two relative differences and the absolute difference tends to change in the same direction as the smaller of the two relative differences ─ where numerators are reversed on the two risk ratios (see Semantic Issues tab on Scanlan’s Rule page)

5. Fig 1. Ratio of (1) Advantaged Group (AG) Success Rate to Disadvantaged Group (DG) Success Rate at Various Cutoffs Defined by AG Success Rate

6. Fig 2. Ratios of (1) AG Success Rate to DG Success Rate and (2) DG Fail Rate to AG Fail Rate

7. Fig 3. Ratios of (1) AG Success Rate to DG Success Rate, (2) DG Fail Rate to AG Fail Rate, and (3) DG Fail Odds to AG Fails Odds

8. Fig 4. Ratios of (1) AG Success Rate to DG Success Rate, (2) DG Fail Rate to AG Fail Rate, and (3) DG Fail Odds to AG Fails Odds; and Absolute Diff Between Rates

9. Table 1 Illustration of the Problem and Intimation of the Solution (in terms of a favorable outcome increasing in overall prevalence)
Period Yr Yr Yr Yr 4
AG Rate 40% % % %
DG Rate 23% % % %
Measures of Difference (Blue=decrease; Red=increase)
Ratio
Ratio
Odds Ratio
Absol Diff
EES (z)

10. Estimated Effect Size (EES)
Difference between means of hypothesized underlying distributions of risks of experiencing an outcome, in terms of percentage of a standard deviation, assuming normality of the distributions

11. Table 2 Simplified Illustration of the Solution (in terms of a favorable outcome increasing in overall prevalence)
Period Yr Yr 2
AG Rate 40% %
DG Rate 23% %
Measures of Difference Change Direction
Ratio Increase
Ratio Decrease
Odds Ratio Decrease
Absol Diff Increase
EES (z) Decrease

12. Table 3 Illustration of Meaning of Various Ratios at Different Prevalence Levels
DGFailRate
AGFailRate
EES
1.2
60.0%
50.0%
0.26
18.4%
15.4%
0.12
1.5
75.0%
0.68
45.0%
30.0%
0.39
2.0
40.0%
20.0%
0.59
10.0%
0.44
1.0%
0.5%
0.24
2.5
24.2%
9.7%
0.60
7.4%
2.9%
3.0
44.0%
14.7%
0.90
14.4%
4.8%
2.7%
0.9%

13. Caveat – Compositional Differences
Differences in the proportions groups being analyzed comprise of the total population in settings being compared undermine otherwise valid measurement approaches
See Heller et al. (BMJ 2002), Boström and Rosén (SJPH 2003), D43
Solution seems always to compare same proportions (e.g., top vs. bottom quintile), which may often limit analyses to income
Less of an issue for US racial comparisons

14. Table 4 Illustration Based on Morita et. al
Table 4 Illustration Based on Morita et. al. (Pediatrics 2008) Data on Black and White Hepatitis B Vaccination Rates Pre and Post School-Entry Vaccination Requirement (see D52)
Period
Grade
Year
WhRt
BlRt
Fav
Ratio
Adv
AbsDf
EES
Pre
Requ 5
(Y1)
1996 8% 3%
2.67
1.05
0.05
0.47
Post
(Y2)
1997
46%
33%
1.39
1.24
0.13
0.34 9
32%
1.44
1.26
0.14
0.37
89%
84%
1.06
1.45
0.24

15. Table 5 Illustration of UK Changes Over Time from Table 4
Table 5 Illustration of UK Changes Over Time from Table 4.13 of The Widening Gap (rates per 100,000)
Cohort
Year
Class I
Class V
Mort
Ratio
Survival
AbsDf
EES
55-64
1921
2247
3061
1.36
814
0.14
1931
2237
2535
1.13
298
0.06
1951
2257
2523
1.12
266
0.05
1961
1699
2912
1.71
1213
0.25
1971
1736
2755
1.59
1019
0.21
1981
1267
2728
2.15
1461
0.32
1991
953
2484
2.61
1531
0.39

16. Table 6 Illustration of UK Differences across Age Groups from Table 4
Table 6 Illustration of UK Differences across Age Groups from Table 4.13 of The Widening Gap
Year
Cohort
Class I
Class V
Mort
Ratio
Survival
AbsDf
EES
1991
25-34 39
187
4.8
148
0.47
35-44
101
382
3.8
281
0.42
45-54
306
916
3.0
610
0.39
55-64
953
2484
2.6
1531

17. Table 7 Illustration of Comparisons as to Different Conditions from Lawlor (AJPH 2006) (Aberdeen 1950 birth cohort) (rates are per 10,000) (see D28)
Cond
Class I
Class V
Adv
Ratio
Fav
AbsDf
EES
CHD
8.30
20.50
2.5
12.2
0.28
Stroke
2.30
7.80
3.4
5.5
0.34

18. Table 8 Illustration of Age Group Comparisons in Whitehall Studies from Marang-van de Mheen (JECH 2001) (rates are per 1,000)
Age
HGMR
LGMR
MortRatio
SurvRatio
AbsDf
EES
55-59
6.80
13.90
2.05
7.1
0.27
60-64
11.30
19.90
1.76
8.6
0.22
65-69
17.50
28.10
1.61
10.6
0.20
70-74
30.90
47.50
1.54
16.6
75-79
50.60
70.00
1.38
19.4
0.16
80-84
78.30
107.60
29.3
0.19
85-89
144.30
181.60
1.26
37.3

19. Table 9 Illustration Based on Boström and Rosén (SJPH 2003) Data on Mortality by Occupation in Seven European Countries (see D43 caveat)
Country
EES
EES
Denmark
0.14
0.13
England and Wales
0.11
0.15
Finland
0.16
0.23
Ireland
0.10
0.19
Norway
0.12
Spain
Sweden
0.17

20. Problems with the Solution
Always practical issues (we do not really know the shape of the underlying distributions)
Sometimes fundamental issues (e.g., where we know distributions are not normal because they are truncated portions of larger distributions, see D43); cf. BSPS 2007, Fig. 6
Absolute minimum issue (D43,B6)

21. Conclusion
If we are mindful of the problems, the approach provides a framework for cautiously appraising the size of differences between rates.
Regardless of problems, the approach is superior to reliance on standard binary measures of differences between rates without regard to the way those measures tend to be correlated with the overall prevalence of an outcome.

22. Formula to derive EES?

23. Example of 8 of 76,960 rows in table downloadable from jpscanlan.com
EES
AG Fail
DG Fail
0.60
0.5
0.30
0.6141

24. Supp Table 1 Illustrations Based on Escarce and McGuire (AJPH 2004) Data on White and Black Coronary Procedure Rates, 1986 and 1997 (see D48)
Proc
Year
Wh Rt
Bl Rt
Fav
Ratio
Adv
AbsDf
EES
Angrm
(Y1)
1986
0.86%
0.43%
1.99
1.05
0.04
0.25
(Y2)
1997
2.28%
1.61%
1.42
1.09
0.07
0.14
Angpls
0.10%
0.03%
3.09
1.01
0.01
0.32
0.26%
0.16%
1.61
0.15
ArtByp
0.31%
0.08%
3.78
1.02
0.02
0.41
0.59%
2.25
1.03
0.03
0.27

25. Supp Table 2: Illustration Based on Hetemaa et al
Supp Table 2: Illustration Based on Hetemaa et al. (JECH 2003) Data on Finnish Revascularization Rates, 1988 and 1996, by Income Group (see D21, D58)
Gender
Year AG
RevRt
LowInc
Fav
Ratio
Adv
AbsDf
EES M
(Y1)
1988
17.9%
8.3%
2.16
1.12
.096
0.48
(Y2)
1996
41.2%
25.4%
1.63
1.27
.159
0.44 F
10.0%
3.7%
2.70
1.07
.063
0.51
30.8%
17.1%
1.80
1.20
.137
0.45

26. Supp Table 3: Illustration Based on Laaksonen et al
Supp Table 3: Illustration Based on Laaksonen et al. (JECH 2008) Data on Mortality Rates of Finnish Men by Owner or Renter Status (see follow-up on D43)
Age
OwnMort
RentMort
AdvRatio
FavRatio
EES
40–44
1.46%
4.26%
2.91
1.03
0.46
45–49
2.46%
6.04%
2.45
1.04
0.42
50–54
3.68%
9.68%
2.63
1.07
0.49
55–59
5.62%
13.09%
2.33
1.09
0.47
60–64
8.88%
19.89%
2.24
1.14
0.5
65–69
14.33%
29.38%
2.05
1.21
0.53
70–74
24.62%
41.85%
1.70
1.30
0.48
75–79
36.55%
57.75%
1.58
1.50
0.56

27. Supp Table 4 Illustration from Valkonen et al
Supp Table 4 Illustration from Valkonen et al. (JEPH 2000) Based on All Cause Mortality in Finland for Three Time Periods
Gender
Period
AGMort
DGMort
AdvRatio
FavRatio
EES M
0.64%
0.96%
1.50
0.15
0.53%
0.93%
1.75
0.21
0.46%
0.85%
1.86
0.22 F
0.29%
0.35%
1.21
0.07
0.26%
0.36%
1.36
0.11
0.24%
1.48
0.14 f