OUTLINE AND GUIDE TO SCANLAN’S RULE PAGE
(Apr. 24, 2009; rev. June 1, 2013)
The Scanlan’s Rule page of this site consists of a main page (which is accessed by clicking on the yellow wording “Scanlan’s Rule”) and more than 25 sub-pages. Because the mechanics of the site sometimes cause that key page to get overlooked, a sub-page styled “Summary to SR” provides a link back to the main Scanlan’s Rule page. An index to that page follows. Following the index is a listing of sub-pages to the Scanlan’s Rule page that expand on issues raised in the Scanlan’s Rule page or treat additional issues.
This page often will be less up to date than description of the Scanlan’s Rule sub-pages on the Home Page.
Outline to Main Page
Introduction
A. Clarifying Points
1. Merely Tendencies Though Powerful Ones
2. Theoretical Basis
3. Meaning of Changes
4. One Pattern Implied in the Other
4a. Scale Issues
4b. Subgroup Effects
5. Increasing Representation among Population Experiencing and Failing to Experience an Outcome
6. The Value of Health Disparities Studies
7. A Measure Unaffected by Prevalence
8. Meaning of “Overall Prevalence.”
9. Settings Differentiated Temporally or Otherwise
10. Effects of Lowering Cutoffs on Employment Tests
11. Absolute Differences.
12. Odds Ratios
13. Phi Coefficient
13a. Cohen’s Kappa Coefficient
14. Longevity
15. Gini Coefficient etc.
16. Irreducible Minimums
17. Concentration Index
18. Probit Analysis
19. Case Control Studies
20. Meta-Analyses
B. Illustrations of SR1 and SR2
1. Feminization of Poverty 1
2. Feminization of Poverty2.
3. Racial Differences in Infant Mortality
4. Racial Differences in Adverse Birth Outcomes among Advantaged Groups
5. Whitehall Studies
6. Nordic Health Disparities
7. NCAA’s Proposition 48
8. Terminations from Employment
9. Racial Impact of the Three-strikes Law
10. Studies of Healthcare Disparities Relying on Absolute Differences
11. NHANES Data
12. Pay-for-Performance Programs
13. Age Patterns
Listing of Sub-Pages Treating Particular Issues in Depth or Providing Other Relevant Material.
The numbering of the pages below does not comport with the placement on the website, as the numbering has not been revised each time a page has been inserted.
1. Semantic Issues sub-page discusses certain technical semantic issues that have some bearing on patterns described in the main Scanlan’s Rule page.
http://jpscanlan.com/scanlansrule/semanticissues.html
2. Employment Tests sub-page addresses whether, considered in light of the points made generally on the Scanlan’s Rule page, lowering a cutoff on a test in fact reduces the disparate impact of the test in a meaningful way.
http://www.jpscanlan.com/scanlansrule/employmenttests.html
3. Case Study sub-page uses a case study approach to illustrating some of the issues raised on the Scanlan’s Rule page and its sub-pages. The page is related to the Relative Versus Absolute sub-page of MHD.
http://jpscanlan.com/scanlansrule/casestudy.html
4. Case Study Answers sub-page provides answers to the questions posed.
http://jpscanlan.com/scanlansrule/casestudyanswers.html
[The material on the Case Study and Case Study Answers sub-page was later expanded upon in the Relative Versus Absolute sub-page of the Measuring Health Disparities. That sub-page provides what I think may be the most useful demonstration that there can be only one reality as to the comparative size of differences between the well-being of two groups reflected by pairs of outcome rates.]
5. Subgroups Effects sub-page discusses the way observers mistakenly identify subgroup effects on the basis of the way factors are associate with different proportionate changes in the rates of groups with different base rates without recognizing the extent to which the different proportionate changes are functions of the different base rates or that the group with the larger proportionate decrease in an outcome will tend to have the smaller proportionate increase in the opposite outcome. The page also discusses the more important issue of the estimation of the absolute risk reduction and corresponding number needed to treat based across a range of baseline rates based on an observed risk reduction in a clinical trial.
http://www.jpscanlan.com/scanlansrule/subgroupeffects.html
6. Feminization of Poverty sub-page addresses the way that increases in the proportion of the population comprised by members of female-headed families are interpreted without recognition that decreases in the prevalence of an outcome will tend to cause groups particularly susceptible to the outcome to comprise a larger proportion of the population experiencing the outcome than they did previously as well as a larger proportion of the population failing to experience the outcome. See Section B1 and B2 the main Scanlan’s Rule page.
http://www.jpscanlan.com/scanlansrule/feminizationofpoverty.html
7. Explanatory Theories sub-page addresses the way that researchers believing they have identified a larger difference between rates in one setting than another may devise explanations for such perceived larger difference, usually without a sound basis for the perception that the difference is larger.
http://jpscanlan.com/scanlansrule/explanatorytheories.html
8. Mortality and Survival sub-page had been an earlier version of what is now the Mortality and Survival page. It is retained solely to refer users of old links to the new page.
http://jpscanlan.com/mortalityandsurvival2.html
9. Immunization Disparities sub-page addresses patterns by which various measures of disparities in immunization and other health care procedures tend to reach different conclusions with attention given to the January 2011 Health Disparities and Inequalities Report of the Centers for Control and Prevention.
http://jpscanlan.com/scanlansrule/immunizationdisparities.html
11. Truncation Issues sub-page, which is related to the Cohort Considerations sub-page
of MHD, discusses why the patterns described in the introduction to the Scanlan’s Rule page may vary when the populations examined are truncated portions of larger populations, as well as reasons why the Solutions approach on MHD is unsuitable in such circumstances. The matter is also treated on the Life Table Illustrations sub-page of the Scanlan’s Rule page.
http://jpscanlan.com/scanlansrule/truncationissues.html
12. Framingham Illustrations sub-page uses information from online calculator of heart attack risks based on the Framingham studies to illustrate the patterns described on the main Scanlan’s Rule page.
http://jpscanlan.com/scanlansrule/framinghamillustrations.html
13. Life Table Illustrations sub-page uses life table to data to illustrate the predominance of the distributional forces in circumstances where the differences in prevalence in different settings are great, as is invariably the case with regard to mortality when the two settings involve substantially different ages.
http://jpscanlan.com/scanlansrule/lifetableillustrations.html
14. NHANES sub-page uses data from the National Health and Nutrition Examination Survey to illustrate the patterns described on the main Scanlan’s Rule page.
http://jpscanlan.com/scanlansrule/nhanesillustrations.html
15. Illogical Premises sub-page, which is related to the Subgroup Effects sub-page, explains why it is illogical to regard it as somehow normal that two groups with different base rates should experience equal proportionate changes in an outcome rate (given that it is not possible for two groups with different base rates to experience equal proportionate changes in such rates while also experiencing equal proportionate changes in rates of experiencing the opposite outcome).
http://jpscanlan.com/scanlansrule/illogicalpremises.html
16. Representational Disparities sub-page explains why it is not possible to appraise the size of a disparity when solely on the basis of the proportions a group comprises of persons eligible to experience an outcome and of persons who experience the outcome.
http://jpscanlan.com/scanlansrule/representationaldisp.html
17. Statistical Significance SR sub-page explores whether, given that the same properties of normal distributions that underlie the patters described on the Scanlan’s Rule page, a test of statistical significance given unchanged population size would meet the key criterion for an effective measure of the size of difference between outcome rates (i.e.,, that the measure remain unchanged when there occurs a change in overall prevalence akin to that effected by lowering a test cutoff).
http://jpscanlan.com/scanlansrule/statisticalsignifsr.html
18. Comparing Averages sub-page explains why, irrespective of adjustment considerations, the issues discussed generally on the main page affect comparisons of an average of outcome rates for more than one sub-group with another average of outcome rates for more than one sub-group.
http://jpscanlan.com/scanlansrule/comparingaverages.html
19. Meta-Analysis sub-page briefly explains that factors that tend generally to undermine sub-group analyses similarly undermine meta-analyses of effects on dichotomous outcomes.
http://jpscanlan.com/scanlansrule/metaanalysis.html
20. Case Control Studies sub-page page addresses sub-page addresses a fundamental problem with case control studies in that, while one may be able to derive an approximation of the relative risk from such study, one cannot derive the actual rates.
http://jpscanlan.com/scanlansrule/casecontrolstudies.html
21. Illogical Premises II sub-page explains that, for reasons similar to those discussed on the Illogical Premises sub-page, it is illogical to regard the rate ratio as a sound measure of association.
http://jpscanlan.com/scanlansrule/illogicalpremisesii.html
22. Inevitability of Interaction sub-page, which explains why equal proportionate changes will never be observed as to either rate save on the rare occasion when a meaningful differential effect, by happenstance, causes the relative changes in different baseline rates for some outcome to coincide.
http://jpscanlan.com/scanlansrule/inevitableinteraction.html
23. The Interactions by Age sub-page discusses and illustrated the pattern whereby almost invariably in comparisons of age groups with substantially different mortality rates, one will find opposite patterns of interaction depending on whether one examines a factors effect on mortality or on survival (that is, that the age group with the smaller proportionate effect on its mortality rate will show the larger proportionate effect on its survival rate).
24. RERI sub-page discusses explains that the RERI (relative excess due to interaction) is a problematic measures for the same reason that the rate ratio is a problematic measure of association.
http://jpscanlan.com/scanlansrule/reri.html
25. The Criminal Record Effects sub-page discusses a situation where the author focused on effects of a factor on a favorable outcome and found a differential effect that is the opposite of that one would find with the more common approach of examining effects on adverse outcomes.
http://jpscanlan.com/scanlansrule/criminalrecordeffects.html
26. The Mortality/Survival Illustration sub-page uses data on cancer survival by race and stage for various types of cancer to illustrate the pattern by which as which stages with higher survival rates tend to show larger relative differences in mortality, but smaller relative differences in survival, than stages with lower survival rates.
http://jpscanlan.com/scanlansrule/mortsurvillustration.html
27. Credit Score Illustrations sub-page use data on racial differences in credit scores from a putative class action to illustrate the pattern whereby the lower the cutoff the greater tends to be the relative difference in failing to meet it and the smaller tends to be the relative difference in meeting it.
http://jpscanlan.com/scanlansrule/creditscoreillustration.html
28. Income Illustrations sub-pages uses income data to show the lower the income level, the greater tends to be the relative difference in failing to reach it and the smaller tends to be the relative difference in reaching it.
http://jpscanlan.com/scanlansrule/incomeillustrations.html
29. Collected Illustrations sub-page merely collects links to the illustration pages in order to facilitate referencing those pages.
http://jpscanlan.com/scanlansrule/collectedillustrations.html
30. Sears Case Illustration page explains the relationship of evidence in the EEOC v. Sears, Roebuck & Co. to recognition of the pattern whereby 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.
http://jpscanlan.com/scanlansrule/searscaseillustration.html