Emerging Themes in Epidemiology - Latest Comments

Understanding contrasting patterns of relative differences in survival and relative differences in mortality

James Scanlan — 2012-01-12T20:11:36Z

Hockey et al.[1] state that the lack of convergence over time between the survival rates of the Australian Longitudinal Study of Women¿s Health (ALSWH) cohort and the Australian female population was unexpected given prior research finding convergence over time of mortality rates of sample and unsampled populations. This observation overlooks the pattern by which 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.[2-4] For reasons related to the shapes of the underlying risk distributions, as populations age and survival generally declines, relative differences between the survival rates of healthier and less healthy groups tend to increase while relative differences in mortality rates of the two groups tend to decrease.

The pattern is evident in the cumulative survival and mortality ratios, as shown in Table A to this comment.[5] Consistently, as cumulative survival decreases over time, relative differences in survival tend to increase while relative differences in mortality tend to decrease. Very likely, the underlying data would also show that the increasing relative differences in cumulative survival by age shown in Hockey Table 2 are accompanied by decreasing relative differences in mortality.

In theory, the same distributional forces should be at work with regard to the interval-specific relative differences, as discussed in the Cohort Considerations sub-page of the Measuring Health Disparities page of jpscanlan.com .[6] Table 1 of Hockey et al. merely shows that relative differences in interval-specific survival fail to get smaller, not that they get larger. The pattern could reflect random variation, given the small number of ALSWH cohort deaths in each interval, and could reflect the combination of the distributional forces (tending to increase the survival differences) and a meaningful reduction in the difference between the mean health of the ASLWH cohort and the Australian female population at large (tending to reduce the relative survival difference). In any case, as shown in the referenced Table A, while there is no consistent pattern for changes in interval-specific relative mortality differences from interval to interval, interval-specific relative differences in mortality are generally smaller in the later intervals. See the Life Table Illustrations sub-page of the Scanlan¿s Rule page of jpscanlan.com [7] and the Life Table Information document [8] for patterns of relative differences in survival and relative differences in mortality based on life tables of healthier and less health populations in the United States.

Hockey et al. note that relative survival was originally used with regard to cancer survival. Relative survival is often discussed in cancer journals. Generally, however, such discussion fails to recognize the contrasting patterns by which relative survival and relative mortality tend to be affected by the overall prevalence of an outcome. Thus sometimes demographic differences in survival and mortality are discussed interchangeably without recognizing that as cancer survival rates increase, relative differences in survival and relative differences in mortality tend to change in opposite directions. See the Mortality and Survival page of jpscanlan.com.[9]

It is not clear just how these patterns might affect interpretations of the generalisability of a patterns observed in ALSWH cohort to the population at large. But one should recognize that general improvements in health will tend to reduce the relative difference in survival but increase the relative difference in mortality between the cohort and the larger population.

References:

1. Hockey R, Tooth l, Dobson A. Relative survival: a useful tool to assess generalisability in longitudinal studies of health in older persons. Emerging Themes in Epidemiology 2011, 8,3: http://www.ete-online.com/content/8/1/3.

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_Disparities.pdf

3. Scanlan JP. Race and mortality. Society 2000;37(2):19-35: http://www.jpscanlan.com/images/Race_and_Mortality.pdf

4. Scanlan JP. Divining difference. Chance 1994;7(4):38-9,48: http://jpscanlan.com/images/Divining_Difference.pdf

5. http://jpscanlan.com/images/Table_A_to_Comment_on_Hockey_et_al.pdf

6. http://jpscanlan.com/measuringhealthdisp/cohortconsiderations.html

7. http://jpscanlan.com/scanlansrule/lifetableillustrations.html

8. http://jpscanlan.com/images/LIFE_TABLE_INFORMATION.pdf

Estimation of treatment effects across a range of baseline rates should not be based on assumptions of either constant relative risks or constant odds ratios

James Scanlan — 2012-01-12T20:11:12Z

Wang et al.[1] note that it is generally accepted that the relationship between baseline risk and risk under treatment is linear (i.e., that the relative risk will be constant) and that absolute benefits will be greatest among high-risk patients, but that there exists an alternative assumption of a curvilinear relationship based on the odds ratio. While observing that there is no theoretical support for either approach, the authors conclude that the assumption of a curvilinear benefit reflected by a constant odds ratio will be more useful for estimating risk reductions.

The authors are correct in questioning the assumption of constant relative risk. The assumption is fundamentally illogical for the simple reason that it is impossible for a factor that causes equal proportionate changes in outcome rates for two groups with different baseline rates of experiencing the outcome to cause equal proportionate changes in the opposite outcome. That is, for example, if Group A has a baseline rate of 5% and Group B has a baseline rate of 10%, a factor that reduces the two rates by equal proportionate amounts, say 20% (from 5% to 4% and from 10% to 8%), would necessarily increase the opposite outcome by two different proportionate amounts (95% increased to 96%, a 1.05% increase; 90% to 92%, a 2.2% increase). And since there is no more reason to expect that two group would undergo equal proportionate changes in one outcome than there is to expect they would undergo equal proportionate changes in the opposite outcome, there is no reason to expect that the two groups would undergo equal proportionate changes in either outcome.

For reasons inherent in the shapes of normal distributions of factors associated with experiencing or avoiding an outcome, it is more reasonable to expect that a treatment that reduces an outcome rate will tend to cause a larger proportionate decrease in that outcome for groups with lower base rates while causing a larger proportionate increase in the opposite outcome for other groups.[2-5] The same aspects of normal distributions that underlie these patterns provide a theoretical basis for expecting a curvilinear relationship between baseline risk and risk under treatment. But the relationship is based, not on the odds ratio, but on the differences between means of the hypothesized underlying risk distributions reflected in the observed risk reduction for a particular baseline rate.[4,5]

A comparison of the estimated absolute risk reductions under that approach compared to the constant risk ratio and constant odds ratio approaches may be found in Table 3 of reference 5.

References:

1. Wang H, Boissel JP, Nony P. Revisiting the relationship between baseline risk and risk under treatment. Emerging Themes in Epidemiology 2009;6:1: http://www.ete-online.com/content/6/1/1

2. Scanlan JP. Race and mortality. Society 2000;37(2):19-35: http://www.jpscanlan.com/images/Race_and_Mortality.pdf

3. Scanlan JP. Divining difference. Chance 1994;7(4):38-9,48: http://jpscanlan.com/images/Divining_Difference.pdf

4. Scanlan JP. Interpreting Differential Effects in Light of Fundamental Statistical Tendencies, presented at 2009 Joint Statistical Meetings of the American Statistical Association, International Biometric Society, Institute for Mathematical Statistics, and Canadian Statistical Society, Washington, DC, Aug. 1-6, 2009: PowerPointPresentation: http://www.jpscanlan.com/images/Scanlan_JSM_2009.ppt; Oral Presentation: http://www.jpscanlan.com/images/JSM_2009_ORAL.pdf

5. Subgroup Effects sub-page of Scanlan¿s Rule page of jpscanlan.com: http://www.jpscanlan.com/scanlansrule/subgroupeffects.html

Additional issues to be considered by a World Council of Epidemiology and Causality

James Scanlan — 2010-04-08T08:45:42Z

Bhopal identifies seven important mistakes of methodology or presentation in epidemiology and makes a timely call for a World Council of Epidemiology and Causality to address these and related issues.[1] I suggest adding the following items to the list.

1. Discussing differences between outcome rates without consideration of the extent to which the differences are affected of the overall prevalence of an outcome.

In over a hundred references made available on the Measuring Health Disparities page of jpscanlan.com[2] (the most important of which are probably references 3-5 below), I discuss the ways that standard measures of differences between outcome rates are affected by the overall prevalence of an outcome. Most notably, the rarer an outcome, the greater tends to be the relative difference in experiencing it and the smaller tend to be the relative difference in avoiding it. Absolute differences between rates and odds ratios are also affected by the overall prevalence of an outcome, though in more complicated ways (as most fully discussed on the Scanlan’s Rule page of jpscanlan.com [6]). While the aforementioned references usually have addressed these patterns with regard to their implications for interpreting data on health inequalities – that is, in the context of discussion of the ways race/ethnicity or socioeconomic status affects an outcome rate – the patterns are equally relevant to discussion of any effort to determine the extent of some association. But, in health inequalities research or otherwise, the implications of overall prevalence have been almost invariably ignored in the discussion of strengths of association.

In recent years, others, including some quite prominent epidemiologists, have reached similar, if not necessarily identical, conclusions about the way that standard measures of differences between rates are affected by the overall prevalence of an outcome and the need to consider the implications of overall prevalence in interpreting measures of differences between outcome rates.[7-9] They have also noted some of the dangers in ignoring such issues.[10] If either my own views or the views of others just mentioned are correct in substantial part, much standard epidemiological methodology warrants reconsideration. A World Council of Epidemiology and Causality is precisely the forum in which to address such issues.

2. Discussing effects of factors on mortality and survival (or the two outcomes in any dichotomy) interchangeably without recognition that the effects on one outcome may be, or even will tend to be, the opposite of the effect on the other.

One of the implications 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 is that as an outcome like mortality decreases in overall prevalence, relative differences in mortality rates tend to increase while relative differences in survival rates tend to decline. Similarly, within subpopulations where adverse (or favorable) outcomes are rare, relative demographic differences in experiencing such outcomes will tend to be large while relative differences in avoiding the outcomes will tend to be small. Because these patterns are little understand, however, researchers may often talk about effects on things like mortality and survival interchangeably. In doing so, they typically assume that an effect observed with regard to one outcome will automatically hold for the other outcome. In fact, however, not only may the opposite effect hold for the other outcome, there is reason to expect that commonly to occur. This seems especially to be a problem in discussion of cancer mortality and survival issues, as discussed in the Mortality and Survival sub-page of the Scanlan’s Rule page of jpscanlan.com.[11]

3. Carelessness in characterization of differences between rates with respect to the size of a relative difference and the failure to distinguish percents from percentage points.

I maintain a web page [12] showing the quite surprising predominance in major medical and other scientific journals (with the notable exception of the New England Journal of Medicine) of the characterization of, for example, a 3% outcome rate as “three times greater than” a 1% outcome rate. Giving the matter the least thought, one ought to recognize that 3% is either “three times as great” as 1% or “two times greater than” 1% and that the figure “three times greater than” 1% would be 4%. Scientific journals ought to be giving the matter more than the least thought.

I also maintain a web page [13] addressing the pattern whereby researchers will state, for example, that something increase a rate by 10%, requiring the reader to go several pages into the article to learn whether in circumstances where the first rate is 20% the second rate is (a) 22% or (b) 30%. Whether or not is technically incorrect to say 10% when one means (b), it is the simplest thing in the world to use the term “percentage points” when one means (b).

Both of these issues lend themselves to treatment in guidelines issued by a World Council.

4. Treating nonsignificant associations as if they provide no evidence of an association or provide evidence of the absence of an association.

That an association be statistically significant has reasonably been regarded as a necessary condition for researchers to conclude that there is an association. Frequently, however, when a study shows an association in nonsignificant terms (and sometimes even when the association approaches significance) researcher will report the result as if it indicates that absence of an association. Sometimes researchers even then proceed to opine on why there is no association. But a nonsignificant finding as to an association still will be some evidence that there exists an association. Even if it is quite week evidence, it is still the best evidence available as to whether there exists an association. That is not a reason why researchers should commonly rely on nonsignificant associations to suggest that there is an association that might be revealed were the study sample larger. But it is a reason why the observed directions of effects should be reported even when they are not significant. It is also a reason why nonsignificant associations should never be reported as suggesting the absence of an association.

References:

1. Bhopal R. Seven mistakes and potential solutions in epidemiology, including a call for a World Council of Epidemiology and Causality. Emerging Theme in Epidemiology 2009,6:6: http://www.ete-online.com/content/6/1/6

2. Measuring Health Disparities page of jpscanlan.com: http://jpscanlan.com/measuringhealthdisp.html

3. Scanlan JP. Can we actually measure health disparities? Chance 2006:19(2):47-51: http://www.jpscanlan.com/images/Can_We_Actually_Measure_Health_Disparities.pdf

4. Scanlan JP. Race and mortality. Society 2000;37(2):19-35 (reprinted in Current 2000 (Feb)): http://www.jpscanlan.com/images/Race_and_Mortality.pdf

5. 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

6. Scanlan’s Rule page of jpscanlan.com:
http://jpscanlan.com/scanlansrule.html

7. Carr-Hill R, Chalmers-Dixon P. The Public Health Observatory Handbook of Health Inequalities Measurement. Oxford: SEPHO; 2005: http://www.sepho.org.uk/extras/rch_handbook.aspx

8. Houweling TAJ, Kunst AE, Huisman M, Mackenbach JP. Using relative and absolute measures for monitoring health inequalities: experiences from cross-national analyses on maternal and child health. International Journal for Equity in Health 2007;6:15: http://www.equityhealthj.com/content/6/1/15

9. Eikemo TA, Skalicka V, Avendano M. Variations in health inequalities: are they a mathematical artifact? International Journal for Equity in Health 2009;8:32: http://www.equityhealthj.com/content/pdf/1475-9276-8-32.pdf

10. Bauld L, Day P, Judge K. Off target: A critical review of setting goals for reducing health inequalities in the United Kingdom. Int J Health Serv 2008;38(3):439-454.

11. Mortality and Survival sub-page of Scanlan’s Rule page of jpscanlan.com: http://www.jpscanlan.com/scanlansrule/mortalityandsurvival.html

12. Times Higher/Greater Issues sub-page of Vignettes page of jpscanlan.com:
http://www.jpscanlan.com/vignettes/timeshigherissues.html

13. Percentage Points sub-page of Vignettes page of jpscanlan.com: http://www.jpscanlan.com/vignettes/percentgepoints.html

The eighth mistake of epidemiologists

Saeed Dastgiri — 2010-04-08T08:45:05Z

Dear Editor,
I read with interest the paper published by Professor Raj Bhopal in an earlier issue of the Emerging Themes in Epidemiology entitled "Seven mistakes and potential solutions in epidemiology, including a call for a World Council of Epidemiology and Causality" (1). The article describes the details of seven major mistakes made by epidemiologists giving seven solutions to avoid them. Professor Bhopal has finally called, as a conclusion, for a World Council of Epidemiology to help to apply the epidemiologic works in human populations.

There is another discipline beside "Epidemiology" which is usually called "Biostatistics or Medical Statistics". Although epidemiologists and biostatisticians have been working and collaborating together since many years ago, and they are even located in some universities and research institutes under a unique umbrella inside a department, there is now a clear distinction in the definition of the "epidemiology" and ""Biostatistics or Medical Statistics".

Epidemiologists are scientists working on the population health. They try to identify the population health problems while biostatisticians working on the data modeling and analysis in every aspects of biomedicine including very specific clinical issues and population health. It seems now that it is time for epidemiologists and biostatisticians to see themselves as independent scientists in the field of medical sciences. I would therefore like to add one more mistake usually made by epidemiologists as they consider themselves as biostatisticians sometimes. Obviously an epidemiologist should know deeply the statistical concepts as the same as other scientists in the other fields of biomedicine. However epidemiologists should be aware that "Epidemiology" is now a separate field from "Biostatistics or Medical Statistics".

In summary, I would like to recommend the eighth mistake as follows:

8. Insufficient attention to the definition of epidemiology and population health by epidemiologists. (VIII Work on population health only as the field of "Epidemiology".)

Sincerely,
Saeed Dastgiri

Dr Saeed Dastgiri
National Public Health Management Centre (NPMC)
School of Medicine
Tabriz University of Medical Sciences
Tabriz
IRAN

Reference
1. Bhopal R: Seven mistakes and potential solutions in epidemiology, including a call for a World Council of Epidemiology and Causality. Emerg Themes Epidemiol 2009, 6(6):1-9.