Interactions by Age
(Nov. 20, 2012; rev. June 4, 2013)
Prefatory note added May 31, 2013: As reflected in the text following this note, this page was originally created to illustrate the way that subgroup analyses by age would tend to show that being in a disadvantaged group tends to have a larger relative effect on mortality but smaller effect on survival among younger age groups (where mortality is less common) than among older groups. Breakdowns by age are particularly useful for this purpose, at least when the age groups have substantially different mortality, because the prevalencerelated forces will generally be evident regardless of the what other forces may be at work. But the illustrations are equally pertinent to issues addressed on the Mortality and Survival page, which discusses the way that, particularly in studies of demographic differences in cancer outcomes, researchers commonly refer to disparities in mortality and disparities in survival interchangeably, often stating they are analyzing one while in fact analyzing the other, and do so unaware that relative differences in mortality and relative differences in survival tend to change in opposite directions as survival rates generally change.
This page is related to the Subgroup Effects , Illogical Premises, Illogical Premises II, Inevitability of Interaction, and Life Tables Illustrations subpages of the Scanlan’s Rule (SR) page of jpscanlan.com. All those subpages concern the illogical expectation that, absent a subgroup effect, a factor will have the same relative effect upon different baseline rates.[i] The first three subpages explain that it is illogical to expect a factor to cause equal proportionate changes in different baseline rates since it is not possible for a factor to cause equal proportionate changes in two different baseline rates of experiencing an outcome while causing equal proportionate changes in rates of experiencing the opposite outcome. That is, 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). As explained on the Inevitability of Interaction subpage, since a factor must yield different proportionate changes in two groups’ rates of experiencing either one outcome or the other, subgroup effects/interaction, as these concepts are generally understood, necessarily will exist whenever two groups have different baseline rates of experiencing an outcome. But these are spurious subgroup effects.[ii]
As explained on the Subgroup Effects subpage, as a result of the failure to understand the statistical patterns described there and elsewhere on this site, studies almost universally seek to identify subgroup effects on the basis of a departure from a constant risk ratio (and, also almost universally, assume a constant relative risk reduction across different baseline rates when employing the risk reduction observed in a clinical trial to estimate the absolute risk reduction and corresponding number needed to treat in circumstances involving a baseline rate different from that in the trial). The reason such studies fail to find a spurious subgroup effect in every case is simply that there are too few observations for the spurious subgroup effect to be consistently observed or for the interaction term to be statistically significant. Further, the smaller the difference in the baseline rates,[iii] the less likely that a spurious subgroup effect will be observed. But because adverse outcome rates tend to vary greatly by age, mainly increasing after age 40 and doing so in a manner whereby, for example, mortality rates of persons above age 60 are much higher than mortality rates of persons between 40 and 60, the differences between baseline rates are of a nature that one will observe spurious subgroup effects by age with great frequency. See also the Framingham Illustrations subpage of SR, which suggests that because of the substantially different heart attack risks of men and women with the same risk factor profiles one will commonly find spurious interactions by gender with respect to a factor that affects heart attack risk.
The Life Tables Illustrations subpage of SR explains that 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 found with great consistency when comparisons of effects on mortality by age group are examined, particularly when the age groups being compared are quite disparate (hence with large differences in baseline mortality). The illustrations of racial and gender differences by age group shown on that page and in the Life Table Information Document are simply another way of looking at what might be regarded as analyses of the effects of race or gender on mortality by agedefined subgroup.
Similarly, anytime one examines relative effects of a factor by age subgroups, one is likely to find a spurious interaction (that is, differing relative effects by age group), at least where the age groups have substantially different baseline adverse outcome rates. See the Comment on Berrington de Gonzalez (and its Table A), which discusses findings that being overweight or obese has a greater effect on mortality among the young than the old. See also the illustration of the effects of beta blockers on mortality/survival by age group in Table 1 of the Subgroup Effects subpage. .
Other illustrations of the patterns whereby any factor that affects an outcome like mortality/survival will commonly show larger relative effects on mortality among younger age groups and larger effects on survival among older age groups – though involving situations where the studies did not address the matter in terms of subgroup effects – may be found in Table 1 to the Mortality and Survival page (involving relative differences in fiveyear mortality/survival of patients with oral and pharyngeal cancer by race), Table 6 to the 2008 Nordic Demographic Symposium (involving differences in mortality/survival among Finnish men by renter and owner status).
See also discussion of finding by Devonshire et al.[iv] of greater efficacy of treatment with fingolimod among younger multiple sclerosis patients by Sormani and Bruzzi.[v] In any circumstance where older individuals have substantially greater baseline adverse outcome rates than younger individuals there is reason to expect that a factor that increases or decreases baseline outcome rates will cause a larger proportionate change in among younger age groups while causing a larger proportionate change in the opposite outcome among older age groups. But nonspurious subgroup effects must be identified according to the procedure described in the Subgroup Effects subpage or some like procedure that is unaffected by baseline rates.[vi]
Tables 1 and 2 below, which are slightly modified excerpts from the tables in the Life Table Information Document, provide succinct illustrations of the effects on mortality and survival of being in a disadvantaged group in comparisons (with the advantaged group listed first) of white women and white men, white men and black men, black women and black men, and white women and black women. Table 1 show the patterns of rates ratios for rates at which disadvantaged and advantaged groups die before, and rates of ratios at which advantaged and disadvantaged groups survive beyond, ages 60 and 80 (along with the EES, for estimated effect size, which is explained in the Subgroup Effects page). Table 2 presents comparable information with respect dying before or living beyond 60 and 80 among persons alive at 50 and 70. The illustration in Table 2 uses data more like that commonly employed in analyses of outcome rates where observers categorize subjects by age. But, since such illustrations involve truncated populations, the EES is a less accurate indicator of the strength of the forces causing rates to differ (as discussed in the Truncation Issues and Life Tables Illustrations subpages of the Scanlan’s Rule page). The tables show that the prevalencerelated patterns are evident regardless of the way the strength of the forces causing rates to differ may be changing.
Table 1. Rates at Which Pairs of Advantaged and Disadvantaged Groups Die Before Ages 60 and 80, with Ratios of (a) Disadvantaged Group’s Rate of Dying to Advantaged Group’s Rate of Dying and (b) Advantaged Group’s Rate of Surviving to Disadvantaged Group’s Rate of Surviving, with Estimated Effect Size [ref N/b4128a1]
b4128 a 1 age interaction illustration 1

Cat

Age

AGMort

DGMort

DGAGMortRatio

AGDGSurvRatio

EES

WFWM

60

8.19%

13.96%

1.70

1.07

0.32

WFWM

80

37.91%

51.93%

1.37

1.29

0.37








WMBM

60

13.96%

24.25%

1.74

1.14

0.39

WMBM

80

51.93%

67.36%

1.30

1.47

0.41








BFBM

60

14.58%

24.25%

1.66

1.13

0.36

BFBM

80

49.18%

67.36%

1.37

1.56

0.50








WFBF

60

8.19%

14.58%

1.78

1.07

0.35

WFBF

80

37.91%

49.18%

1.30

1.22

0.29








Table 2. Rates at Which Pairs of Advantaged and Disadvantaged Groups Alive at Ages 50 and 70 Die Before Ages 60 and 80, with Ratios of (a) Disadvantaged Group’s Rate of Dying to Advantaged Group’s Rate of Dying and (b) Advantaged Group’s Rate of Surviving to Disadvantaged Group’s Rate of Surviving, with Estimated Effect Size.
b4128 a 2 interval illustration for age interaction

Cat

PrAge

Age

DGMort

AGMort

DGAGMortRatio

AGDGSurvRatio

INTEES

WFWM

50

60

7.14%

4.26%

1.67

1.03

27

WFWM

70

80

34.12%

24.81%

1.38

1.14

28









WMBM

50

60

13.14%

7.14%

1.84

1.07

35

WMBM

70

80

43.27%

34.12%

1.27

1.16

24









BFBM

50

60

13.14%

7.58%

1.73

1.06

32

BFBM

70

80

43.27%

30.15%

1.43

1.23

37









WFBF

50

60

7.58%

4.26%

1.78

1.04

30

WFBF

70

80

30.15%

24.81%

1.22

1.08

17









[i] The page is similarly related to any number of pages on this site that pertain to analyses that purport to find something meaningful when a factor does not cause equal proportionate changes in different baseline rates, including the Explanatory Theories subpage of the Scanlan’s Rule page and the Reporting Heterogeneity subpage of the Measuring Health Disparities page.
[ii] As reflected in the Illogical Premises II subpage of the Scanlan’s Rule page, implicit in these points is a challenge to the rate ratio as a measure of association. See my Goodbye to the rate ratio. BMJ Feb. 25, 2013 (responding to Hingorani AD, van der Windt DA, Riley RD, et al. Prognosis research strategy (PROGRESS) 4: Stratified medicine research. BMJ2013;346:e5793).
[iii] I do not address here issues concerning the appraisal of the size of the difference in the baseline rates. Such issue, however, is explicitly or implicitly addressed in many places on this site, wherever the size of a difference in circumstances reflected by two pair or rates is discussed. An illustration of the recommended approach in a context pertinent to the instant discussion may be found in the paragraphs following Table LT1 of the Life Tables Illustration subpage.