Hao Wang, Jean-Pierre Boissel and Patrice Nony*
Corresponding author: Patrice Nony firstname.lastname@example.org
Emerging Themes in Epidemiology 2009, 6:1 doi:10.1186/1742-7622-6-1
(2012-01-12 20:11) James P. Scanlan, Attorney at Law
Wang et al. 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.
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
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