The
Case Against Relative Risk
Larry Birnbaum,
PhD, MA, EPC
Department
of Exercise Physiology
The College
of St. Scholastica
Duluth, MN
RELATIVE
RISK HAS been used in epidemiological studies for many years. It
has been used extensively in cholesterol studies that have associated high
total cholesterol levels, as well as low HDL and high LDL cholesterol levels,
with an increased (relative) risk of coronary heart disease (CHD).
It has also commonly appeared in cancer studies in which one or more factors
have been correlated with an increased (relative) risk of cancer.
In consideration of the immense consequences of these studies, it seems
absurd that few have questioned the validity of relative risk. At
least few critiques have appeared in mainstream journals. Indeed,
the entire scientific community should scrutinize the use of relative risk.
Hopefully, this editorial will motivate some of the more powerful sectors
of the scientific community to openly discuss relative risk. Is it
a valid statistical test? Is it even a statistical test? If
not, why is it used?
In an attempt
to determine what relative risk (RR) is, let us first examine how relative
risk is calculated. A contingency table is used to categorize people
into one of four groups, those with and without a disease in conjunction
with those who have and have not been exposed to a risk factor. Relative
risk is then calculated from the data in the manner shown below.
|
Diseased
|
Not Dieseased
|
|
Exposed
|
A
|
B
|
A + B
|
Not Exposed
|
C
|
D
|
C + D
|
|
A + C
|
B + D
|
|
RR = A/(A +
B) divided by C/(C + D)
Hennekens CH,
Buring JE, Epidemiology in Medicine, 1987, p78. (1)
Relative risk
has been defined as the probability of disease in the exposed group divided
by the probability of disease in the unexposed group (2).
This sounds legitimate, but ultimately relative risk greatly amplifies
differences between two groups when those differences are either insignificant
or do not even exist. Let us use an example to explore how misleading
relative risk can be.
Consider two
groups of subjects who have their cholesterol levels measured and are followed
over a period of five years. There are 1,000 subjects in each group.
In group I, the average cholesterol level is 180 mg/dL; in group II, 240
mg/dL. Over the five year period one person in group I dies of CHD;
two in group II. Group II is the exposed group (i.e., elevated cholesterol)
and those that died of CHD fall into the diseased category. Thus,
the numbers in the contingency table would be as follows:
|
CHD
|
No CHD
|
|
Elevated Cholesterol
|
2
|
998
|
1000
|
Normal Cholesterol
|
1
|
999
|
1000
|
RR = 2/1000
divided by 1/1000 = 2
Since a relative
risk of 1.0 indicates that the incidence rates of disease are identical
in the exposed and unexposed groups, the RR value is typically subtracted
from 1.0 and reported as a percent increased or decreased risk. In
the above example, a cholesterol level of 240 mg/dL may be said to carry
a 100% greater risk of death due to CHD than a cholesterol level of 180
mg/dL. In fact, the absolute increased risk is 0.1%. By using
relative risk, the difference is exaggerated 1,000 fold in this example.
What would
happen to the RR value if the denominators in the exposed and unexposed
groups were different? Let’s change the total number of subjects
in the exposed group to 500 in the example above. The RR value is
now calculated to be 4.0 or a 300% increase in relative risk, whereas the
increase in absolute risk is 0.3%. Interestingly, if the number of
subjects in the unexposed group is changed to 500, the RR value becomes
1.0 or 0% and the absolute risk is also 0%. Clearly, the denominator
is a crucial part of the equation.
Relative risk
appears to be a mechanism used to exaggerate differences between two groups.
Obviously, a 100% increased risk is far more startling than a 0.1% increase
in risk. It is not difficult to see how the public can be frightened
into avoiding certain behaviors because of the “strong” association with
disease, when in fact the association is either weak or nonexistent.
Nor is it difficult to understand how the average citizen may make the
jump to causation. After all, 100% is 100%. Doesn’t that mean
that if I am exposed to the risk factor, I will definitely get the disease
(i.e., the risk factor causes the disease)? This is problematic for
several reasons. First of all, making a weak or nonexistent association
appear strong is fraudulent. Secondly, it may lead to inappropriate
and costly public policy (e.g., reduce the risk factor to reduce the disease
when in fact the association between the risk factor and disease is insignificant).
It could also lead to changes in public behavior that carry other adverse
consequences (e.g., long-term administration of drugs that produce harmful
side effects). Additionally, it may have dire consequences for one
or more economic sectors (e.g., the dairy industry) while simultaneously
benefiting another sector (e.g., pharmaceuticals). Perhaps the most
problematic outcome is the potential loss of confidence in the scientific
community by the general public. If the purported risk factor is
markedly reduced and incidence of the disease is unchanged, the public
will be less likely to believe (be fooled by) the next “significant” risk
factor proclaimed by the scientific community.
Science has
made great achievements in a relatively short period of time. While
there have been setbacks and progress has been slower than desirable in
some areas, confidence in science is still relatively high. Let’s
keep that confidence high. When the scientific community finds a
true cure for cancer and/or heart disease, proclaim it. In the meantime,
don’t try to make insignificant “risk” factors appear significant.
This only serves to cloud and confuse the issues. Stick with the
grudging, tedious work of science using valid statistical analyses to demonstrate
significance where significance truly exists. In this manner, science
will continue to march forward, and mysteries will continue to unfold.
References
1.
Hennekens CH, Buring JE, Epidemiology in Medicine. Little,
Brown and Company, Boston/Toronto, 1987.
2.
Pagano M, Gauvreau K, Principles of Biostatistics. Duxbury
Press, Belmont, CA. 1993
Copyright
©1997-2007
American Society of Exercise Physiologists All Rights
Reserved.