Scrutinizing the evidence for breast
cancer procedures and treatments
    Lying with statistics: How conventional
    medicine confuses the public with absolute
    risk vs. relative risk

    Which drug would you rather take? One that reduces your risk
    of cancer by 50 percent, or another drug that only eliminates
    cancer in one out of 100 people? Most people would choose
    the drug that reduces their risk of cancer by 50 percent, but
    the fact is, both of these numbers refer to the same drug.
    They’re just two different ways of looking at the same statistic.
    One way is called relative risk; the other way is absolute risk.

    Here's how it works: Let’s say that in a trial involving 100
    people, two people would normally get breast cancer during
    the trial duration, but when all 100 people are put on the drug,
    only one person gets breast cancer, meaning the reduction of
    breast cancer is one person out of 100. Yet the
    pharmaceutical industry will exclaim that the relative risk
    reduction is 50 percent because one is 50 percent of two. In
    other words, the risk is cut in half from a relative point of view.

    The headlines promoting this drug, therefore, will always talk
    about the relative risk -- "A whopping 50 percent reduction in
    risk!" -- and these headlines will be parroted by the
    mainstream press, medical journals, the FDA, doctors and
    drug marketing reps who are always pushing and
    exaggerating the supposed benefits of their drugs while
    minimizing their risks. Because, you see, even though this
    drug may help one out of 100 people, its side effects create
    increased risks to all 100 people. Everyone suffers some
    harm from the potential side effects of the drug, even if that
    harm is not immediately evident. Yet only one out of 100
    people was actually helped by the drug.

    When you look at drug claims, especially new miracle-
    sounding claims on drugs like Herceptin, be aware that these
    statistics are routinely given as relative statistics, not
    absolute. The numbers are distorted to make the drugs look
    more effective than they really are. Herceptin, for example,
    produced only a 0.6% absolute reduction in breast cancer risk,
    yet the medical hucksters pushing this drug are wildly
    screaming about it being a "breast cancer cure!" and
    demanding that practically all breast cancer patients be
    immediately put on it. Yet it's not even effective on one
    person out of a hundred. See my Herceptin Hype article for
    more details.

    Reverse the perspective for natural treatments

    At the same time, when conventional medicine promoters
    want to discredit a natural substance, an herbal remedy or the
    effects of nutrition on health, they always talk about absolute
    risk. If taking green tea supplements reduce the risk of
    cancer by that same 50 percent, eliminating cancer in one out
    of 100 patients, the news about that supplement would be
    something like this: "Green tea doesn’t work. Only helps one
    out of 100 patients."
    In fact, a study comparing some anti-cancer drug with green
    tea might report: "New breakthrough drug reduces cancer
    risk by 50 percent! Green tea only helps one out of 100."

    It’s the old joke about an Olympic race between the United
    States and the old Soviet Union. In the race, there were only
    two participants. The Soviet runner came in first, the U.S.
    runner came in second, but the U.S. newspapers reported, "U.
    S. Wins Silver Medal, Soviet Union Comes In Next to Last."

    Now you know how drug companies, the FDA, the popular
    press and many doctors lie with this numerical shell game. It's
    a clever way to promote the minuscule benefits of
    pharmaceuticals while discrediting the enormous healing
    effects of natural remedies.

    Now, do you want to hear some real statistics on cancer? I’ll
    share a few. Out of every 100 women who might get breast
    cancer, 50 of them can avoid breast cancer by simply getting
    adequate levels of vitamin D in their body, and that’s available
    free of charge through sensible exposure to natural sunlight,
    which produces vitamin D. This vitamin, all by itself, reduces
    relative cancer risk by 50 percent, which is better than any
    prescription drug that has ever been invented by any drug
    company in the world.

    Combine that with green tea, and your prevention of breast
    cancer gets even stronger. Even the World Health
    Organization says that 70 percent of all cancers are
    preventable, and in my view, that number is conservative,
    because if you combine sunlight therapy and green tea with
    anti-cancer herbs, anti-cancer foods such as garlic, onions,
    raw broccoli and raw sprouts, plus some rain forest herbs that
    are well-known for inhibiting the growth of cancer cells, then
    you can boost your cancer prevention success to well over 90

    There’s nothing in the world of pharmaceutical medicine that
    even comes close. Yet the only thing you’ll ever hear from
    the drug company-controlled mainstream media, medical
    journals, the FDA and most old-school doctors is that natural
    remedies are useless, but prescription drugs have all been
    scientifically proven. Sure they have, if you fall for the relative
    risk gimmick and can't do basic math.
Journal of Clinical Oncology, Vol 21, Issue 23 (December),
2003: 4263-4264
© 2003 American Society for Clinical Oncology


Is Relative Risk Reduction a Useful Measure for
Patients or Families Who Must Choose a Method of

H. Sam Wieand
University of Pittsburgh Cancer Institute Biostatistics Facility,
Pittsburgh, PA

IN THIS issue of the Journal of Clinical Oncology, Chao et al
report the results of a study that examined the impact of
using four different risk/benefit measures when
communicating survival benefits to individuals charged
with deciding whether to recommend chemotherapy for
their mothers. The four measures defined by the authors
were relative risk reduction, absolute risk reduction,
absolute survival benefit, and number needed to treat.
Two hundred four individuals (51 per measure) were
randomly assigned to make a decision after being given
survival information using one of the measures, then were
allowed to make a new decision after receiving the value
of all four measures.

The principal findings were that individuals who received
only the relative risk reduction information were
significantly more likely to endorse chemotherapy, were
the least confident in their decision, and were highly likely
to change their decision when presented with the other
three measures of risk/benefit. In fact, the percentage of
individuals who recommended chemotherapy when
presented with only relative risk reduction for a small
tumor was 51.0%, but this figure decreased to 39.2% when
the individuals were presented with all the information. For
a larger tumor, 70.6% of the individuals recommended
chemotherapy when presented with relative risk
information, but the figure decreased to 45.1% when the
individuals were provided with complete data.

Decisions based on any of the three other methods of
communicating risk did not change nearly as frequently as
the decision based on relative risk reduction when all four
measures were subsequently presented. The authors
concluded that absolute survival benefit was the best

A potential weakness of the study (noted by the authors)
was that, for practical reasons, the individuals used in this
study were medical students, who almost certainly would
understand these measures better than many of the
individuals who have to make these difficult decisions in
real life. However, this fact only heightens the point that
even bright, medically oriented people were
uncomfortable using relative risk, a common measure in
medical research, to make a treatment decision for a
relative. Three examples presented below help illustrate
the difference between the four measures and provide
some insight into why the relative risk reduction might be a
poor measure to use alone when making an individual
treatment decision.

Table 1 lists the survival information used in the first
scenario presented to individuals in the Chao et al. study.
The assumption is that historical data show a particular
type of breast cancer patient has an 85% chance of
surviving at least 10 years without chemotherapy and an
87% chance with chemotherapy. We can obtain several
measures of risk/benefit from the table. For example, from
the first column of data, we see that the 10-year survival
rate increases by 2% (from 85% to 87%); in other words, the
absolute survival benefit (at 10 years) is 2%. Conversely,
the risk of dying within 10 years is 15% without
chemotherapy and 13% with chemotherapy (second column
of the table), so the absolute survival decrement is 2%. The
authors refer to this as the absolute risk reduction.

Table 1. A Summary of Survival Risks From a Chao et al1
No. of Patients (N = 100)

    Expected to Survive Expected to Die

    Without chemotherapy 85 15
    With chemotherapy 87 13
    (2% absolute increase) (2% absolute decrease)


NOTE. Relative risk of death = 13/15. Therapy reduces
relative risk by 2/15. If 50 patients receive therapy, one
more will survive than with no therapy. Absolute survival
benefit = 2%; absolute risk reduction = 2%; relative risk
reduction = 13.3% (2/15); number needed to treat = 50.  

Table 1. A Summary of Survival Risks From a Chao et al.
One could also summarize the right column of the table in
the following way. If a person has a 15% chance of dying
within 10 years without chemotherapy and a 13% chance of
dying within 10 years with chemotherapy, the relative risk
of death for a patient receiving chemotherapy (relative to
the patient not receiving chemotherapy) is 13 divided by 15
(86.7%). Hence the relative risk reduction is 13.3%. The final
measure, number needed to treat, stands for the number
of patients who would need to be treated before
chemotherapy would result in one more survivor. Because
the increase in survival is 2% (two divided by 100), 50
patients would need to be treated to result in an increase
of one survivor.

The contrast between relative risk reduction and the other
measures is particularly striking if one considers Tables 2
and 3. If, as in Table 2, one has a 98% probability of
surviving 10 years without chemotherapy and a 99% chance
with chemotherapy, the absolute survival benefit is 1%,
whereas the relative risk reduction is 50%. It is unlikely that
many patients would opt for chemotherapy for the 1%
absolute survival benefit, despite the 50% reduction in
relative risk.

On the other hand, if, as in Table 3, a person had a 50%
chance of surviving 10 years without chemotherapy, and a
75% chance with chemotherapy (still a relative risk
reduction for death of 50%), it seems likely that most
patients would opt for the chemotherapy. The fact that the
relative risk reduction is 50% in both cases is less
important for decision making than the 25% absolute
survival benefit (Table 3) versus 1% (Table 2). The work of
Chao et al1 and the above tables indicate that the survival
percentages (85% and 87% for the first example) and the
percentage absolute benefit (2%) are of considerably more
value to a patient than the relative risk reduction.

Table 2. A Summary of Survival Risks for a Low-Risk Patient
No. of Patients (N = 100)


    Expected to Survive Expected to Die:
    Without chemotherapy 98 2
    With chemotherapy 99 1
    (1% absolute increase) (1% absolute decrease)

NOTE. Relative risk of death = 1/2. Therapy reduces relative
risk by 1/2. If 100 patients receive therapy, one more will
survive than with no therapy. Absolute survival benefit =
1%; absolute risk reduction = 1%; relative risk reduction =
50% (1/2); number needed to treat = 100.  

Table 3. A Summary of Survival Risks for a High-Risk Patient
I do not mean to imply that relative risk reduction has no
importance; in fact, relative risk reduction can be a useful
concept for a physician when determining absolute risk.
For a particular disease and treatment, the relative risk
reduction is often invariant across subsets of patients; in
other words, treatment will have the same relative risk
reduction in men and women, patients with stage I, II, and
III disease, and so on. This is expected unless there is an
obvious potential interaction, such as when a hormonal
therapy is used in pre- and postmenopausal women. To
see how this invariance property can be used to assist in
determining the absolute survival benefit for a patient,
suppose a clinical trial comparing a new therapy with no
treatment reports a relative risk reduction of 25% for 5-year
survival, but the report does not provide data for specific
stages. If a physician at an institution has a stage II patient
who presents with the disease, the trial results are
insufficient to provide the patient with an absolute survival
benefit. However, if historical data show 4% of untreated
stage II patients at the institution die within 5 years, the 4%
rate can be multiplied by the 25% relative risk reduction to
conclude that the treatment should result in reducing the
4% failure rate to 3%. This translates into an absolute
survival benefit of 1%. If historical data had indicated that
the 5-year survival rate for untreated stage II patients was
80%, the 25% relative risk reduction associated with
treatment would be expected to reduce the 5-year death
rate from 20% to 15%. The absolute survival benefit would
be 5%.

Table 3. A Summary of Survival Risks for a High-Risk Patient
No. of Patients (N = 100)

    Expected to Survive Expected to Die:  
    Without chemotherapy 50 50
    With chemotherapy 75 25
    (25% absolute increase) (25% absolute decrease)


NOTE. Relative risk of death = 25/50. Therapy reduces
relative risk by 25/50. If four patients receive therapy, one
more will survive than with no therapy. Absolute survival
benefit = 25%; absolute risk reduction = 25%; relative risk
reduction = 50% (25/50); number needed to treat = 4.  

In summary, relative risk reduction is known to be a useful
tool for researchers and can be of value to a physician
when determining absolute risk reduction. However, it
does not seem to be a useful measure for patients or
families who must choose a method of treatment. Absolute
survival benefit seems to be a much more useful measure
in that setting.

The author indicated no potential conflicts of interest.


1. Chao C, Studts JL, Abell T, et al: Adjuvant chemotherapy for breastcancer: How
presentation risk influences decision making. J Clin Oncol 21: 4299–4305, 2003
Two Explanations of Relative Risk
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