I was at a meeting tonight and put in a plug for my book, Statistical
Evidence in Medical Trials, by mentioning that it was intended to help people
understand the controversies and the seemingly contradictory research that
appears in the medical journals. I went on to give an example: hormone
replacement therapy for post-menopausal women. It's a good example, because
half of the people in the audience have either had to or will have to make a
decision about whether they should take estrogen supplements. The other
example which I like to cite is whether men should consider taking a test to
look at their PSA levels to try to detect prostate cancer.
Anyway, a woman talked to me afterwards and wanted to know what I thought
about a particular author who had written about hormone replacement therapy.
I had to defer any comments because I was unfamiliar with this particular
author. She then informed me that she had taken hormone replacement therapy
and it gave her breast cancer. Thankfully, the cancer has responded well to
treatment, but I was struck by the certainty of her comment about how the
estrogen supplements caused her cancer.
The lack of uncertainty bothered me, and it highlights an important thing
to remember about research in general and Statistics in particular.
Statisticians describe the behavior of groups and often are unable to make
specific and precise statements about a particular individual. That is
perhaps a bit of an oversimplification, but this is a general concept worth
remembering. There is a great Sherlock Holmes quote that speaks to this
issue:
You can, for example, never foretell what any one man will do, but you
can say with precision what an average number will be up to. Sir Arthur
Conan Doyle The Sign of Four (1890), as quoted at
www.ewartshaw.co.uk/data/jehsquot.pdf.
What does the research about hormone replacement therapy say? Here's the
abstract from the 2002 JAMA study that is considered by many to be the
definitive result:
CONTEXT: Despite decades of accumulated observational evidence, the
balance of risks and benefits for hormone use in healthy postmenopausal
women remains uncertain. OBJECTIVE: To assess the major health benefits and
risks of the most commonly used combined hormone preparation in the United
States. DESIGN: Estrogen plus progestin component of the Women's Health
Initiative, a randomized controlled primary prevention trial (planned
duration, 8.5 years) in which 16608 postmenopausal women aged 50-79 years
with an intact uterus at baseline were recruited by 40 US clinical centers
in 1993-1998. INTERVENTIONS: Participants received conjugated equine
estrogens, 0.625 mg/d, plus medroxyprogesterone acetate, 2.5 mg/d, in 1
tablet (n = 8506) or placebo (n = 8102). MAIN OUTCOMES MEASURES: The
primary outcome was coronary heart disease (CHD) (nonfatal myocardial
infarction and CHD death), with invasive breast cancer as the primary
adverse outcome. A global index summarizing the balance of risks and
benefits included the 2 primary outcomes plus stroke, pulmonary embolism
(PE), endometrial cancer, colorectal cancer, hip fracture, and death due to
other causes. RESULTS: On May 31, 2002, after a mean of 5.2 years of
follow-up, the data and safety monitoring board recommended stopping the
trial of estrogen plus progestin vs placebo because the test statistic for
invasive breast cancer exceeded the stopping boundary for this adverse
effect and the global index statistic supported risks exceeding benefits.
This report includes data on the major clinical outcomes through April 30,
2002. Estimated hazard ratios (HRs) (nominal 95% confidence intervals [CIs])
were as follows: CHD, 1.29 (1.02-1.63) with 286 cases; breast cancer, 1.26
(1.00-1.59) with 290 cases; stroke, 1.41 (1.07-1.85) with 212 cases; PE,
2.13 (1.39-3.25) with 101 cases; colorectal cancer, 0.63 (0.43-0.92) with
112 cases; endometrial cancer, 0.83 (0.47-1.47) with 47 cases; hip
fracture, 0.66 (0.45-0.98) with 106 cases; and death due to other causes,
0.92 (0.74-1.14) with 331 cases. Corresponding HRs (nominal 95% CIs) for
composite outcomes were 1.22 (1.09-1.36) for total cardiovascular disease
(arterial and venous disease), 1.03 (0.90-1.17) for total cancer, 0.76
(0.69-0.85) for combined fractures, 0.98 (0.82-1.18) for total mortality,
and 1.15 (1.03-1.28) for the global index. Absolute excess risks per 10 000
person-years attributable to estrogen plus progestin were 7 more CHD
events, 8 more strokes, 8 more PEs, and 8 more invasive breast cancers,
while absolute risk reductions per 10 000 person-years were 6 fewer
colorectal cancers and 5 fewer hip fractures. The absolute excess risk of
events included in the global index was 19 per 10 000 person-years.
CONCLUSIONS: Overall health risks exceeded benefits from use of combined
estrogen plus progestin for an average 5.2-year follow-up among healthy
postmenopausal US women. All-cause mortality was not affected during the
trial. The risk-benefit profile found in this trial is not consistent with
the requirements for a viable intervention for primary prevention of
chronic diseases, and the results indicate that this regimen should not be
initiated or continued for primary prevention of CHD. Risks and
benefits of estrogen plus progestin in healthy postmenopausal women:
principal results from the Women's Health Initiative randomized controlled
trial. JE Rossouw et al. Jama 2002: 288(3); 321-33.
[Medline]
[Abstract]
[Full text]
[PDF]
This research did not show that if you take estrogen supplements, you will
get breast cancer. If you read the full article, you will find that of the
8,506 women on hormone replacement therapy, 166 developed invasive breast
cancer. Of the 8,102 women who took placebo, 124 developed invasive breast
cancer. So for the vast majority of women, nothing happened, even after five
years of follow-up on average.
Among the women where something bad happened, it happened more often in the
active treatment group. Now you can't just take the ratio of 166 / 8506 or
124 / 8102 to get a risk of breast cancer, since the women were followed for
a variable amount of time, but the more complex statistics tell pretty much
the same story.
There are multiple outcomes in this study and when you look at the big
picture, you find out that for the average woman, the probability of all the
beneficial effects was more than offset by the probability of all the
detrimental effects. But in all honestly, the average woman in the study did
not have anything bad happen to her, so the average women is healthy with or
without hormone supplements.
If a smoker who dies at age 50 from lung cancer can say that smoking caused
his/her early death, then can the rare smoker who lives to age 90 claim that
smoking was responsible for that longevity?
Suppose in a randomized trial, the first nine patients to get Drug A died
and the last one survived. Among those who got Drug B, the first nine
patients lived, and the last one died. It sounds like Drug B is a lot better,
but if you were the last patient recruited to the study, you were better off
with Drug A. In other words, you're probably better off with Drug B, but we
can't guarantee that everyone who takes Drug B will have a better outcome
than if they took Drug A.
It is human nature, perhaps, but anytime a tragedy befalls us, we have a
strong need to find an absolute cause or an explanation. But in the world of
statistics there is no absolute cause, only odds and probabilities. It is a
cold comfort, perhaps, to speak about chances and tendencies, but it is also
more intellectually honest. There's a t-shirt that they sell every year at
the Joint Statistics Meetings that proclaims in bold letters on the front
"Being a statistician means never having to say you're certain."
By the way, the website where I found the Arthur Conan Doyle quote from is
a treasure trove of good quotes. Here is another one:
Bayesian statistics is difficult in the sense that thinking is
difficult. Donald A. Berry Teaching Elementary Bayesian Statistics with
Real Applications in Science, American Statistician 51:241'246 (1997), as
quoted at
www.ewartshaw.co.uk/data/jehsquot.pdf.
07/08/2008.
