!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
CHANCE News 9.07
June 7, 2000 to July 2, 2000
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Prepared by J. Laurie Snell, Bill
Peterson and Charles Grinstead,
with help from Fuxing Hou and
Joan Snell.
Please send comments and
suggestions for articles to
jlsnell@dartmouth.edu.
Back issues of Chance News and
other materials for teaching a
Chance course are available from
the Chance web site:
Chance News is distributed under
the GNU General Public License
(so-called 'copyleft'). See the
end of the newsletter for
details.
Chance News is best read with
Courier 12pt font and 6.5" margin.
===========================================================
He uses statistics like a drunken man uses a
lamp post, more for support than illumination.
Andrew Lang
===========================================================
Contents of Chance News 9.07
1. Forsooth!
2. Its http://exploringdata.cqu.edu.au
3. Why are men killed by lightning more often
than women?
4. How many coughs can we expect in a concert?
5. Two other monthly chance news sources.
6. Do doctor's free lunches affect their choice
of drugs?
7. Alcohol may reduce Alzheimer's risk.
8. Study finds courts void most execution sentences.
9. Dr.
Laks reads the New York Times.
10. As the rich get richer do the poor get poorer?
Note: If you would like to have a
CD-ROM of the Chance Lectures
that are available on the Chance
web site, send a request to
jlsnell@dartmouth.edu with the
address where it should be sent.
There is no charge. If you have
requested this CD-ROM and it has
not come, please write us again.
<<<========<<
>>>>>==============>
May 2000 Vol 27 #9 RSS News:
People living around the town centre [Luton] are at
the bottom of the poverty-induced ill-health pile,
statistics released on Friday, reveal, with some
residents nearly 25 per cent more likely to die
than the national average.
Luton on Sunday
29 November 1998
Women who use HRT for long periods are slightly more
at risk of breast cancer but they do not seem to die
more often from the disease.
The Times
Temperatures of around nine centigrade, at a time of the
year when nearly double that is normal, also added to the
problems of the organizers [of a tennis competition].
BBC Ceefax p335
7 March 2000
DISCUSSION QUESTIONS:
(1) Why can't we find our own
Forsooth items?
(2) Why is the last item a
forsooth item? Do you think
it deserves a forsooth!?
<<<========<<
>>>>>==============>
In Chance
News 9.06 we mentioned Rex Boggs' interesting web site
to assist teachers of the basic
statistics courses but did not
give the URL in the e-mail version
of Chance News 9.06. Here it is:
http://exploringdata.cqu.edu.au
<<<========<<
>>>>>==============>
In Chance
News 9.05 we discussed an ABC report that stated that
84% of those killed by lightning
are men. In a discussion
question we asked why women are
so much better off? We have
received four suggestions:
(1) Men are taller
(2) Golf
(3) Men seem to enjoy risking their lives more than women do.
(4) Men tend to work outside more often.
(1) The last explanation was
suggested by Tom Kotsos who helps
Dr. Mary Cooper maintain a lightning
web site.
At this web site, under
"Lightning Injury Facts" you can learn
which of the many claims about
lightning are myths and which are
facts. Under Epidemiology (a.
Gender) you will find that the
claim that about 84% of the
deaths are males has been documented
by studies in several different
countries.
DISCUSSION QUESTION:
We have ordered
a lightning data set, available from the
National
Climate Data Center.
information about lightning injuries
and deaths since 1959. This
includes gender and location. The
location categories are:
(1) Under trees
(2) In or near water, boating
(3) Golfing
(4) Under trees on golf course
(5) Farming, construction or near
heavy equipment
(6) Out in the open: fields,
playgrounds, ballparks, yard, street
(7) Telephone related
(8) Other electronics related:
radio, TV
(9) Various other or unknown
Do you think the number in each
category will be more or less in
the order of the categories?
After looking at the deaths by
location and gender, will we know
anything more about why more men
are killed than women?
<<<========<<
>>>>>==============>
In The Observer
(28 May, 2000, Pg. 7) Fiona Maddocks reviewed a
concert in the Royal Festival
Hall, London, in which pianist
Andras Schiff played Bach's
Well-Termpered Clavier (Book II). In
her review Maddocks wrote:
Probability Theory no doubt could give a better
equation, but even common sense tells us that if
an (optimistic) five per cent of the audience has
a cold and each of them coughs randomly three times
in a long evening
with precious few opportunities to
clear the tubes, we'll be running at two coughs a
minute. Mr Schiff ought to cancel any February
engagements.
DISCUSSION QUESTION:
Could probability theory do
better than common sense?
<<<========<<
>>>>>==============>
In the June
1 issue of John Paulos' ABCNEWS.com column "Whose
Counting" Paulos, discusses
the Parrando paradox: two simple coin
tossing games each of which is
unfavorable but if, for a
sequence of plays, you randomly
choose one of the two games to
play you have a favorable game.
(See Chance
News 9.01 and 9.02).
In his July
1 column, Math Vs. Miracles, Paulos uses the recent
news about miracles, such as
those relating to Mother Drexel and
Fatima, to ask what are miracles
and how are they related to
science?
Paulos provides his usual
insightful discussion of both of these
topics. To find the June column
go to:
Also remember that Vital
Stats is a
discusses chance news (See Chance
discusses a number of interesting
our own choices. This make us
wonder
we both miss.
<<<========<<
>>>>>==============>
Joan Garfield
suggested the next item.
Inside the happiness business.
New York, 15 May, 2000
David D. Kirkpatrick
Dr. Robert Goodman
www.nofreelunch.org
The
pharmaceutical industry -- to whom is it accountable?
New England Journal of Medicine,
22 June, 2000, 342(25), p. 1902
Editorial by Marcia Angell (Can
be read on No free lunch site)
The New York magazine article is
a popular account of how drug
companies try to educate doctors
about the merits of their
products. It contains a case study of a particular
drug Celexa
launched in 1998 to compete with
well known anti-depressants
Prozac, Zoloft, and Paxil. Kirkpatrick states that Celexa is the
only one whose market share is
increasing (it now has more than
13% of the $6.3 billion
market). According to the article:
The reason for Celexa's stunning success is not science
but marketing. Drug-industry consultants Scott-Levin
say U.S. pharmaceutical companies spent about $10 billion
last year on drug promotions.
Most of that--$9 billion --
went toward marketing to doctors (about $12,000 for each
doctor in the U.S.). Drug makers command an army of more
than 68,000 sales people, one for every eleven doctors in
the U.S.
The rest of the article explains
in more detail how this army of
sales people try to influence the
choice of doctors. This
includes wining and dining at the
fanciest restaurants, free pens,
coffee mugs, stethoscopes,
textbooks for medical students, and
samples of their drugs. Also drug companies sponsor seminars on
topics relating to their drugs,
invite doctors to serve on
advisory boards for new drugs,
and support their research.
Of course, all this is just
free-enterprise at work. The real
question is, are the doctors
unduly influenced by the perks they
get in prescribing medicine for
their patients. Dr. Goodman is
one doctor who feels the answer
is a resounding YES! He has
established the "no
free lunch" web site
fellow doctors not to accept free
lunches.
that doctors are unduly influenced
in his
presentation" that you will
find at the bottom
We recommend that you view this
presentation.
know what a formulary is.
Here is how The
Formulary
defines formulary.
A formulary is a list of prescription drugs that a health
plan has approved for use by doctors. Health plans that have
formularies develop their own unique list of "approved
drugs." Formularies may change at any time.
Health plans may only pay for medications that are on this
"approved" list, unless your doctor goes through the
health
plans Prior Authorization process.
Goodman refers to his slide
presentation to a study "Physicians'
behavior and their interactions
with drug companies" by Cren and
Landefeld, JAMA, 271(9), 2 March
1994, pp 684-689.
In this study the researchers
compared two groups of physicians at
the University Hospitals of
Cleveland: one was the 40 physicians
who, in a one year period, had
requested that drugs be added to a
hospital formulary and the other
a group of 80 chosen randomly
from a group of 330 who had not
made such requests. From the slide
show we learn that:
Physicians who had requested formulary changes were
more likely to have accepted money from drug companies
to attend or speak at symposia (OR=5.1, 95% CI, 2-13.2)
Physicians were more likely to have requested additions
of drugs made by companies with whose reps they had met
(OR = 4.9, 95% CLI, 3.2-7.4)
Another study "The effects
of pharmaceutical firm enticements on
physician prescribing
patterns" by Orlowski and Chest, JAMA, July
1992,102(1) 270-273, showed that
all-expense paid trips to
luxurious resorts changed
physicians' patterns for prescribing
drugs even though they believed
these trips had no effect.
The pharmaceutical industry has
also come under attack for the
high price of their drugs and
their inability to provide
affordable drugs for developing
countries. The companies claim
that they have to spend years
developing a new drug, it is a risky
business, and their sole
responsibility is to their shareholders.
In an editorial, outgoing editor-in-chief of the New England
Journal of Medicine, Marcie
Angell, challenges these explanations.
Angell points out that in many cases the risk is removed by the
fact that the government pays for
the early research which
determines the drugs viability.
She comments that the fact that
over the past ten years the
pharmaceutical industry has been by
far the most profitable industry
in the United Sates does not
suggest that it is a risky
business.
DISCUSSION QUESTIONS:
(1) Of course there is a positive
side to the interaction of the
doctors with the reps: it is
important to learn about new drugs,
the samples can be given to poor
patients who cannot afford the
drugs etc. Do you think these
compensate for the possible bias
they introduce?
(2) What do you think would happen to a judge who accepted fancy
dinners from representatives of a
company involved in a case
before the judge?
<<<========<<
>>>>>==============>
The next topic
was suggested by Tom Falcone.
Drinkers can raise a toast to new
study. Alcohol may reduce
Alzheimer's risk, but
moderation's the key.
Chicago Tribune, 11 June, 2000,
Sec. 1 p. 1
Ronald Kotulak
Effects of smoking, alcohol and
APOE genotype on Alzheimer's
disease.
Alzheimer's Reports, Vol. 3 Issue
2, 2000
Cupples, et. al.
Numerous studies have suggested
that moderate drinking can help
prevent heart attacks. See, for
example, Chance News 4.16.
The
Chicago Tribune discusses a
study, reported in the journal
Alzheimer's Reports, that
suggests that alcohol can also help
prevent Alzheimer's disease. The
study also considered the effect
of smoking since previous studies
have suggested that smoking
might prevent Alzheimer's
disease. This new study did not support
this.
The study was a case-control or
retrospective study. Such a study
is designed to see if some
previous behavior or characteristic is
a risk factor for or helps
prevent a disease. A case-control study
chooses a group that has the
disease (cases) and a group that does
not have it (controls) and
compares the proportion in each group
that has the behavior or
characteristic being studied.
The cases in this study were 238
Boston-area patients who had
Alzheimer's disease and the
controls were 699 people obtained by
attempting to match the 238 cases
with 3 subjects of the same
gender and age. The controls were chosen from the ongoing
Framingham Study. Subjects were
classified according to their
consumption of alcohol into three
groups: low, moderate, high.
Men who drank less than .25
drinks per day were classified as low,
more than .25 but at most 2 as
moderate, and more than 2 as high.
For women, less than .25 were
classified as low, .25 up to as much
as 1 as moderate, and more than 1
as high.
The Tribune article presented two
bar graphs that gave the
percentage of low, moderate, and
high persons in the case and in
the control groups. Knowing these
numbers and the totals in each
group provides the following
table.
cases
controls
low 116
(48.7) 257 (36.8)
moderate 87
(36.5) 282 (40.3)
high 35
(14.8) 160 (22.9)
total
238 699
Under the bar graphs, the
conclusions were stated as: moderate
drinkers were 60 percent as
likely to develop Alzheimer's disease
as non-drinkers and heavy drinkers
were 50 percent as likely to
develop Alzheimer's as
non-drinkers.
These conclusions are expressed
in terms of relative risk. For
example the 60 percent should be
the ratio of the number of
moderate drinkers in the
population whom we expect to get
Alzheimer's disease to the number
of low (considered non-drinkers
here) we expect to get
Alzheimer's disease. If we used the
information in the table we would
estimate that the chance that
a moderate drinker would get Alzheimer's is 87/(87+282) = .236
and for a non-drinker it is 116/(116+257)
= .311. This would give
a relative risk of .236/.311 = .758.
estimate for the
cases and controls were
they had used more controls
just because they had more controls!
we also, could not see where the
60 percent
relative risks came from. This
led to our
this mystery.
It turns out that epidemiology
does tell us how to estimate
relative rates from data from
case-control studies. Jerome
Cornfield was the first to tell
us how in his paper: "A method of
estimating comparative rates from
clinical data", Journal of the
National Cancer Society
11:1269,1951. We follow his approach in
our explanation of how this is
done.
Let X be the proportion of the
population that has Alzheimer's
disease during a specific period
of time. Assume that the
distribution of our three
categories of drinkers that we found in
the case-control study is
representative of this population. Then
we can summarize the relevant
data for the general population as
follows:
has Alzheimer's
does not have Alzheimer's
low .487X .368(1-X)
moderate .365X .403(1-X)
high .148X .229(1-X)
From this, we can find the proportion of the population in each
category of drinkers that has
Alzheimer's disease. These
proportions are:
Low
.487X/(.368 + .119X)
Middle .365X/(.403 + .038X)
High
.148X/(.229 + .009X)
Thus if we know X we can obtain
the desired relative risks for
those in each of the categories
of drinkers.
If we do not know X, but can
assume that Alzheimer's is a
relatively rare disease, so X is
small, we can approximate these
proportions by:
Low
.487X/.368 = 1.323X
Middle
.365X/.403 = .906X
High
.148X/.229 = .646X
Now the relative risk for Alzheimer's
disease, choosing low as our
reference, becomes is
Relative risk
Low
= 1
Middle =
.906/1.323 = .68
High =
.646/1.323 = .49
and is independent of X. Thus we end
up with approximations to the
relative risk that uses only
information obtained from our
original case-control study. The two assumptions that we used to
do this were that the disease is
relatively rare and that our case
control study gives us reasonable
information about the proportion
in each category of drinkers for
those who have the disease and
those who do not.
Thus we can estimate that
moderate drinkers in the population are
68% as likely to develop
Alzheimer's disease as non-drinkers and
heavy drinkers 49 percent as
likely as non-drinkers. This is
close to the conclusions given in
the Tribune but the percentages
are not quite the same. In fact
our percentages are called crude
estimates by the
researchers. The percentages 60 and 50
given in
the Tribune article are the
result of carrying out a more
sophisticated analysis which
controls for some of the possible
confounding factors and this
solves our mystery!
DISCUSSION QUESTIONS:
(1) Given that the study
suggested that heavy drinking gave the
best protection against
Alzheimer's disease, why do you think the
headline of the article included:
but moderation is the key?
(2) It is estimated that about 4
million people have Alzheimer's
disease so it is rare in the
population as a whole. However, this
increases to between one and two
people in 100 at age 65, and one
in five by age 80. How does this
affect our assumption that it is
a rare disease?
(3) The article quotes one expert as saying:
This is a good epidemiological study. But like
many epidemiological studies, it raises more
questions than it answers, and that's exactly
what epidemiological studies do. They raise
questions. They
don't give answers.
What questions do you think he
had in mind? Do you think the
authors would agree with this
assessment of epidemiological
studies? Do you?
<<<========<<
>>>>>=============>
Death penalty
overturned in most cases; Justice:
study finds
courts void execution more than
two-thirds of the time. Results
fuel debate over capital
punishment.
Los Angeles Times, 12 June 2000,
A1
Henry Weinstein
In 1972, the US Supreme Court
declared all existing death penalty
statutes unconstitutional, and
the prisoners then on death row
were spared execution. Since that time, 34 states have enacted
new death penalty laws. The results of all death-penalty cases
from 1973 to 1995 are reviewed in
a newly released study headed by
Columbia University law professor
James Liebman. During that
period, the death penalty was
imposed in 5760 cases. The study
examined all 4578 cases that have
gone through the full appeals
process, which includes direct
appeals of the trial record in
state court, and post-conviction
reviews at the state and federal
level. Overall within this group, 68% of the death sentences were
overturned. The full
report from the study is available from the web.
The researchers conclude that
American capital sentences are
"systematically fraught with
error that seriously undermines their
reliability." The principal errors identified involve
"egregiously
incompetent" defense or unethical prosecution. In
many cases, defense lawyers
failed to find and present relevant
evidence that might point to
innocence or at least mitigate the
sentence. (There are anecdotal stories of lawyers
showing up
drunk or sleeping at the trial.)
In other cases, police or
prosecutors were aware of
mitigating evidence but failed to
properly disclose it. When the cases were retried after the
reversals, 82% resulted in
sentences less than the death penalty,
and another 7% ended with the
defendant found not guilty.
Many observers find these results
troubling. Senator Patrick
Leahy of Vermont says "There
should be zero tolerance for
mistakes, not a 60%-70%
tolerance. You certainly could not run
a
public utility or an airline or a
hospital that way."
Death penalty advocates see
things differently. The L.A. Times
quotes University of Utah law
professor Paul Cassell as saying:
"You will find more
reversals of capital sentences...because they
are reviewed more closely. In some ways, this confirms that the
system is working as it
should." In a recent letter to the editor
(We're not executing the
innocent, The Wall Street Journal, 16
June 2000, A14), Cassell went
further, calling the 68% error rate
a "deceptive factoid,"
since the study did not find a single case
in which an innocent man was
executed. He further objects that
the study counts as errors those
cases for which the death
sentence was re-imposed at the
new trial. He writes:
Under such curious scorekeeping, the report can list 64
Florida post-conviction cases as involving "serious
errors", even though more than one-third of these cases
ultimately resulted in a re-imposed death sentence, and in
not one of the Florida cases did a court ultimately
overturn the murder conviction.
You can find the text
of this letter, along with other pro-death
penalty arguments also from the
web.
Study author James Liebman responded
to Cassell in his own letter
to the editor (Wrong by the
margin of a life, The Wall Street
Journal, 23 June 2000, A19). He writes:
Mr. Cassell says "more than a third" of cases retried
in Florida result in a new death sentence. The truth is
29%. In any case,
whether it's two-thirds or more than
70% of Florida's cases that were wrong by the margin of a
person's life, does he really believe that's "close
enough for government work?"
...Mr. Cassell thinks it's our job to produce an innocent
person executed by the state.
Our study, however, is
about what the courts say, not about the reliability of
American capital verdicts.
And over decades and in
dozens of states the courts have found nearly 7 in 10
such verdicts too flawed to carry out. If Amtrak's
trains repeatedly crashed, would we demand a dead body
before doing something about it?
The LA Times article gave further
testimony from Liebman that the
system is "broken and
wasteful." Over the period of the
study,
only 5% of condemned prisoners
have been executed, and their
average wait on death row during
the appeals process was 9 years.
Liebman sees this as evidence
that the system is choking on its
own high error rates. Virginia was the only state that carried
out more than 25% of its death
sentences. The state is known for
limiting the appeals process, and
its 19% reversal rate was the
lowest found in the study. Liebman attributes this to "low error
detection," while Cassell
sees Virginia as a model that should be
emulated by other states.
A perspective from overseas can
be found in the British journal
The Economist, which has recently
published three articles on the
death penalty:
America's death-penalty lottery, 10 June 2000, 15-16;
Dead man walking out, 10 June 2000, 21-23;
Murder one, 16 June 2000, 33.
The first two predate the release
of the Columbia study. The first
laments the "random quality
of capital punishment" in America.
Overall, the death penalty is
sought in less than 5% of potential
capital cases. However, it is not applied uniformly; for
example, Texas imposes it forty
times as often as New York. The
death penalty is sought more
often when defense appears weak,
which creates a disadvantage for
poor defendants.
In "Dead Man Walking
Out" The Economist notes that, while there
have been 640 executions in the
US since 1973, 87 prisoners have
been released in light of new
evidence. It finds the rate of one
release for every seven
executions troubling. Echoing earlier
comments by Senator Leahy and
Prof. Liebman, the article observes
that "if an airline crashed
once for every seven times it reached
its destination, it would surely
be suspended immediately."
Moreover, between 1973 and 1993
an average of 2.5 death row
prisoners a year were found
innocent, while from 1993 to 1999 the
rate was 4.6 a year. Noting that Texas has accounted for more
than a third of the 640
executions, the article questions Gov.
George W. Bush's confidence in
asserting that all those defendants
were guilty and had full access
to the courts. Indeed, last year
Bush vetoed legislation aimed at
reforming procedures for poor
defendants. The bill would have formed an independent
commission
to appoint public defenders and
required representation within 20
days.
The article also points out that
American public support for
capital punishment now appears to
be eroding. From an historical
high of 80% in favor in 1994, the
support had fallen to 66% in a
February Gallup poll. And only 52% favor the death penalty when
life-without-parole is given as
an option.
Dr. Frank Newport,
Editor-in-Chief of the Gallup Poll, discussed
the trends in a June 21 CNN spot
about the Gary Graham case in
Texas. You can view video the clip from the "Gallup on the
Air"
links on the Gallup
home page.
You can find the historical
record of Gallup's findings on the
death penalty also on the Gallup
web site.
In the most recent poll, 91% said
they believed that sometime in
the last 20 year an innocent
prisoner had been executed. And 65%
agreed with the statement that
"a poor person is more likely than
a person of average or above
average income to receive the death
penalty for the same crime."
The Economist notes that there
has never been conclusive proof
that the death penalty actually
deters murder. John Lamperti of
Dartmouth has written a
review of the relevant literature, which
you can find in the Teaching Aids
section of the Chance website.
Finally, the most recent
Economist article, "Murder One," reports
on the Columbia study, which it
welcomes as the "first real data"
in a debate that has been often
framed in ideological or emotional
terms. Summarizing the pervasiveness of errors, the article notes
that 85% of the states which have
the death penalty have error
rates exceeding 60%. Virginia is again identified as an outlier:
"For its size it executes
five times as many people as other
states and reverses only a
quarter the number of cases."
DISCUSSION QUESTIONS:
(1) The L.A. Times article reports that "...state courts
initially overturned 47% of the
death sentences, having found
serious legal flaws. Later
federal review discovered 'serious
error'...in 40% of the remaining
cases, resulting in an overall
68% reversal rate
nationwide." How was the overall
rate computed?
(2) The article later states that "since 1975, 87 inmates have
been freed from death rows across
the nation for reasons including
mistaken identification,
prosecutorial misconduct or newly
discovered exculpatory evidence,
including the results of DNA
tests that have led to eight
exonerations." How does this
relate
to the 7% figure cited for
defendants found not guilty at
retrials?
(3) Where does the "more than 70%" figure come from in
Liebman's
response to Cassell in the Wall
Street Journal? What does he mean
in his distinction between
"what the courts say" and "the
reliability of American capital
verdicts"?
(4) In "Dead Men Walking Out," The Economist found the
release
rate per year from death row
during 1993-1999 was almost twice the
rate observed during
1973-1993. Does it follow that innocent
defendants are now being
sentenced at a higher rate? What else do
you need to know?
(5) What do you think of the analogies that various commentators
have drawn with safety figures
for hospitals or travel?
(6) How could you try to determine if the death penalty is a
deterrent? (See Lamperti's
article)
<<<========<<
>>>>>==============>
Our next contribution
shows what can happen when a doctor reads
the New York Times. Doctor Mitchell Laks is a doctor-
mathematician having also a
Harvard PhD in mathematics. Mitchell
contributed to Chance
News 6.09 commenting on a baseball article
"The Kind of Sweep That's
Hard to Come By." He showed us
that
these sweeps might be hard to
come by but they could certainly
have come by chance.
Mitchell read an article in the
Times about a medical controversy
that led him to go back to the
sources to see what it was all
about. This caused him to question the validity of the studies
related to the controversy. He explained his concerns briefly in
a letter to the New England
Journal of Medicine:
Volume of Procedures at
Transplantation Centers and Mortality
after Liver Transplantation.
Letter to the editor, 18 May
2000,
Mitchell B. Laks
Such letters must, of necessity
be quite brief. We asked Mitchell
to tell us the whole story of how
he came to write the letter.
Here is his story:
Misunderstandings about the
Effects of Volume on Liver
Transplantation Mortality
Outcomes
The front page of the New York
Times of December 29, 1999 carried
an article "Iowa Turf War
Mirrors Battles on Transplants". It
highlighted the struggle of a
surgeon, Dr. Maureen Martin, to
establish a new liver
transplantation program at a community
hospital in Iowa. It detailed the
opposition that she encountered
from the transplantation group at
the University of Iowa as well
as from surgeons in nearby Nebraska
who felt threatened by the
potential diversion of the
limited supply of local organs from
their programs.
The New York Times article put
the story into the context of the
debate in Washington regarding
the Clinton administration's
proposed rules for the national
distribution of organs according
to "sickest-first"
criteria. The intended goal of the new rules is
a broad sharing of organs across
state lines. Currently organs are
allocated by geographic criteria.
The article reported that this
Clinton proposal is supported by
the country's seven largest
transplantation programs. On the other side of the issue is the
Patient Access to Transplantation
Coalition, a collection of
several dozen mostly midsize
hospitals like the University of Iowa
that have thrived under the
current local allocation system. Each
side is actively lobbying their
congressmen to support their
respective interests. At stake is
income as well as the ability of
hospitals to attract business by
projecting a cutting edge image
to their patients.
The small to mid sized
transplantation centers are thus being
squeezed on both sides. On the
low end they are threatened by
ambitious community hospitals
which seek to start new
transplantation programs by
hiring young newly trained transplant
surgeons. This threatens to erode
the supply of local organs for
transplants. On the high end they
are threatened by the large
volume centers like Pittsburgh,
and UCLA by virtue of the proposed
national "sickest
first" allocation rules. The large centers are
viewed as treating the sickest
patients.
A novel argument was raised by
Dr. Lawrence Hunsicker, director of
transplantation at the University
of Iowa in the debate over the
proposed opening of the new Iowa
transplant center. He is quoted
in the New York Times as saying,
"Medical research shows patients
fare best in centers that perform
at least 20 transplants per
year". He says that the
"number of transplants in Iowa is now
limited by the number of usable
donated organs, about 40 a year".
"So if we had two programs,
and we split evenly, then we would
both be at the very lowest end of
the numbers necessary to
maintain competence". Thus,
he argues, since 20 liver transplants
per year is the minimum for
competence, a second liver transplant
center should not be opened in
Iowa.
If one could establish that 20
transplants was the minimal volume
required for a transplantation
center to maintain competence this
would indeed provide a good
argument against the opening of new
centers, and add scientific
support to the goal of small to mid
sized transplant programs in
limiting the development of new
programs. On the other hand, the
argument does arouse one's
skepticism. After all, even the
largest transplantation centers
began initially with small
numbers. The argument is an attempt to
create a barrier to entry into
the field, and would require
rigorous proof.
The 12/30/1999 New England
Journal article by Edwards et al (1)
from Dr. Hunsicker's group
ostensibly is the basis for this
argument. Unfortunately, however,
both methodological errors and
possible errors of bias mar
significantly the data evaluation and
interpretation in both this paper
and a similar previous paper (2)
by the senior author on cardiac
transplantation.
At first glance, the study is a
typical 'volume outcome' study.
Such studies are done to evaluate
whether high volume centers do
better with procedures than low
volume centers. The take home
message from a significant volume
outcome study is that physicians
should refer their patients for
procedures at the highest volume
centers. Volume outcome studies
typically are structured to
compare centers with volumes in
the top and bottom quartiles for
volume or those in the top and
bottom 10%. For example, compare
two recent NEJM studies (3) and
(4) on coronary angioplasty
procedures and survival after
myocardial infarction respectively.
The recent editorial by Hannan
(5) is helpful in putting volume
outcome studies into perspective.
However the authors of both (1)
and (2) took a different,
nonstandard, approach. They
didn't compare the highest and lowest
volume transplantation centers.
Instead they picked a particular
number of transplants per year -
in this study 20 liver and in the
previous study 9 heart - and
compared the outcomes at centers with
annual volumes more and less than
this number. What criteria did
the authors use to pick 20 or 9
transplants as the dividing
points? These are not numbers
that one would be likely to select a
priori. For example, for liver
transplantation, in the years
discussed in Hunsicker's article
(92-93 essentially) there were
centers in the United States
doing as many as 300, 250, or 150
transplants per year. If one were
to pick a demarcation line a
priori, perhaps one would draw it
at 100 per year (2 times per
week) or 50 per year (1 time per
week) or perhaps even at 26 per
year (1 every 2 weeks). Why did
they choose this unusual boundary
between their two subsets?
Did the authors have any self
interest in their choices? The 1994
paper (2) on cardiac transplants
reviewed data for the years 1988-
1991. The number of cardiac
transplants done during those years at
the University of Iowa were
10,7,10, and 12 respectively, (while
the paper (2) chose 9 as the
dividing line). The paper (1) on
liver transplantation covered
essentially the years 1992 and 1993,
and the number of liver
transplants at the University of Iowa were
9 and 43 (for an average of 26
per year). So by drawing the line
where they did - the authors
include the University of Iowa, on
the successful side in both
instances. (All transplantation
statistics are as reported by the
United Network for Organ Sharing
(UNOS), and are quoted from their
web site www.unos.org).
The authors employed a
statistical methodology which usually
compares the smallest volume
centers and the largest and wrote
their papers to draw a line
between very small centers and all the
rest. They included their own
center on the better side. In
general, it may be correct or it
may be misleading to choose a
particular dividing point. The
question becomes - what criteria do
the authors use to divide the
centers with poor outcome from those
with better outcome?
For example, the choice the
authors made has the effect of linking
centers doing 11-20 transplants
with those doing 1-10. This
requires methodological
justification. Let us grant the
statistical result of the paper
(1), namely that for the years
that they studied there is worse
1 year outcome for centers doing
20 or less transplants. If all
the excess mortality resided in
transplant centers doing 1-10
transplants, then presenting the
results in this way would
incorrectly characterize those centers
doing 11-20 transplants. For
instance, the authors do not present
an analysis comparing centers
with 10 or less transplants with
those doing 11 or more. Nor do
they report a subgroup analysis
comparing those centers doing
1-10, 11-20 and 21-30 transplants.
The standard methodology of a
volume outcome study is not designed
to achieve the kind of
discrimination that the authors seek to
elicit from this data. It appears
that the authors are not doing a
standard volume outcome study. It
would appear that they are
trying to weed out
transplantation centers that are smaller in
volume than their own.
How do the authors explain their
choice of the numbers 20 and 9 in
their papers? In (1) the authors
justify their choice of 20
transplants per year by appealing
to their Figure 1. (In the
paper (2) they use their Figure
2). This figure is a scatter plot
of mortality rate versus
transplantation center volume. They state
that "mortality rates
stabilized at centers that performed more
than 20 transplantations per year
and increased inversely with
transplantation volumes of less
than 20 per year". Unfortunately,
the authors misinterpret their
figure. Such a scatter plot is
expected to show increased
scatter for a random phenomenon with
small sample sizes as we consider
smaller and smaller sample
sizes. This variability, per se,
is not a sign of poor performance
at low volume sites. There is not
increased mortality rates, there
is an increase in the variability
in the mortality rates, with
wider and wider variance in the
rates for smaller and smaller
transplantation volumes. There
are sites with mortality rates of
0% as well as of 100%. But this
is only to be expected in small
sample sizes! This is a
fundamental statistical error. Even if all
the transplant centers in the
country, regardless of size, had
equivalent intrinsic 1 year
mortality rates, (for the study (1)
approximately 20.7%) the observed
mortality rates at small sample
size centers would be expected to
show increased variability. The
authors miss the point that a
center with small volume can have a
high observed mortality rate
simply because they did very few
patients. For example a site with
a mortality rate of 100% for 1
transplantation (or 50% for only
4) might not be criticized for
their mortality rate per se -
while a site with a 30% mortality
that did 1000 transplants might
very well be. A baseball batter
with a lifetime.367 average might
strike out in one at bat without
being banished to the minor
leagues.
Moreover, we have performed Monte
Carlo simulations using those
individual cardiac and liver
transplant center volumes and
assuming equivalent intrinsic
mortality rates for all centers.
These simulations fully reproduced
the behavior observed by the
authors in their figures 1 and 2
respectively. You can see how
beautifully the simulation mimics the data in our simulation
The visible pattern of these
scatter plots of individual centers
is thus not directly related to
the integrated behavior observed
when the data on centers
performing small and larger volumes are
aggregated for volume outcome
analysis.
Thus, on mathematical grounds,
Figure 1 offers no support to the
authors in their choice of
demarcation point between
transplantation centers with good
and poor outcome statistics.
Moreover, even if one mistakenly
accepted their Figure 1 at face
value, their claim certainly
appears debatable. To our eye, for
instance, the graph appears to
"stabilize" (no statistical
definition of
"stabilize" is offered by authors) beyond 20,
perhaps at 30 transplants per
year, in order to include the sites
with mortality rates above 30 and
35 %. Of course, if the authors
had drawn the line of
discrimination at 30 transplants per year
that would have included the
University of Iowa center on the
short side. Their choice of 20 as
demarcation volume number was
thus arbitrary, without a
scientific basis, and possibly self
serving.
One final point. The authors of
(1) give the data for 1 year
survival, but make no mention of
the results for 3 month survival.
It is customary for volume
outcome studies to offer this short
term data as well (see (3),
(4),and (5)). Was this data not
offered because it didn't support
the author's thesis? We can't
find this data on the UNOS web
site for 1992-93.
We, the readers of (1), are thus
left with this message. During
the period 1992-1993, higher
volume liver transplantation centers
did better at 1 year survival
than did low volume centers. The
precise dividing point utilized
by the authors for demarcating
between the high and low volume
centers in (1) (or (2)) has no
scientific significance, (for
example the poorer 1 year outcomes
reported in (1) may in fact be
occurring in those centers with 10
or fewer annual liver transplants
but we cannot say). Therefore
physicians should refer their
patients to high volume centers.
Of interest to referring
physicians may be the data summarized in
Table 1. One can see that there
is quite a variation in the
numbers of transplantations
performed at different centers in the
US. For believers in volume
outcome studies, it is hard to imagine
referring a patient to a center
doing 20-40 transplants per year
(just over 1 every 2 weeks) when
there are 6 centers doing more
than 100 per year (2 a week), and
some as many as 250 per year.
Number of Active US Transplant
Centers by Volume Category
Liver
Cardiac
100 or more 6 1
75-100 5 2
50-74 14
1
40-49 12
5
30-39 13
12
20-39 18
15
10-19 17
50
0-9 20
51
0 10
18
One can dispute the significance
of volume outcome studies in
general. As Hannan (5) points
out, they only reflect average
behavior. Moreover, if the
statistics are tabulated by transplant
center and not by individual
surgeon and team, they may not be the
most appropriate volume indicator
- perhaps the volume done by the
individual transplant surgeon and
team is more important. It is
probably better to look directly
at outcome statistics for centers
and surgeons - thus transplant
center volume data may simply be an
easily obtainable, but possibly
flawed proxy for more significant
outcome information. Moreover,
perhaps not all consumers are
swayed by volume data. I might
prefer, for scientific reasons, to
refer a patient to a center doing
close to 200 transplants a year,
but some patients may prefer the
more personal service that they
may receive at a smaller center
closer to home.
The unscientific choice of a
particular volume number by the
authors of (1) and (2) should not
be allowed to create an
artificial barrier to the
development of new transplant centers.
It is a complex undertaking for a
medical center to develop a
transplantation team. Potential
transplant centers are subject to
stringent regulation, and
appropriately so. However, if a
potential center makes the
appropriate commitment and provides the
requisite resources of personnel
and funding, then, in time, it
may outstrip an older, more
established, center in outcome
measures. The older center may
lose its sense of mission over
time, its key personnel may
develop other primary interests and
retire from the field and the
center may fade in quality.
Unfortunately, business
considerations such as marketing may also
play a role in the growth of new
centers as well. However, in
medicine, as on Wall Street, Adam
Smith's proverbial invisible
hand can continue to play a
salutary role advancing the cause of
best outcomes as long as free
market conditions are permitted to
persist.
It is important to guarantee the
flow of accurate scientific
information. One responsibility
of the medical scientific
community is to serve an
equivalent role for medicine as the
Securities and Exchange
Commission serves for the securities
industry. We must work to insure
that there is full, truthful and
unbiased reporting of medical
outcomes so that the government can
exercise appropriate informed
regulatory oversight and so that
medical consumers can make the
most enlightened choices in the
medical marketplace.
1. Edwards EB, Roberts JP,
McBride MA, Schulak JA, Hunsicker LG.
The effect of the volume of
procedures at transplantation centers
on mortality after liver
transplantation. N Eng J Med
1999;341:2049-2053.
2. Hosepud JD, Breen TJ, Edwards
EB, Daily OP, Hunsicker LG. The
effect of the transplant center
volume on cardiac transplant
outcome: a report of the United
Network for Organ Sharing
Registry. JAMA 1994;271:1844-9.
3. Jollis JG, Peterson ED, DeLong
ER, et al. The relation between
the volume of coronary
angioplasty procedures at hospitals
treating Medicare beneficiaries
and short term mortality. N Eng J
Med 1994;331:1625-1629
4. Thiemann DR, Coresh J, Oetgen
WJ, Powe NR. The association
between hospital volume and
survival after acute myocardial
infarction in elderly patients. N
Eng J Med 1999;340:1640-1648
5. Hannan EL. The relation
between volume and outcome in health
care. N Eng J Med
1999;340:1677-79
<<<========<<
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Parade Magazine, 5 June, 2000
Marilyn vos Savant
A reader writes:
These statistics were included in an article titled
"The Rich Get Richer": "Family incomes for the
poorest 20%
of the population have lagged behind the gains made by
families in the top 20%.
In fact 60% of families have
seen their incomes fall in real terms in the past two
decades." Do you
see any flaws in these statistics?
J. J., Severn, Md.
Marilyn says:
There's plenty wrong with this kind of quintile analysis.
For example, an increase in the income of a household in
any of the lower four income quintiles may increase
averages in other quintiles more than its own quintile.
She then gives an example with
ten salaries which go from $10,000
to $100,000 in increments of
$10,000 and then presents a scenario
similar to this one: The $10,000 salary is for Paige, a
struggling actress in New York
working as a temp. Paige's current
off-Broadway play becomes a hit
and moves to Broadway resulting in
her income increasing to
$100,000. Marilyn then considers how this
changes the quintiles.
Before Paige After Paige is
is discovered discovered
100,000 110,000
90,000 100,000
80,000 90,000
70,000 80,000
60,000 70,000
50,000 60,000
40,000 50,000
30,000 40,000
20,000 30,000
10,000 20,000
Marylin comments:
So the highest-income quintile (and the others) can be
said to have benefited at the expense of the lowest
income quintile. Of course that's a gross misunderstanding
but it's reported routinely.
As you can see, her data does not
really show what she wanted it
to show. Paige's good luck has increased the average
income of
each of the quartiles by the same
amount, $10,000. If we assume
that Paige was such a star that
she got and additional $10,000
bonus, then the average income in
the top quintile does go up more
that the average of the bottom
quintile, or in fact any other
quintile.
Marilyn then remarks that if the
$100,000 was for a physician, who
happens to be an amateur painter
and the physician sells one of
his paintings for $100,000, the
average income of the top quintile
increases without any change in
the lower quintiles.
This topic has been in the news a
great deal recently because of
claims by the leaders of the
anti-World Trade Organization such as
Lori Wallach who stated:
While the macroeconomic indicators have often looked
good, real wages in many countries have declined, and
wage inequality has increased both within and between
countries.
A recent paper "Growth
is Good for the Poor", by David Dollar and
Aart Kraay of the World Bank,
appears to show that the data does
not support Wallach's claim.
Of particular interest to Wallach's
claim is Figure 1 in this
paper. Here we see two scatter plots.
The first is for the log
of the average income and the log
of the average income of the
poor (lowest quintile) for the
countries in the study. The
correlation is .93 and the
regression line has slope 1.07. The
second graph gives the scatter
plot for the average growth rate
over a period of at least five
years for the country as a whole
and the average growth rate for
the poor. Here the correlation is
.72 and the slope of the
regression line is 1.17. These plots
suggest that the income for the
poor does follow that of the
country as a whole.
DISCUSSION QUESTIONS:
(1) What problems do you see with examples of the type that
Marylin uses?
(2) Dollar and Kraay say "We measure mean income as real per
capita GDP at purchasing power
parity in 1985 international
dollars." What does all this mean and why do you
think they
measure income this way?
(3) What do the results in Figure 1 of the Dollar-Kraay paper
tell you about how the poor do
when the economy of a country
changes? What does the fact that
the slopes are nearly 1 tell you?
(4) Dollar and Kraay only consider average incomes. What more
might you want to know to decide
if, as the rich get riche, the
poor really get richer?
<<<========<<
>>>>>=============>
Note: This item was meant for the last Chance News but got left
out by mistake.
Behind-the-seams look;
Rawlings throws open baseball
plant doors.
USA Today, 24 May, 2000, 1C
Gary Mihoces
Researchers Say Core Has Changed.
USA Today, 26 May, 2000, 8C
Hal Bodley
Dan Shaughnessy; Will Juiced Ball
Yield Fruit?
Boston Globe, 11 May, 2000, E1
Dan Shaughnessy
It is obvious to every baseball
fan that in the major leagues,
home runs are being hit at a
greater rate than ever before. In
fact, this year, records have been
set for most home runs in a
day, a week, and a month, and the
season is barely two months
old. The leagues are on a pace to hit 6254 home runs, which is
an increase of 13.1% over last
year's record of 5528.
Several different theories have
been batted about to explain this
pronounced increase. One possible reason is that the ball has
been 'juiced,' i. e. it has been
made so that it rebounds at a
greater rate off of a bat than
previously. Another possibility
is that with the increase in the
number of teams in recent years,
there are many pitchers playing
now who are not very good.
Still another is that ball parks
are smaller than they used to
be. Finally, the hitters may be bigger and stronger.
The first of these articles
describes a tour of the factory in
Costa Rica where all of the balls
used in the major leagues are
made. Rawlings owns the factory and has been the sole supplier
of the major leagues since
1977. The cores are made by the
Muscle Shoals Rubber Company, in
Batesville, Mississippi. This
company has been the sole
supplier of this product for the entire
time that Rawlings has been
making the balls (and supplied
Spalding, the previous maker, as
well). A spokesperson from
Muscle Shoals is quoted as saying
'We haven't changed a thing.'
Wool yarn and cotton string are
wound, by machine, around the
cores. Then, cowhide covers are hand-stitched around the balls.
The hides come from dairy cows,
rather than beef cattle, because
the former have fewer
imperfections. At the plant where the
cowhides are cut, the plant
manager, who has been there for 11
years, is quoted as saying 'We
give the very best to the major
leagues.'
Finally, a sample of the balls
produced each day is tested at the
factory. A pitching machine is used to launch balls
at 85 miles
per hour at a wooden plank made
of northern white ash, which is
what bats are made of. The speed of rebound is measured, and
divided by 85 to obtain the
Coefficient of Restitution, or COR.
The major leagues have specified
that the COR be between 51.4%
and 57.8%. According to Rawlings, the value of the COR
has not
changed in the recent past.
The second article reports on a
collaboration between Universal
Systems, of Solon, Ohio, and the
energy laboratory at Penn State.
Using a CAT scanner designed to
test cores in the petroleum
industry, the researchers
compared the cores used in baseballs in
the 1930s with the ones being
used today. A spokesperson from
Rawlings is quoted as saying that
the core hasn't changed over
this period, but the researchers
report that the changes are very
significant. They stop short of claiming that this has
much
effect on the home run rate.
The last article reports on a study,
commissioned by Major League
Baseball, to determine if today's
baseballs conform to the
established standards. The study is being conducted by Dr. Jim
Sherwood, a professor of
mechanical engineering, and Larry
Fallon, a doctoral candidate,
both at the University of
Massachusetts at Lowell. Bud Selig, the Commissioner of
Baseball, claims that the
baseball is not being doctored. Selig
is quoted as saying 'We're not
that smart.' He thinks that
ballparks are smaller, hitters
are stronger, and the umpires
don't call strikes above the belt
(even though the rule books
state that balls between the
knees and the letters are strikes,
provided they're over the plate).
DISCUSSION QUESTIONS:
(1) Imagine a baseball league with 10 teams, say, which have the
250 best players in the
world. Now imagine expanding this
league
to 20 teams, which now have the
500 best players in the world.
What would happen to the number
of home runs per team in a
season? What would happen to the distribution of individual
totals for home runs (i. e. would
it be more likely that someone
would hit a large number of home
runs)?
(2) Suppose that over time, both hitters and pitchers get
'bigger and stronger' at the same
rate. If everything else were
assumed to be unchanging, would
the number of home runs go up or
down?
(3) When we asked Dr. Sherwood how they were testing the balls
we received the following answer:
We are not at liberty to disclose our test methods at
this time. This is a
comprehensive study being completed
under commission to MLB (Major League Baseball). MLB has
asked us to keep all procedures and results confidential.
The methods and results will be released to the public
when it is appropriate.
There are, however, standard
tests for baseballs as published by the ASTM. You are
welcome to consult these standard test procedures.
We note also Dr. Sherwood
received a grant $390,000 from
Major League Baseball and
Rawlings Sporting Goods for the
establishment of the Baseball
Research Center. Would you be
concerned about a possible conflict
of interest?
NOTE: We received an interesting
explanation from Dave Zavagno about the
way that Universal Systems studies baseballs.
<<<========<<
>>>>>=============>
Chance News
Copyright (c) 2000 Laurie Snell
This work is freely
redistributable under the terms of the GNU
General Public License as
published by the Free Software
Foundation. This work comes with
ABSOLUTELY NO WARRANTY.
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
CHANCE
News 9.07
June 7, 2000 to July 2, 2000
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!