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



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



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?


   11. Are baseball's juiced?


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




(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:









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.




We have ordered a lightning data set, available from the

National Climate Data Center. This data set contains

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





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



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 monthly newsletter that also

discusses chance news (See Chance News 9.05).  The June issue

discusses a number of interesting articles with no overlap with

our own choices. This make us wonder how many interesting articles

we both miss.






Joan Garfield suggested the next item.


Inside the happiness business.

New York, 15 May, 2000

David D. Kirkpatrick


No free lunch.

Dr. Robert Goodman



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 to try to convince his

fellow doctors not to accept free lunches. He reviews the evidence

that doctors are unduly influenced in his "Free lunch slide

presentation" that you will find at the bottom of his homepage. 

We recommend that you view this presentation. You will need to

know what a formulary is.  Here is how The California Internet

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.    




(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


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



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. But this is not a correct
estimate for the population as a whole, since the number of
cases and controls were determined by the researchers.  If

they had used more controls their estimate would be lower

just because they had more controls! Thus Tom Falcone, and

we also, could not see where the 60 percent and the 50 percent

relative risks came from. This led to our trying to solve

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



             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!




(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



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."




(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



(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



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



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


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 






Ask Marilyn.

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



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



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.




(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



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).




(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



(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