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.L
CIGARETTES, CANCER, AND STATISTICS*
SEVEN OR EIOHT years ago, those of us interested in such things
in England heard of a rather remarkable piece of research
carried out by Dr. Bradford Hill and his colleagues of the
London School of IIygiene. We heard, indeed, that it was
thought that hc had made a remarkable discovery to the effect
that smoking was an important cause of lung cancer. Dr.
Bradford tIill was a well-known Fellow of the Royal Statistical
Society, a member of Council, and a past pre.sident--a man of
great modesty and transparent honesty. Most of us thought
at that time, on heari,~g the nature of the evidence, which
I hope to make clear a little later, that~'a good /~rima fade
case had been made for further investigation. But time has
passed, and although further investigation, in a sense, has
taken place, it has consisted very largely of the repetition of
observations of the same kind as t.hosc which Hill and his
colleagues called attention to several years ago. I read a recent
article to the effect that nineteen different investigations in
different parts of the world had all concurred in confirming
Dr. Hill's findings. I think they l~ad concurred, but I think
they were mere repetitions of evidence of the same kind,
and it is necessary to try to examine whether that kind is
sufficient for any scientific conclusion.
The need for such scrutiny was brought home to me very
forcibly about a year ago in an annotation published by the
British Medical Association's .Journal, leading up to the almost
shrill conclusion that it was necessary that every device of
modern publicity should be employed to bring home to the
world at large this terrible danger. When I read that, I wasn't
sure that I liked "all the devices of modern publicity",
and it seemed to me that a moral distinction ought to be
• Lecture delivered at Michigan State Univer~|ty.
I!

drawn at this point. Thcrc is thc attitudc of a man (may I
say, I think it is an entirely rational attitude and one within
his own competcnce to judge) who says, "There sccms to be
some dangcr--I can't assess whether it is infinltcsimal or
serious. This habit of mine of smoking isn't vcry important
to me. I will givc up smoking as a kind of insurance against
a danger which I am quite unable to assess." That seems to
me a perfectly rational attitude. What is not quite so much
the work of a good citizcn is. to plant fear in the minds of
perhaps a hundred million smokers throughout the worldq
to plant it with the aid of all the means of modern publicity
backed by. public money, without knowing for certain that
they have anything to be afraid of in the particular habit.
against which the propaganda is to be directed. After all, a
large number of the smokcrs of the world are not very clever,
perhaps not very strong-minded. The habit is an insidious
one, difficult to break, and consequently in many, many cases
there would be implanted what a psychologist might recognize
as a grave conflict.
If there is cause for fear, let there be warning. But there
is no reason for this in the first rational response that I described
--that does not require scientific proof that there is reason to
fear. There is only the possibility that there is reason.
Before one interferes with the peacc of mind and habits of
others, it seems to me that the scientific evidence~the exact
weight of the evidence frcc from emotion~should be rather
carefully examined. I may say, I am not alone in this. I
have bccn interested to note that leading statisticians in this
country also-and I contact a good many statisticians both in
my own country and here~are exceedingly sceptical of the
claim that decisive evidence has been obtained. In the popular
press, the matter seems to be argued, as always, a little off the
simplest lines. For example, I find people saying, "These
statisticians think this "~" These statisticians think that", or
representing that this kind of evidence which ha~ been pro-
duced has been attacked as being merely statistical. How I
ahould be the last pe~on to. attack evidence for being merely
statistical, because
concerned with th~
bc carried out,
the data suppllcd
give really conclusi
Progress has bcc:
A large part of th~
field, has become
cautions, entirely u
in the expcrimenta
agrlculturc, where
attention of leading
which emcrgcd in
randomization, ant!
We under'stand t|
it is necessary in
diminishing the er
essential in a more
of the estimation
Although replica[
.cient without theI
is, the assignment /
manurial treatment
or diffcrc~t metho~
purpose, in such
the experiment, an
which it is subjec
brought home to
that human judgn
that if one tries to
numbers very far f
card of an ordina~
it's not so well kn~
cards are thought
numbers are thou
and that the Quee~
.clivi.ty of the hun

1 or
:lant
ainst
~ tO
~uch
is of
ld--
iicity
that
labit.
dl, a
cver,
]ious
;nize
there
ribed
)n to
iu of
exact
ather
is. I
t this
,th in
,f the
pular
ffthe
Fhese
~'~ or
pro-
~ow I
Icrcly
statistical, because for a great part of my work I have.been
concerned with the problem of how experimentation should
be carried out, how reasonin~ processes should be applied to
the data supplied by experimentation or by survey so as to
give really conclusive answers.
Progress has been made during the last twenty-five years.
A large part of the educated world, at least in the statistical
field, has become aware that, by taking certain specific pre-
cautions, entirely unchallengabl~ conclusions can be obtained
in the experimental field. The work was done primarily in
agriculture, where problems of experimentation attracted the
attention of leading agronomists at an early time. The keywords
which emerged in the course of these inquiricsoreplication,
randomization, and control--are now widely understood.
We understand that replication is required for two purposes:
it is necessary in order to add precision to our results by
diminishing the error to which they are subject, and it is
essential in a more important way, as supplying the only means
of the estimation of such error.
Although replication is essential in this way, it is not suffi-
cient without the added precaution of randomization, that
is, the assignment of the different treatmcntsowhich may be
manurial treatments, or different varieties of agricultural crops,
or different methods of tillage~to the plots set aside for the
purpose, in such way at random as to guarantee the validity of
the experiment, and in particular of the estimate of error to
which it is subject. This necessity for randomization was
brought home to agriculturists largely because it was found
that human judgment was very liable to err in this matter,
that if one tries to think of numbers at random, one thinks of
numbers very far from at random. If one tries to think of a
card of an ordinary playing deck, it's well known (perhaps
it's not so well known--it is known to me, at least) that red
cards are thought of more readily than black cards, that odd
numbers are thought of more readily than even-numbers,
and that the Queen of Diamonds is a hot favourite. This pro-
clivi.ty of the human, mind affects any consciously guided

choice o1" assignment of material. Agriculturists, at least, do
not trust themselves to choose plots and say that they have
been chosen at random. They use decks of cards or, more
expeditiously, in recent years, some of these large collections
of random sampling numbers which some of you may have
teen at the ends of books of tables and perhaps wondered
what on earth they can be for. They are in constant use in the
design of experiments.
There is a logical aspect, toorofrandomization which needs
emphasls in this connection. Supposing we have an association
--an observable and verifiable association--between two
things. I remember Professor Udny Yule in England pointing
to one wh;ch illustrates my purpose sufficiently well. He
said that in the years in which a large number of apples were
imported into Great Britain, there were also a large number
of divorces. The correlation was large, statistically significant
at a high level of significance, unmistakable. But no one,
fortunately, drew the conclusion that the apples caused the
divorces or that the divorces caused the apples to be imported.
The early logicians would say that post hoe is not the same as
propler hoc, or in other words~as it would be put in the early
years of our century, when statisticians had had perhaps
ten years' experience of the correlation coefficient as a means
of research--that correlation is not causation. The fact is that
if two factors, A and B, are associated~clearly, positively,
with statistical significance, as I say--it may be that A is an
important cause of B, it may be that B is an important cause
of A, it may be that something else, let us say X, is an im-
portant cause of both. If, now, ,4, the supposed cause, has been
randomized--has been randomly assigned to the material from
which the reaction is seen~then one may exclude at a blow
the possibility that B causes A, or that X causes A. We know
pcffcct!y well w!mt causes A~the fall of the dice or the chances
of the random sampling numbers, and nothing else.
But in the case where randomization has not been possible,
these other possibilities lie wide open and thould be excluded,
or at least every effort should be made to exclude them, before
w¢ can assert that
I ~pokc to Bradford
was entirely unwilli
proved. Hc said he
was certainly u,~will
made vociferously dr
reporting to the Me~
to the Amcrican C
totally impossible, so
kind. It is not the fa
the fault of Hill or 1
duce evidence in whi
been laid under a t.
thousand more chos,
have been under con
aday. If that type.
be no difficult),.
The principles of~
were developed ir~ t'
them was greater or
rapidly and ~ealthil
And I suppose durin
books have been wri
pally to make clear x~
applications in chcmi
But the most dif.
principles has alway
because you can do ~
good for it, feeling t
do so. But no onef~
not fccl~that it is ri.
probably will do hi~
mentatlou has not b,
There is a movcmc~:
trials, let us say, of~
way that an imparti
the old may be obt~

st, do
have
more
cdom
.have
,dered
in the
needs
iation
t tWO
inting
He
; were
~mbcr
ificant
~ one,
:d the
orted.
.me aS
: early
:rhaps
means
s that
tively,
:isan
cause
m im-
~ been
J from
~ blow
"know
hances
~ssible,
=luded,
before
we can agsert that causation has been established. When
I spoke to Bradford Hill in the early days of this affair, he
was entirely unwilling to claim that causation had been
proved. He said he didn't see what else it could be, but he
was certainly unwilling to make the claim which is being
made vociferously during the l~st year or two by committees
• reporting to the Medical Research Gouncil in England, and
to the American Gancer Society. Now, randomization is
totally impossible, so far as I can judge, in an inquiry of this
kind. It is not the fault of the medical investigators. It is not
the fault of Hill or Doll or Hammond that they cannot pro-
duce evidence in which a thousand children of teen age have
been laid under a ban that they shall never smoke, and a
thousand more chosen at random from the same age group
have been under compulsion to smoke at least thirty cigarettes
a day. If that type of experiment could be done, there would
be no difficulty.
The principles of experimentation~which, as I mentioned,
were developed in the agricultural field, where the ne/:d for
them was greater or more manifest~have spread, and spread
rapidly and healthily, into the other experimental sciences•
And I suppose during the last fifteen years a dozen important
booLs have been written on the design of experiments, princi-
pally to make clear what these principles are in their particular
applications in chemistry, physics, biology, or what you maywill.
But the most difficult field for the application of thdse
principles has always been the medical field. This is partly
because you can do things to a r~t or rabbit which may not be
good for it, feeling that in a good cause you have a right to
do so. But no One feels~and especially a medical man could
not feel~that it is right to do things to a human being which
probably will do him harm. Gonsequently, deliberate experi-
mentation has not been very widely used in the medical field.
There is a movement at the present time to organize clinical
trials, let us say, of new drugs or of new anfibioticr in such a
way that an impartial judgment in comparing the new with
the old may be obtained by hospital staffs. And that would

involve applyiag tile new and the old at random to some of
the hospital patients. So long as no body of medical opin.ion
'can say with confidence that one is better than the other, or
perhaps that in matters usually as complicated as this, for
what cases one drug is the better and for what cases the other--
so long as that state of .ignorance remains, it would be
perfectly fair, I think, to clear the air by such simple experi-
mentation.
But manifestly we cannot cxpcrlmcnt with the same freedom
that is possible with agricultural animals and laboratory
animals in other sciences. For lack of that, medical research
has had to rely a good deal on uncontrolled experiments,
uncontrolled observations; aud of course from the time of
Jenner onwards there were numerous cases where an observant
(and also, I may say, an experimental) physician may be able
to make out an exceedingly strong case. Jenner's work was
not completely passive. And Dr. Suow, who studied and in
the end quelled the occurrence of cholera in London, used a
very large number of different types of inquiry in order to gain
sufficient confirmation of his important conclusion, namel~',
that it was faecal contamination in the water supply that was
responsible for the cholera, an opinion that is easy to take
for granted at the present time, but which in the absence of
any knowledge of the organisms concerned--or, indeed, know-
ledge that the disease was caused by an organism~was a
considerable advance, just as Jenner's was also in the case of
smallpox. Consequently, when inconclusive evidence is criti-
cised on the ground that it is inconclusive, it is not uncommon
for medical men to defend it, perhaps with certain indignation,
on the ground that in the past medical science has made
notable advances primarily--not solely, never only, but
primarily--by the observational method.
Now, in the sciences we also have cases in which experimenta-
tion is impossible. In astronomy, for example, experimentation,
you might say, has only just begun. And in those sciences we
must use what I may call sideliglgs.
Let me illustrate this possibility with a very few instafices.
The ilrst reports of
They said that the.
in patients was pr~
consumed. That s
drawn, and it was
or in tile cigar did
with lung cancer
this was a puzzlin~
three cases. The
tobacco p;,sses into
indeed, into the lu,
is not what one wo
and Hill guessed
be comparatively c
sort should have t
dreadful disease.
And now I mus~
evldencc it was th~
ning, and in what
The first inquir
number of diffcrc
suffering from
mously aided in r
lung cancers can
are" passed througt
reason to think
and had not been
cancer cases. Arra
habits and thcir
smokers, pipe sm
consumption of to
questions. A simi
cancer patients
questionnaire, and
one of them select.
as being in hospi~
of the classificatio~

some of
opinion
~thcr~ or
this, for
• other~
~uld be
: experi-
freedom
boratory
research
:rimcnts~
time of
bservant
• be able
:ork was
I and in
,, mcd a
r to gain
namely,
that was
to take
)sence of
d, know-
.--was a
e case of
: is criti-
common
ignation,
~ made
aly, but
:rimenta-
entatlon,
ences we
nstances.
The first reports of Hill and Doll made a very simple claim.
They said that the additional amount of lung cancer observed
in patients was proportional to the amount of tobacco they
consumed. That simple conclusion was .quite rapidly with-
drawn, and it was admitted that tobacco consumed in the pipe
or in tile cigar did not appear to have so close an association
with lung cancer as that consumed in the cigarette. And
this was a puzzling tiling. After all, tobacco is burned in all
three cases. The effluvia, sm,oke, or aerosol from the burning
tobacco passes into tile mouth, partly into the throat, partly,
indeed, into the lungs, in all three cases. It is not obvious~it
is not what one would guess at first sight, it was not what Doll
and Hili'guessed at first--that the one sort of smoke should
be comparatively or perhaps wholly innocuous and the other
sort should have the effect of inducing the beginnings of a
dreadful disease.
And now I must go back and recall just what the kigd of
evidence it was that Hill and Doll laid before us at the begin-
ning, and in what ways it has beet) extended by other evidence.
The first inquiry was to take about 15oo. patients in a
number of different hospitals who had been diagnosed as
suffering from lung cancer. Of course the diagnosis is enor-
mously aided in recent times by the use of radiology. The
lung cancers can be perceived by their shadows when X-rays
are' passed through the lungs..Consequently there was good
reason to think that these patients~ahhough they were alive
and had not been examined post-mortem~really were lung
cancer cases. Arrangements were made to record their smoking
habits and their smoking history: non-smokers, cigarette
smokers, pipe smokers, estimates of the amount .of daily
consumption of tobacco in each case, and a number of other
questions. A similar number, perhaps a few more, of non-
cancer patients from the same hospitals received tile same
questionnaire, and the comparison between these two samples,
one of them selected as being lung cancer cases and the other
as being in hospitals from some other condition, was made
of the classification by smoking habit. And it appeared from

that that the cigarette smokers were morc common among
the sufferers from lung cancer than they were among other
patients, and that within the cigarette smokers, henW clgarcttc
smokers were more common among the lung cancer patients
than medium or light cigarette smokers.
The statement that consumers of tobacco in other forms
were associated with lung cancer seems to have largely evapo-
rated. I should say a word about it because it represents a
common cause of error in statistical investigations, namely,
the kind of error which flows from the difficulty of a perfect
classification. Everyone can make a rough classification of
cigarette smokers or pipe smokers or non-smokers, but there
"will be borde.rline cases. There arc people who, though they
may prefer a pipe when they have the opportunity, yet may bc
constrained by duress, such as in the intervals of a play when
there is very little time, to smoke a cigarette. There are also
distinguished and expensive restaurants, as well as aircraft,
who don't like the customer to pull out a pipe. Consequently
there is an overlap in the practices and habits of diffi~rent
people; there may not be exactly the same interpretation put
on the questionnaire by all the different subjects; and, in
fact, a good many pipe smokers may he classified as cigarette
smokers, and vice versa. There is bound to be some mixture
• or" the classes in any inqniry on a complicated question. "And
so the first results did seem to show some effect on pipe
smokers and cigar smokers, but it is quite clear that the
• amount was much smaller than was at first thought, and
certainly no more than might easily arise due to mis-
classification. At least it would be very foolish for anyone who
Mshed to make a case for saying that cigarette smoking was a
cause of lung cancer to bring in the evidence about pipe and
cigar smoking.
When an unexpected discrepancy occurs, it is a common
reaction (I won't say, a failing--it's part really of the scientific
discussion which data deserve) to think up some reason for it.
This, in effect, may be something like what the logicians would
call a "special pleading". That is to say, the making of an
assumption, which r.
true, but which, if t
wise inexplicable. I
or, rather, is contai
much in pipes. Th~
pipe smokers who
But most pipe smC.
without paper. An(
sumption of paper
also, it has been ob
tobacco is burned i:
in the case of the p
is not known to be)
condition for prod~
thing quite unexplo
tobacco smoke whi.
cancer. It is also kn
and for cigars is mc
is that used in cig
source of cigarette
prepare the tobacco
aware, that the pric
in fermentation,
weight than is nece:
tobacco is rather li~
could claim even--.
fermented conditlor
cigarettes, that
fumes which the bu
is full of such things
One of the first 1
me on the matter,
inhale; pipe smoker
or~ an extremely in
country, I believe,
some don't. When
smoking was all rig

among
• other
~,arette
aticnts
cvapo-
~nts a
amcly,
perfect
ion of
: there
h they
nay be
when
re also
rcraft,
uently
fferent
)n put-
ad, in
~arcttc
tixture
• And
n pipe
at the
:, and
, mis-
was a
)c and
mmon
.entitle
for it.
would
of an
assumption, which might be tt'uc, which might, indccd, not be
true, but which, if true, would help to explain what is other-
wise inexplicable. For example, the cigarette contains paper,
or, rather, is contained by paper• One doesn't smoke paper
much in pipes. "l'hcre are, indeed, special papers supplied to
pipe smokers who wish to enjoy their tobacco in that way.
But most pipe smokers and, I suppose, all cigar smokers, do
without paper. And it could be, therefore, that it's the con-
sumption of paper that is the really dangerous practice. Then,
also, it has been observed that the temperature at which the
tobacco is burned is higher in the case of the cigarette titan
in the case of the pipe, and, it could be (though it certainly
is not known to be) that burning at a higher temperature is a
condition for producing something quite unknown, some-
thing quite unexplored, something quite hypothetical, in the
tobacco smokc which would be capable of producing lung
cancer. It is also known that the tobacco used as pipe tobacco
and for cigars is more thoroughly fermented before use than
is that used in cigarettes, or at least in the predominant
source of cigarette tobacco, in Virginia. I think those who
prepare the tobacco produced in Virginia are rather acutely
aware, that the price per pound is high, there is loss of weight
in fermentation, and it is as well not to lose to per cent. more
weight than is necessary. And so, on the whole, the Virginia.
tobacco is rather lightly fermented. You could imagine.--you
could claim even--as a special pleading, that it was the un-
fermented condition of the Virginia tobacco, largely used in
cigarettes, that was responsible for the supposedly noxious
fumes which the burning of such tobacco produces. Discussion
is full of such things.
One of the first people in the United States that spoke to
me.on the matter, a lady, said, "Of course, clgarette smokers
inhale; pipe smokers don't." And of course she laid her finger
on an extremely important point. Cigarette smokers in this
country, I believe, generally inhale. In England, some do and
some don't. When I was a little boy, it was thought that
smoking was all right and did you no harm, but inhaling w.as
~9

perhaps a perverse practice and might not do you any good.
And so, at any rate my generation, and perhaps some decades
of younger men, had a certain amount of warning against
this particular practice. I imagine it is something llke that
that explains the difference in practice between the two
countries.
Now, Doll and Hill, in their first inquiry~the one that
I've gone over approximately--did include in their question-
naire, which was put both to the c~neer patients and to the
patients from other diseases, the question: "Do you inhale?"
And the result came out that there were fewer inhalers among
the cancer patients than among the non-cancer patients. That,
I think, is an exceedingly important finding. I don't think
Hill and Doll thought it an important finding. They said
that perhaps the patients didn't understand what inhaling
meant! And what makes it far more exasperating, when they
put i,uo effect an exceedingly important research, based on
the habits of the medical profession, by asking about 6o,ooo
doctors in Great Britain to register their smoking habits, and
about 40,000 of them did so co-operatively, I am sorry to say
that the question about inhaling was not in that questionnaire.
I suppose the subject of inhaling had become distasteful to
the research workers, and they just wanted to hear as little
about inhaling as possible. But it is serious because the
docto~ could have known whether they were inhalers or not;
they could have known what the word meant; perhaps they
would have consulted each other sufficiently to lay down a
definition which the rest of us could understand. At any rate,
there would have been no alibi if the question had been put
to a body of 40,000 physicians.
$o, our evidence about inhaling is embarrassing and diffi-
cult. There is no doubt that inhaling is more common among
heavy cigarette smokers than among light cigarette sn~okers
in Great Britain, where inhaling is not nearly a universal
practice. There is no doubt that cancer is commoner among
the heavy cigarette smokers than among the light cigarette
smokers. Oomequently, if inhaling had no effect whatever,
• oo
you would expect to fi
patients than among th
be an indirect corrclat
with the quantity smo
reported everything wa
aggregate data, it app
fewer inhalers than the:
though, if one could
who smoke the same nt
negative association bct~
me that the world ouglv
Before I stop, in fact,
is a case for fiathcr rcs
areas which would seen
would stress the import:
• tively easily with ratl~c
unmistakably what the
is found to be strongly
be consonant with the
wafted over the surface
cancerous and thence a
either no association
should have to reject
causation of cancer.
The subject is compl
stage that the logical d
B causing A, or someth
then, that lung cance~
condition which must
in those who are goln~t
of the causes of smoki
be excluded. I don't tla
such a cause. But the p~
a certain amount of sli~
of smoking cigarettes m
some extent, and I thin
irritatlon~a slight dis
