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\textit{Centennial Review}, \textbf{2} (1958), 151--166.
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{\Large CIGARETTES, CANCER, AND STATISTICS}
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{\Large\textit{Sir Ronald Fisher}}
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\noindent \textsc{Seven or eight} 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 Hygiene. We heard, indeed, that it was thought that he had
made a remarkable discovery to the effect that smoking was an important
cause of lung cancer. Dr.\ Bradford Hill was a well-known Fellow of the
Royal Statistical Society, a member of Council, and a past president-a
man of great modesty and transparent honesty. Most of us thought at that
time, on hearing the nature of the evidence, which I hope to make clear
a little later, that a good prima facie 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 those 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 had 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
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 drawn at this point.
There is the attitude of a man (may I say, I think it is an entirely
rational attitude and one within his own competence to judge) who says,
There seems to be some danger-I can't assess whether it is
infinitesimal or serious. This habit of mine of smoking isn't very
important to me. I will give 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 citizen
is to plant fear in the minds of perhaps a hundred million smokers
throughout the world- 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
smokers 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 peace of mind and habits of others, it
seems to me that the scientific evidence-the exact weight of the
evidence free from emotion-should be rather carefully examined. I may
say, I am not alone in this. I have been 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
skeptical 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 has been produced has been
attacked as being merely statistical. Now I should be the last person to
attack evidence for being merely statistical, because for a great part
of my work I have been concerned with the problem of \textit{how}
experimentation should be carried out, \textit{how} reasoning 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 precautions, entirely
unchallengable 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 key words which emerged in the course of these
inquiries-replication, 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 sufficient
without the added precaution of randomization, that is, the assignment
of the different treatments---which 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 favorite. This proclivity of the human
mind affects any consciously guided choice or 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 seen 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, too, of randomization which needs emphasis 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 which 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
\textit{post hoc} is not the same as \textit{propter hoc}, or in other
words-as it would be put in the early years of our century, when
coefficient as a means of research---that \textit{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 important cause of both. If, now, $A$, 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 perfectly
well what 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 should be excluded, or at least every
effort should be made to exclude them, before we can assert 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 last year or two by committees reporting to the
Medical Research Council in England, and to the American Cancer 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 produce
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 need for them was greater or more
experimental sciences. And I suppose during the last fifteen years a
dozen important books have been written on the design of experiments,
principally to make clear what these principles are in their par-ticular
applications in chemistry, physics, biology, or what you may will.

But the most difficult field for the application of these principles has
always been the medical field. This is partly because you can do things
to a rat 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. Consequently, deliberate
experimentation 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 antibiotics in such a way that an
impartial judgment of comparing the new with the old may be obtained by
hospital staffs. And that would involve applying the new and the old at
random to some of the hospital patients. So long as no body of medical
opinion 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 experimentation.

But manifestly we cannot experiment with the same Free dom that is
possible with agricultural animals and labora-tory animals in other
sciences. For lack of that, medical research has had to rely a good deal
on uncontrolled experiments, uncontrolled observations; and 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.\ Snow, 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, namely, that it was fecal 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, knowledge 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 criticised on the grounds 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
primarily-by the observational method.

Now, in the sciences we also have cases in which experimentation 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
sidelights.

Let me illustrate this possibility with a very few instances. 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 withdrawn, and it was admitted that tobacco consumed in the pipe
or in the cigar did not appear to have so close an association with lung
cancer as that consumed in the cigarette. And this was a puzzling thing.
After all, tobacco is burned in all three cases. The effluvia, smoke, or
aerosol from the burning tobacco passes into the 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 Hill 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 d read In I disease.

And now I must go back and recall just what the kind of evidence it was
that Hill and Doll laid before us at the beginning, and in what ways it
has been extended by other evidence.

The first inquiry was to take about 1500 patients in a number of
different hospitals who had been diagnosed as suffering from lung
cancer. Of course the diagnosis is enormously 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-although 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 the 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 more common among the
sufferers from lung cancer than they were among other patients, and that
within the cigarette smokers, heavy cigarette 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 evaporated. 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 borderline cases. There are people who, though they may
prefer a pipe when they have the opportunity, yet may be 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 different 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 be classified as cigarette smokers, and vice
versa. There is bound to be some mixture of the classes in any inquiry
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 misclassification. At
least it would be very foolish of anyone who wished 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 deserves) 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 might be true, which
might, indeed, not be true, but which, if true, would help to explain
what is otherwise inexplicable. For example, the cigarette contains
paper, or, rather, is contained by paper. One doesn't smoke paper much
in pipes. There 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 consumption 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 than 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 smoke 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 unfermented 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, cigarette 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
was 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 like 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---\textit{did} include in their questionnaire, which was
put both to the cancer 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
probably the patients didn't understand what inhaling meant. And what
makes it far more exasperating, when they put into effect an exceedingly
important research, based on the habits of the medical profession, by
habits, and about 40,000 of them did so cooperatively, 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 it as possible.
But it is serious because the doctors 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.

So, our evidence about inhaling is embarrassing and difficult. There is
no doubt that inhaling is more common among heavy cigarette smokers than
among light cigarette smokers 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. Consequently, if inhaling had no effect whatever, you would
expect to find more inhalers among the cancer patients than among the
non-cancer patients. There would be an indirect correlation through the
association of both with the quantity smoked. Now, of course, in what
was reported everything was thrown together; and yet, in the ag-gregate
data, it appeared that the cancer patients had the fewer inhalers than
the non-cancer patients. It would look as though, if one could make the
inquiry by comparing people who smoke the same number of cigarettes,
there would be a negative association between cancer and inhaling. It
seems to me the world ought to know the answer to that question.

Before I stop, in fact, I hope I shall make clear that there is a case
for further research, and I shall only mention two areas which would
seem to be profitable for investigation. I would stress the importance
of what could be done comparatively easily with rather little expense,
namely, to ascertain unmistakably what the facts are about inhaling. If
inhaling is found to be strongly associated with lung cancer, it would
be consonant with the view that the products of combustion, wafted over
the surface of the bronchus, might induce a pre- cancerous and thence a
cancerous condition. But if there is either no association at all or a
negative association, we should have to reject altogether that simple
theory of the causation of cancer. The subject is complicated, and I
mentioned at an early stage that the logical distinction was between $A$
causing $B$, $B$ causing $A$, something else causing both. Is it
possible, then, that lung cancer-that is to say, the pre-cancerous
condition which must exist and is known to exist for years in those who
are going to show overt lung cancer---is one of the causes of smoking
cigarettes? I don't think it can be excluded. I don't think we know
enough to say that it is such a cause. But the pre-cancerous condition
is one involving a certain amount of slight chronic inflammation. The
causes of smoking cigarettes may be studied among your friends, to some
extent, and I think you will agree that a slight cause of irritation-a
slight disappointment, an unexpected delay, some sort of a mild rebuff,
a frustration-are commonly accompanied by pulling out a cigarette and
getting a little compensation for life's minor ills in that way. And so,
anyone suffering from a chronic inflammation in part of the body
(something that does not give rise to conscious pain) is not unlikely to
be associated with smoking more frequently, or smoking rather than not
smoking. It is the kind of comfort that might be a real solace to anyone
in the fifteen years of approaching lung cancer. And to take the poor
chap's cigarettes away from him would be rather like taking away his
white stick from a blind man. It would make an already unhappy person a
little more unhappy than he need be.

For my part, I think it is more likely that a common cause supplies the
explanation. Again, we do not know. I do not put forth any explanation
as proved, but as requiring in-vestigation. The obvious common cause to
think of is the genotype. We are all different genotypes. I suppose in
this nation there must be well over 15o million different geno-types. If
one studies cancer in mice (and I suppose about half the mice of the
world are kept to study cancer with), if one examines any of the many
(and there are thousands) of inbred lines of mice (where we can get a
hundred or two hundred individuals of the same genotype to study)-if you
take, then, any two such lines of differing genotypes, they will, I
believe, invariably be found to differ in the frequency, in the age
incidence, and in the type of cancer which those mice suffer from.
Consequently if there is any genotypic difference between the different
smoking classes, we may expect differences in the type or frequency of
cancer that they display.

That is the second line of research which I should like to advocate, a
little bit more difficult than that which is concerned with inhaling,
but certainly well within the capacity of Modern methods in human
genetics. It certainly could be ascertained, as a matter of fact,
whether in the different smoking classes of nonsmokers, cigarette
smokers, pipe smokers, cigar smokers (the minor classes, perhaps, of
snuffers and chewers perhaps might not be sufficiently numerous, but in
those first main four classes it could certainly be ascertained) whether
there was evidence that they differed genetically. It wouldn't be a long
shot to guess that they did. After all, we choose these things for
ourselves. I know that there are families in which there would be some
pressure on a growing boy or girl to be a nonsmoker because his father
and mother firmly believe that smoking is an objectionable habit, or
perhaps an irreligious habit. But most of us choose for ourselves, and
even though one may have been exposed to opportunities---temptations, if
you like---to smoke cigarettes from a fairly early boyhood, it is not
uncommon to find people who never smoke anything but a pipe. Why?
Because they are made that way. They are the sort of men who take to the
pipe and don't take to cigarettes, just as there are other men who would
never take to a pipe but constantly feel the need of cigarettes. it is
not, then, a very long shot to guess that there is a genetic component
which distinguishes the different smoking classes. And that is the
second piece of research which I think is extremely urgent.

I have criticised the over-confidence shown at least in public
utterances or published reports of anonymous committees on this subject,
and I do not suppose that Bradford Hill, at least, is at all to blame
for that overconfidence. The worst effect of that overconfidence, so
far, is that it seems to have held back the various teams of workers.
They are well supplied with money---the Medical Research Council is not
stinting money on cancer research, and the American Cancer Society is
obviously exceedingly well supplied with money. And yet, I think nothing
but overconfidence that they had found the solution, that they had the
game in the bag, could have prevented them from following up some of the
other lines of inquiry which are much needed. I have said nothing, for
example, so far of the very striking fact that at the same level of
cigarette smoking, dwellers in towns have considerably more lung cancer
than dwellers in the country. I don't know any extensive piece of
research which has been set on foot to get to the bottom of that
important difference.

The desire to make a strong sensation, to bring home the terrible danger
to these passive millions, has led writers to stress the very alarming
fact that lung cancer is a disease increasing, one of the few important
diseases that are increasing in frequency. It is not so important in the
United States as it is in England, but it is an important cause of death
in both countries. It has been increasing over the last fifty years. It
is frightening. But it shouldn't be used to frighten people.

The change over recent decades gives not the least evidence of being due
to increasing consumption of tobacco. We can't tell much about the
absolute magnitude of this secular change. It is certain that radiology
has facilitated the detection of lung cancer enormously, that
available for our populations than they formerly were. I do not know
that there are not remote and secluded communities where patients with
lung cancer are not looked at by radiologists, but that proportion of
our populations must be still decreasing. Again, the attention of the
medical profession has been forcibly drawn to lung cancer, and it
invariably happens that when the attention of the medical profession is
drawn to any disease, that disease begins to take up more space in the
official reports-it is more often seen and more often diagnosed with
confidence; death certificates more often include that particular
disease. Consequently it is not easy to say how much of the increase is
real. I think part of it must be real, because there's no doubt that the
populations concerned have been enduring or enjoying a very considerable
increase in urbanization. The big metropolitan cities have been growing
rapidly. In England, smaller towns have been running together into
extensive masses called conurbations, like those of Clydeside or
Merseyside or the Birmingham region. Even in the country, even in what
used to be remote villages, there are motorbuses regularly which take
the young men and women into cinemas perhaps six or eight miles away.
You might say that the whole population during the last twenty, thirty,
forty years has been becoming steadily urbanized, and as the urban rate
for lung cancer is considerably greater than the rural rate, in my
country as in yours, we must recognize here the possibility of one real
cause of the increase in lung cancer. There may be others.

But the only good comparison we can make in respect of the time-change
is that between men and women. The same apparatus, the same
radiologists, the same physicians diagnose both men and women. Whatever
effects improved apparatus may have, whatever effects an increased
attention to the disease may have, will be the same in the two sexes.
Whatever effects urbanization may have you would think might be the same
in the two sexes. Consequently, we can, at least, inquire whether the
rate of increase of lung cancer in men is the same, or greater, or less,
than the rate of increase of lung cancer in women. For it is certainly
true, I think in both our countries, that whereas the smoking habits of
men have not changed very dramatically over the last fifty years, yet
the smoking habits of women have changed a very great deal. And on
making that comparison, it appears that lung cancer is increasing
considerably more rapidly--absolutely and relatively-in men than it is
in women, whereas the habit of smoking has certainly increased much more
extensively in women than in men. There is, in fact, no reasonable
ground at all to associate the secular increase in lung cancer as has
been done with dramatic eloquence, I suppose as part of the campaign of
bringing home the terrible danger, just as though it was impossible that
statistical methods of inquiry should supply a means of checking that
very rash assumption.

And so I should like to see those two things done, one im-mediately and
quickly: an inquiry into the effects of inhaling, and secondly, a more
difficult but certainly a possible task of seeing to what extent
different smoking classes were genotypically conditioned. And I believe
that only overconfidence, if it is allowed to have its way, could
prevent those further inquiries from being made.

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