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\noindent
\textit{Smoking: The Cancer Controversy}, Edinburgh: Oliver and Boyd
1959, pp.\,45--47.
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\Huge{276A}
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\Large{INHALING}
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\noindent
\textsc{When}, several years ago, it appeared that a verifiable
association could be established between smoking an cancer of the lung,
and before there was any reason to doubt the simple theory that the
products of combustion could so act on the surface of the bronchus as to
induce the growth of a cancer, it was natural to seek the powerful
confirmation of this theory which would be obtained if those practising
inhalation of cigarette smoke appeared with much higher frequency among
the cancer patients than among those suffering from other conditions.

The failure of Hill and Doll's retrospective inquiry to supply such
corroboration took these workers by surprise, and at first they could
scarcely believe the question had been understood.  The investigators
who actually questioned the patients, however, seem to have had no doubt
of this; and the statisticians had the embarrassing choice between
frankly avowing that one striking and unexpected result of their enquiry
was clearly contrary to the expectations of the theory they advanced, or
to take the timid and unsatisfactory course of saying as little about ti
as possible.

It has taken some years, therefore to elicit the tables below,
\begin{center}
\begin{tabular}{llrrrrrrrrrr}
\multicolumn{12}{c}{\textsc{Table 1}} \\
& & \multicolumn{10}{c}{\textit{Maximum daily cigarettes}} \\
& & \multicolumn{2}{c}{1--4}   & \multicolumn{2}{c}{5--14}
& \multicolumn{2}{c}{15--24} & \multicolumn{2}{c}{25--49}
& \multicolumn{2}{c}{$>$49} \\ \hline
Men   & Cancer  &  7 & 17 & 141 & 67 & 133 & 63 & 96 & 78 & 21 & 24 \\
& Control & 17 & 21 & 162 & 80 & 157 & 44 & 74 & 44 & 16 &  7 \\ \hline
Women & Cancer  &  3 &  3 &   7 &  8 &   7 &  5 &  5 &  3 &  0 &  0 \\
& Control &  2 & 10 &   2 &  7 &   6 &  0 &  0 &  0 &  1 &  0
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\medskip

(I=Inhaler, N=Non-inhaler)
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which are a reconstruction of the original observations.  I have asked
for, and have now obtained, confirmation that these are the actual
counts originally made.  Certain pipe and cigar smokers were originally
included on the basis of total tobacco consumed, and I have not been
able to secure their removal.

The women are too few to be discussed further; for each of the five
tables for men, we may ask how many of the inhalers would have shown
cancer, if the proportion had been the same as that among the
non-inhalers.

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\begin{tabular}{cccc}
\multicolumn{4}{c}{\textsc{Table 2}} \\
Cigs.\ \textit{per diem} & Expected & Observed & Deficiency \\
1--4 & \phantom{0}10.737 & \phantom{0}\phantom{0}7 & \phantom{0}3.737 \\
5--14 & 138.380 & 142 & $\!\!-$3.620 \\
15--24 & 153.095 & 133 & 20.095 \\
25--49 & 109.119 & \phantom{0}96 & 13.119 \\
$>$ 49 & \phantom{0}33.260 & \phantom{0}21 & 12.260 \\ \hline
Total & 444.591 & 399 & 45.591
\end{tabular}
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If, following the method of the Medical Research Council, these
differences were ascribed to inhalation as a cause, then inhalers may
congratulate themselves of reducing the cancer incidence by over 10 per
cent.,using a very simple, and even enjoyable, method of prevention.
This is indeed an under-estimate, for pipe smokers seldom inhale, and
have a low cancer incidence, so that their inclusion has lowered the
apparent advantage of inhaling\footnote{See Note [lower down the page]}.

To test the significance of this apparent protection due to inhaling, we
must recognize the effects of random sampling not only due to the
limited number of inhalers, but equally of the non-inhalers with whom
they are compared.  This is conveniently done by reducing the deficiency
in the ratio of the non-inhalers to the total.

No particular importance need be attached to the test of significance.
It disposes at about the 1 per cent.\ level the hypothesis that inhalers
and non-inhalers have the same cancer incidence.  Even equality would be
a fair knock-out for the theory that smoke in the lung causes cancer.
The fact, however, and it is a fact that should have interested Hill and
Doll in 1950, is that inhalers get fewer cancers. and the difference is
statistically significant.

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\begin{tabular}{ccc}
\multicolumn{3}{c}{\textsc{Table 3}} \\
Cigs.\ \textit{per diem} & Reduced deficiency & Sampling variance \\
1--4 & \phantom{0}2.290 & \phantom{0}3.49 \\
5--14 & $\!-$1.947 & 24.60 \\
15--24 & 10.174 & 19.54 \\
25--49 & \phantom{0}5.301 & 17.10 \\
$>$49 & \phantom{0}3.485 & \phantom{0}3.75 \\ \hline
Total & 20.299 & 68.48 \\
Standard error\ \ \ \ & \phantom{0}8.274
\end{tabular}
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Should not these workers have let the world know, not only that they had
discovered the cause of lung cancer (cigarettes), but also that they had
discovered the means of its prevention (inhaling cigarette smoke)?  How
had the M.R.C.\ the heart to withhold this information from the
thousands who would otherwise die of lung cancer?

Those who refuse the jump from association to causation in the case of
cigarette smoking will not be tempted to take it in the case of
inhaling; but the M.R.C.\ and its Statistical Research Unit think this
argument is valid in the first case.  Can they refuse to admit it in the
second?

\bigskip\bigskip

\footnotesize{\textsc{Note:} Data from which 78 have been removed as
they did not smoke cigarettes, but which still include mixed smokers of
pipes and cigarettes give the enhanced effect expected and show apparent
protection'' of about 13 per cent.}

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\textit{Smoking: The Cancer Controversy}, Edinburgh: Oliver and Boyd
1959, pp.\,45--47.
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