BMJ 2000;320:417-418 ( 12 February )
Papers
Reanalysis of epidemiological evidence on lung cancer and passive
smoking
J B Copas, professor,
J Q Shi, research fellow.
Department of Statistics,
University of Warwick, Coventry CV4 7AL
Correspondence to: J B Copas jbc@stats.warwick.ac.uk
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Abstract |
Objective:
To assess the epidemiological evidence for an increase in the risk of lung cancer resulting from exposure to
environmental tobacco smoke.
Design:
Reanalysis of 37 published epidemiological studies previously included in a meta-analysis allowing for the possibility of publication bias.
Main outcome measure:
Relative risk of lung cancer
among female lifelong non-smokers, according to whether her partner was
a current smoker or a lifelong non-smoker.
Results:
If it is assumed that all studies that have ever been carried out are included, or that those selected for review
are truly representative of all such studies, then the estimated excess
risk of lung cancer is 24%, as previously reported (95% confidence
interval 13% to 36%, P<0.001). However, a significant correlation
between study outcome and study size suggests the presence of
publication bias. Adjustment for such bias implies that the risk has
been overestimated. For example, if only 60% of studies have been
included, the estimate of excess risk falls from 24% to 15%.
Conclusion:
A modest degree of publication bias leads to a substantial reduction in the relative risk and to a weaker level
of significance, suggesting that the published estimate of the
increased risk of lung cancer associated with environmental tobacco
smoke needs to be interpreted with caution.
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Key messages
- A systematic review of epidemiological studies on passive
smoking estimated the increased risk of lung cancer as 24%
- There is clear evidence of publication bias in these studies
- Reanalysis of the data allowing for the possibility of
publication bias substantially lowers the estimate of relative risk
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Introduction |
Exposure to environmental tobacco smoke (passive smoking) is
widely accepted to increase the risk of lung cancer, but different epidemiological studies have produced varying estimates of the size of
the relative risk. Hackshaw et al reviewed the results of 37 such
studies that estimated the relative risk of lung cancer among female
lifelong non-smokers, comparing those whose spouses (or partners) were
current smokers with those whose spouses had never
smoked.1 Of the 37 studies, 31 reported an increase in risk, and the increase was significant in seven studies. The remaining six studies reported negative results, but none of these was
significant. Pooling these results using a method which allows for
statistical heterogeneity between studies, Hackshaw et al concluded
that there is an overall excess risk of 24% (95% confidence interval
13% to 36%).1 This is strong epidemiological evidence
for an association between lung cancer and passive smoking (P<0.001).
The approach used by Hackshaw et al does not allow for the
possibility of publication bias
that is, the possibility that
published studies, particularly smaller ones, will be biased in favour
of more positive results. We reanalysed the results and looked for evidence of publication bias.
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Methods and results |
The figure shows the relative risks from the 37 epidemiological
studies analysed by Hackshaw et al1 plotted against a
measure of the uncertainty in that relative risk. This uncertainty (s) decreases as the size of the study increases so that large studies are
on the left of the plot and small studies on the right. The plot shows
a trend for smaller studies to give more positive results than the
larger studies (correlation=0.35, P<0.05, or P=0.012 by Egger's
test2). This graph is similar to the funnel plot used in
the meta-analysis of clinical trials, when a trend such as this is
interpreted as a sign of publication bias.3 This bias
arises when a study is more likely to be written up and submitted to a
journal and more likely to be accepted for publication if it reports
positive results than if its results are inconclusive or negative.
Since it is reasonable to assume that publication is more likely for
larger (small s) than smaller (large s) studies, the problem of
publication bias will be most evident among the smaller studies, as
suggested by the figure. By "publication" we mean the whole process
of selecting a study for review.
View larger version (10K):
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Plot of relative risk of lung cancer versus s (standard
deviation of log relative risk). Overall weighted average of relative
risk is shown as dotted line and fitted value (publication
probability=0.8) as dashed line
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We reanalysed the results of the 37 epidemiological studies
to allow for the trend evident in the figure. Our method describes the
apparent relation between relative risk and study size by a curve. This
gives a good fit to the observed points. The basic idea of the
method is that there is no real relation between study outcome and
study size, the relation that we observe is simply an artefact of the
process of selecting these studies.
Our method has been published,4 and further details
are available from us on request. The estimated average
relative risk depends on a statistical parameter that can be
interpreted as the probability that a paper with a certain value of s
is published (publication probability. If the publication probability
is 1, all papers are published and so there is no possibility of
publication bias; the relative risk is then estimated as 1.24 (24%
risk excess), agreeing as expected with Hackshaw et al's
result.1 But smaller values of publication probability
give smaller estimates of relative risk. We do not know how many
unpublished studies have been carried out. Therefore there is no way of
estimating the publication probability from any data: all we know is
that there is a significant correlation in the funnel plot, so that
some degree of publication bias is needed to explain this trend.
The table gives the estimated relative risk for values of
publication probability between 0.6 and 1, together with 95%
confidence intervals and P values. The P value is less than 5% only
when the publication probability is more than about 0.7. The indirect estimate of 19% excess risk derived from studies on biochemical markers (table 5 of Hackshaw et al's paper1) agrees with
the epidemiological analysis when the publication probability is about 0.9.
View this table:
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Estimated relative risk and number of unpublished smaller and
larger studies for various values of publication probability
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For any given value of publication probability it is possible to
estimate the number of studies which have been undertaken but not
published. This is shown in the final two columns of the table. If the
publication probability is 0.8 then there are a total of 23 unpublished
studies so that the 37 selected ones represent a sample of 37/60=62%
of all such studies that have been undertaken. If this is the case,
then the excess risk is likely to be closer to 15% than 24%. The
dashed line in the figure shows the fit from our statistical model when
the publication probability is 0.8; this curve fits the available
evidence well.
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Conclusions |
Although the trend in the figure seems clear, Bero
et al suggest that the number of unpublished studies is unlikely to be large,5 and so the problem of publication bias may be less severe here than in systematic reviews of other aspects of medicine. However, the possibility of publication bias cannot be ruled out altogether, and at least some publication bias is needed to explain the
trend we found. Our results show that the publication probability does
not have to fall much below 1.0 before there is quite a substantial reduction in the estimated risk.
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Acknowledgments |
Contributors: The reanalysis was done jointly by JBC
and JQS. JBS was responsible for the presentation of the paper and is
the guarantor.
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Footnotes |
Funding: Economic and Social Research Council.
Competing interest: None declared.
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References |
| 1.
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Hackshaw AK, Law MR, Wald NJ.
The accumulated evidence on lung cancer and environmental tobacco smoke.
BMJ
1997;
315:
980-988[Abstract/Full Text].
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| 2.
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Egger M, Smith GD, Schneider M, Minder C.
Bias in meta-analysis detected by a simple graphical test.
BMJ
1997;
315:
629-634[Abstract/Full Text].
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| 3.
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Egger M, Smith GD.
Misleading meta-analysis.
BMJ
1995;
310:
752-754[Full Text].
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| 4.
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Copas JB.
What works; selectivity models and meta analysis.
J R Stat Soc Am
1999;
162:
95-109.
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| 5.
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Bero LA, Glantz SA, Rennie D.
Publication bias and public health policy on environmental tobacco smoke.
JAMA
1994;
272:
133-136[Medline].
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(Accepted 1 November 1999)
© British Medical Journal 2000
(none)
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Abstract
Introduction