Letters

Lung cancer and passive smoking

Turning over the wrong stone

Increased risk is not disputed

Nothing new was said

Scales for visual test of publication bias are unfair

Authors' reply

Turning over the wrong stone

EDITORIn their reanalysis of the epidemiological evidence on lung cancer and smoking Copas and Shi¹ assert that after allowing for publication bias the apparent average excess risk of lung cancer from passive smoking² would drop from 24% to 15%. Despite the lack of supporting data,³ we are asked to believe solely on the basis of statistical inference that such data must be hiding under a stone. They are, however, turning over the wrong stone.

More important than publication bias is the underestimation of risk that occurs when these studies assess exposure solely on the basis of whether non-smokers either lived or did not live with a smoker,² when other exposure exists.

Where other exposure is commonfor example, in childhood, in social situations, or in the workplacethe risk of lung cancer may be seriously underestimated. Spouses of non-smokers exposed in other circumstances will be misclassified as non-exposed, contaminating the referent group, and attenuating the risk estimate. For example, Hackshaw et al estimate that the odds ratio would have been 1.42 (95% confidence interval 1.21 to 1.66) if those with spousal exposure alone were compared with those who were truly unexposed.² By comparison, in a recent meta-analysis of risk associated with workplace exposure, Wells found an estimated relative risk of 1.39 (1.15 to 1.68) for the five studies meeting basic study quality standards.⁴ Repace and Lowrey found that when both workplace exposure and an unexposed referent group were taken into account in the American Cancer Society study of passive smoking and lung cancer, a population relative risk of 1.2 increased to 1.7.⁵

Repace and Lowrey modelled the risk of workplace exposure, estimating the average relative risk at 2.0 for office workers in the United States in the 1980s. This result is consistent with a value reported by Reynolds et al for women with 30 or more years of workplace exposurenamely, at ages at which lung cancer mortality begins to become significant.⁵

Moreover, all of these analyses focus on average risk. Repace et al estimated that individuals at the 95th centilefor example, those experiencing high smoker density and low air exchangehave an exposure, and a risk, as much as four times as high as those at the median. This result is commensurate with observations of dose⁵ and risk.²

Turning over stones may indeed alter the estimated risk, but turning over the right stone indicates that in the original meta-analysis, the actual passive smoking-lung cancer risk is underestimated, not overestimated.

Kenneth C Johnson, senior epidemiologist. 
Environmental Risk Assessment and Case Surveillance Division, Cancer Bureau, Laboratory Centre for Disease Control Health Protection Branch Health Canada, Ottawa, Ontario, Canada K1A 0L2 Ken_LCDC_Johnson{at}hc-sc.gc.ca

James Repace, health physicist. 
Repace Associates, Secondhand Smoke Consultants, Bowie, MD 20720, USA repace{at}erols.com

Competing interests: None declared.

Increased risk is not disputed

EDITORIn their paper on lung cancer and passive smoking,¹ Copas and Shi say that in our review of passive smoking and lung cancer there is clear evidence of publication bias and that allowing for this substantially lowers the estimate of relative risk (which we reported as 1.24 before correction for other biases and confounding and 1.26 after correction).² Neither is correct.

It is proposed that large studies will tend to be published regardless of their result but small studies published only if they are positive (publication bias). As Copas and Shi point out, studies with a large standard error (indicating a small study) tend to be associated with a large relative risk (correlation coefficient 0.35, P=0.03), implying that there may be some unpublished small negative studies. An indication of the size of the effect can be obtained by restricting the analysis to those studies with smaller standard errors which are less susceptible to increase publication bias. If the six studies with the largest standard errors (>0.5) are excluded there is no evidence for an association between standard error and relative risk (correlation coefficient 0.13, P=0.48) and the estimate of risk is 1.22; even if the 12 studies with the largest standard errors (>0.4) are excluded the estimate is 1.23; neither is materially different from the estimate based on all 37 studies (1.24). This indicates that the effect of unpublished studies is likely to be negligible.

There is further evidence against material publication bias in that 32 of the 39 studies reported non-significant results and in 16 (41%) the authors had either concluded that there was no effect (13) or that the evidence was inconclusive (3), suggesting that the passive smoking literature is one with a strong tendency for positive results to be published while negative results remain unpublished.

Even if one accepts the calculations of Copas and Shi, their relative risk estimate, which assumes that as many as 20% of all studies are unpublished, is 1.15, not substantially different from our own estimate (1.26) and well within the confidence interval on our result (1.06 to 1.47).² Even under the extreme assumption that 40% of studies were not published their estimate (1.11) would still be consistent with ours. Copas and Shi do not dispute that there is an increased risk of lung cancer due to passive smoking nor do they seriously challenge our estimates of its magnitude.

Allan Hackshaw, lecturer. 
a.k.hackshaw{at}mds.qmw.ac.uk

Malcolm Law, reader. 
Nicholas Wald, professor. 
Wolfson Institute of Preventive Medicine, Department of Environmental and Preventive Medicine, London EC1M 6BQ

Competing interests: None declared.

Nothing new was said

EDITORMy reaction to this paper is a big yawn. Copas and Shi think that there is evidence of publication bias against small studies that reach the negative conclusion that second hand smoke causes lung cancer. This is nothing new, nor is the analysis they present (based on something called a funnel plot).¹

Copas and Shi agree that a meta-analysis of the published studies on passive smoking and lung cancer shows a significant increase in risk of 1.24. They compute that if only 60% of the studies that have ever been done were published and that the remaining 40% of studies that were done but never publishedand that no one has ever heard ofwere all negative, then the increase in risk would only be 1.11 and not significant.

There is no evidence that these studies were ever done. Our investigation suggests that there is no publication bias.²

Copas and Shi also point out that if only 70% of the studies were published, and all the unpublished studies showed no elevation in risk, then the pooled risk would be 1.13 and significant (P=.052).

So, you could argue that they proved that, while failure to publish negative studies would lower the true risk of lung cancer associated with passive smoking, under any reasonable guess at how much "unpublished" research there was, there would still be an increase in risk. But despite the fact that many people have tried to find these unpublished studies, no one has been able to find them. The tobacco industry would make sure we knew about them.

What Copas and Shi say is that if several people did studies that found no effect of passive smoking and lung cancer and found no increase in risk, and we suddenly knew about these papers, then our estimate of how much the risk was increased would be smaller. But the risk would still be increased.

The real killer from second hand smoke is heart disease, not lung cancer. Heart disease kills about 10 times more people than lung cancer. Not even the tobacco industry has contested the evidence on asthma.

So . . . what's the big deal?

Stanton A Glantz, professor of medicine. 
University of California, San Francisco, CA 94143-0130, USA glantz{at}medicine.ucsf.edu

Competing interests: None declared.

Scales for visual test of publication bias are unfair

EDITORFunnel plots can be useful to detect publication and related bias. The funnel plot in the review of the epidemiological studies of passive smoking and lung cancer by Copas and Shi is, however, biased.¹ In the absence of publication bias the plot can be assumed to be symmetrical only if relative risks are plotted on a logarithmic scale. The scale used by Copas and Shi is not logarithmic and will give the visual impression of publication bias even when there is none. Studies indicating that exposure to passive smoking increases the risk of lung cancer will spread out on the graph because the relative risk may range from 1.0 to infinity; in contrast studies showing a reduction in risk will be compressed in the range of 1.0 to zero. Visual interpretation of the data is therefore not possible by using the scale presented.

Christopher Cates, general practitioner. 
Manor View Practice, Bushey Health Centre, Bushey WD2 2NN chriscates{at}emailmsn.com

Competing interests: None declared.

Authors' reply

EDITORWe thank the respondents for their comments on our paper. We agree with Johnson and Repace that the truth will be hiding under stones. Some of these stones (causes of bias) were considered in the earlier review by Hackshaw et al¹ They found that some stones give an increase in risk, others a decrease, and that on aggregate they tend to cancel out. What we have done is to add one more stone (publication bias) and use it to redo their calculation of the overall risk. It is not the wrong stone, just one of several stones.

Johnson and Repace start their letter by asserting that we claim that the excess risk decreases from 24% to 15%. We have not come up with a single best estimate. This is impossible without making assumptions that cannot be proved about how many unpublished studies there are. Our conclusion is that at least some publication bias is needed to explain the trend in the funnel plot, and that allowing for even a small amount of study selection can give a substantially lower figure.

The paper by Bero et al, which we did refer to in our paper, suggests that there is no publication bias.² We would emphasise the word "suggest"neither their arguments nor the fact that no unpublished papers have been found mean that none exists. Our analysis does not dispute that the risk is increased; the question is by how much. Neither do we claim that the unpublished papers were all negative. We can say nothing at all about them, just that there may be a pool of studies from which the ones in the review are a selection. Our method lets the funnel plot tell us how much bias there may have been in this selection.

Just because more people die of heart disease than of lung cancer does not necessarily mean that there are more deaths attributable to passive smoking. A rather similar review by He et al, who are looking at studies of passive smoking and heart disease, comes up with a relative risk of 1.28.³ Thus, in relative terms, the elevation of risk is fairly similar.

In their letter, Hackshaw et al point out that most of the range of estimates we discuss is within their confidence band. Publication bias is another source of statistical uncertainty but, unlike ordinary sampling variability, acts in the downward direction only. Whatever confidence range is given, it tends to be just the single figure which is remembered. If there is good reason to think this is an overestimate, then surely this needs to be pointed out.

Finally, Cates is right in pointing out that we did not use logarithmic scales in our funnel plot. We decided to plot the raw figures so they could be compared more easily with the various values of relative risk discussed in the earlier article by Hackshaw et al. But this is just the presentation. Our analysis was in fact based on log relative risks. To keep our paper as simple as possible we omitted all such statistical technicalities. A complete description of our method, including graphs on logarithmic scales, will appear later this year in the new statistical journal Biostatistics.⁴

John Copas, professor. 
Jain Qing Shi, research fellow. 
University of Warwick, Coventry CV4 7AL

Competing interests: None declared.

1.	Hackshaw AK, Law MR, Wald NJ. The accumulated evidence on lung cancer and environmental tobacco smoke. BMJ 1997; 315: 980-988.
2.	Bero LA, Glantz SA, Rennie D. Publication bias and public health policy on environmental tobacco smoke. JAMA 1994; 272: 133-136.
3.	He J, Vupputuri S, Allen K, Prerost MR, Hughes J, Whelton PK. Passive smoking and the risk of coronary heart diseasea meta-analysis of epidemiologic studies. New Engl J Med 1999; 340: 920-926[Abstract/Free Full Text].
4.	Copas JB, Shi JQ. Meta-analysis, funnel plots and sensitivity analysis. Biostatistics 2000 (in press).