## Passive smoking and health risks.

“Passive smoking may be good for you” or so the tobacco companies would like us to believe! This idea arose from a misrepresentation of the confidence interval for data on passive smoking, and provides a good example of why we need a working knowledge of some statistics to deal with the propaganda that comes our way in General Practice. Sadly statistics is reported to be one of the subjects least liked by medical students, and those of us who have been in practice for more than a few years may be unfamiliar with some of the ways that results of studies are now reported. There has been a shift away from the use of p values towards Confidence Intervals (CI) in many medical journals, and the British Medical Journal now expects authors of papers to present data in this way.

## Don’t forget common sense

Before going into more detail about the use of Confidence Intervals the example quoted for passive smoking above may be swallowed by the public, and even in some cases by journalists, but hopefully most GPs would be suspicious that such a finding just does not make sense. It does not fit with all the other data that has emerged in the past 20 years, and therefore needs some further looking at. Never leave common sense behind when looking at statistical reports!

## Confidence Intervals or P values

So what are Confidence Intervals all about and how did they get misused in this example? In general when research is undertaken the results are analysed with two separate questions in mind. The first is how big is the effect being studied (in this case how big is the risk of lung cancer for passive smokers)? The second question is how likely is it that the result is due to chance alone? The two issues are connected, because a very large effect is much less likely to have arisen purely by chance, but the statistical approach used is different depending on which question you are trying answer. The “p” value will only answer the question “what is the chance that the study could show its result if the true effect was no different from placebo”? The Confidence Interval describes how sure we are about the accuracy of the trial in predicting the true size of the effect.

Both questions relate to the fact that we cannot know what the effect would be of a treatment or risk factor on everyone in the world; any study can only look at a sample of people who are treated or exposed to the risk. We then have to assume that if, say, one hundred identical studies were carried out in the same way on different groups of patients the results found would be normally distributed around the average effect size of the treatment. The larger the number of patients included in the trial the closer the result of that trial are likely to be to the true effect in the whole population. The result of any particular trial can therefore be presented as showing an effect of a certain size, and the Confidence Interval describes the range of values between which you can be 95% certain that the true value lies.

## The data on Passive Smoking

Perhaps this can be illustrated with the passive smoking data. The results were that the on passive smoking study in seven European countries showed that there was an extra risk of developing lung cancer of around 16% for non-smokers who were exposed to smoke in the workplace or who had a spouse who smoked. This was comparing 650 lung cancer cases with 1542 controls in Europe and was accompanied by an estimate that 1100 deaths occurred each year in the European Union as a result of passive smoking.

The 95% Confidence Interval associated with this data is shown in the diagram and the tobacco industry had just chosen to highlight the lower end of the Confidence Interval, which shows a small chance that passive smoking could be associated with a 7% lower rate of lung cancer! Unsurprisingly they did not report the equal chance that the risk may be as high as 44% more lung cancer in passive smokers, and the Sunday Telegraph swallowed the story whole. More details are provided in the excellent article by Simon Chapman in the BMJ 1998;316:945.

Gardner and Altman mention this danger in their book “Statistics with Confidence”, and they suggest that results should be presented with the effect size, confidence interval and p value to prevent this kind of misunderstanding. The first two chapters are well worth reading if you want a fuller understanding of the rationale behind the use of Confidence Intervals. A final point about the Confidence Interval is that when it crosses the no-difference line (as shown in the diagram above) then the results do not reach significance at the level chosen (usually 5%).

Simon Chapman points out however that a meta analysis in the BMJ in the 18 October 1997 issue compared 4626 cases with 477924 controls and showed a 24% excess risk of lung cancer in non-smokers living with smokers. The 95% Confidence Interval was 13%to 36% which is well clear of the no-difference line and hence highly statistically significant, with a p value of >0.001. Again this data was conveniently ignored.

The moral of the story is that you cannot believe it just because you read it in the Newspaper. As far as the advantages of passive smoking are concerned, they can join the other myths and misunderstandings documented in one of my favourite books Follies and Fallacies in Medicine by Skrabanek and McCormick.

Statistics with Confidence MJ Gardner and D Altman BMJ Publishing 1989

Follies and fallacies in Medicine Skrabanek and McCormick Tarragon 1998