Sometimes statistical models really can predict what will happen

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was produced by the Winton programme for the public understanding of risk based in the Statistical Laboratory in the University of Cambridge. The aim was to help improve the way that uncertainty and risk are discussed in society, and show how probability and statistics can be both useful and entertaining.

Many of the animations were produced using Flash and will no longer work.

I have just put an article up on the science blog on The Times website about the recent 'breakthrough' in screening for colorectal cancer. Not only was this, for once, a real breakthrough, but it was almost exactly as predicted in a publication 17 years ago.

I have a massive conflict of interest in this story: I know the researchers, was on the MRC Committee that part-funded the study, sat on the Trial Steering Committee and am now its Chair. But I make no apologies for bringing attention to this wonderful piece of science.



I am not a statistician but if 170000 people were randomised then 100 cancer deaths were saved in approximately 85000 people. So for any individual there is a 1 in 850 chance of benefit or 0.00118%. Put another way 99.9988% of patients undergoing the test do not benefit. Please correct me if I am wrong. Is this what we tell the people before they are screened because if we did I am not sure anyone would have the test.

This comment assumes equal numbers of control and intervention groups and 100% follow-up. The calculation of percentages is also out by two orders of magnitude. Look at the the abstract of the article and it is clear that the authors' central estimate is that deaths from colorectal cancer were cut by one in just less than 500 people screened. An absolute risk reduction of 0.2%. Presumably doctors who understand absolute risk reduction might use this figure, or the one on the incidence of these cancers. They might use the relative risk reductions figures (43% cut in mortality). Either way they need to be balanced against good data on the risks of the procedure to help the patient make an informed choice.

Thanks for the correction on the percentage. Still the absolute risk reduction is very low. The actual (not estimate) reduction in colorectal cancer deaths based on the figures in the abstract is still 1 in 850, so 849 sigmoidoscopies are of no benefit. I struggle with this sort of absolute risk reduction. There is clearly statistical and overall population benefit but when confronted with an individual patient they are only interested in their own personal benefit which is very small. For other surgical interventions there is much debate on the merits or otherwise of intervening even when the overall absolute benefits are greater than this. I realise this is but one of many examples in medicine eg cholesterol and blood pressure lowering therapy. I think that therapies with these low absolute risk reductions are almost never explained properly to patients and are always couched in terms of relative risk