Screening for breast cancer

As of the 23rd May 2022 this website is archived and will receive no further updates. 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.

Since 1988, women over 50 in the UK have routinely been offered screening for breast cancer, even if they have no other symptoms, and in 2004/05 1.7 million women were screened. Those with a positive mammogram are recalled for further investigations, at considerable cost in anxiety, resources and pain and discomfort. But how many of these women really have breast cancer?

First of all, we need some information about how the test performs. It has been estimated that in women between 50 and 70 years old, mammography will detect approximately 85% of breast cancers. In other words, out of 100 women with breast cancer, we expect around 85 to have a positive result, and 15 to have a negative result.

We also need to know how accurate the test is with women who don't have cancer. It has been estimated that around 10% of women with no cancer will still receive a positive result. In other words, out of 100 women without breast cancer, we expect around 10 to have a positive result, even though they don't have cancer. The remaining 90 will receive a correct (negative) result.

Finally, we need to know something about the underlying incidence of breast cancer in this population. This varies quite a lot by ethnicity and nationality, but in the UK it has been estimated that around 10 out of 1000 women aged 50 to 70 have breast cancer.

These numbers might seem a bit confusing, but we can use the animation below to see what we would expect to happen to 1000 typical women age 50-70 from the UK who attend screening.

You need to install the Adobe Flash Player to see the animation.

Of these, we expect around 10 to have breast cancer. Of those 10, we expect roughly 9 (rounded to nearest whole woman!) to have a positive mammogram, and we expect around 1 to have a negative mammogram.

This leaves 990 who don't have cancer. Of these, we expect around 99 (10%) to have a positive result, and 891 (90%) to have a negative result.

So, what proportion of those with a positive test result will have the cancer? In total, out of 1000 women, we expect around 9 + 99 = 108 will test positive. Of these, we expect around 9 will actually have cancer. That is, around 9/108, or 8%, of those with a positive result will actually have cancer. This seems a bit surprising -- even if you have a positive mammogram, you still probably don't have cancer. This is despite the fact that 85% people with cancer receive a positive result!

What about those who have a negative result? In total, around 892 (the vast majority!) will have a negative result. Of these, only 1 actually has cancer -- that's around 0.1% -- so if you screen negative it is quite reasonable to be reassured.

More information on breast cancer screening in the UK can be found on the Cancer Research UK website, who also provide the estimates of the mammogram accuracy which we have used.

When deciding whether to roll out a new mass screening programme (for example, for diseases such as prostate cancer), the benefits must be weighed against the costs of the test, the risks of taking the test, and cost to people who receive a positive result, and must undergo further invasive, stressful and possible risky testing, even if they do not actually have the cancer. This kind of analysis illustrates that even fairly accurates tests can lead to substantial investigations of people who turn out not to have the disease.

File BayesTheoremBreastCancer_1.xml529 bytes


It would be useful for some comment on the processes leading to a large difference between the calculations above and the observed values from the screening programme in the UK. i.e. From the CR-UK website ( ) for the UK in 2004/5 * 83,000 women were recalled for further tests – 4.8% of women screened (c.f. 10.8%) * Nearly 14,000 cancers were detected – 17% of those undergoing further tests, 0.8% of all women screened (c.f. 8% and 0.9%) where * More than 2 million women aged 50-70 years were invited for screening * 1.7 million women were screened * 2004 was the first year that women aged 65 to 70 were invited for breast screening

It is important to remember that your doctor does not necessarily think you have cancer if he or she suggests a screening test. Screening tests are given when you have no cancer symptoms. marire sani

I am a woman in the 50-70 age bracket and have been included in the NHS breast cancer screening programme since its inception. There are inaccuracies in the information on your website which I feel may have a negative impact on the health of women who read it. 1. You appear to be misinformed about what it means to have a ‘positive’ result from a mammogram. My understanding, as a recipient of the screening, is that the initial mammogram (often conducted in a mobile unit in a Park and Ride, or megastore, car park) provides evidence of any apparent abnormalities which should be further investigated. It does not provide evidence of breast cancer. 2. There is nothing frightening for women in being called to the Breast Clinic for further investigation, should this be necessary. A letter sent to me, in October 2009, stated clearly: “I should like to reassure you that many women need this additional check and the great majority are subsequently found to be absolutely normal.” 3. Your final paragraph may seem to readers to apply to breast cancer screening, but it does not have any relation to the facts of undergoing further investigation at an NHS Breast Clinic. First, there are no risks associated with having a mammogram. Second, there is nothing stressful or risky about most of the procedures which are used for further investigation, for example: a second digitised mammogram, an ultra-sound examination, aspiration of any breast cysts. The only stressful procedure is a biopsy which entails removing tiny samples of areas of ‘thickening’ or ‘tumours’. This is done with by inserting an instrument under local anaesthetic, in a manner similar to giving an injection. It would be a useful addition to your statistics to provide the percentage of women who are given this procedure during ‘further investigation’, following mammogram. I believe it to be a tiny proportion. Biopsies are essential to diagnose breast cancer and provide very welcome reassurance to those whose results prove negative. 4. When women contract breast cancer, early diagnosis is the primary factor in survival. Twenty years ago women who had breast cancer frequently died, not of course of the primary cancer but of the secondaries, for example in the bones. These only develop when the tumour has developed to sufficient size. The early diagnosis of breast cancer for women of my age group is often the result of mammogram screening. In many cases, in my experience, there is no ‘lump’ at this early stage that can be felt by manual examination. Mammogram screening for my age group saves lives. The numbers may seem small statistically, but each one represents a life and the happiness of friends and family. The mammogram ‘mass screening programme’ also prevents a large number of women in my age group from needing expensive follow-up treatment after surgery. New surgical techniques of carrying out a biopsy of the ‘sentinel lymph nodes’ make further treatment unnecessary for women whose breast cancer is diagnosed early. This represents a huge cost saving for the NHS directly resulting from the mass screening programme using mammography.

Assuming a 100% coverage is achieved (say in certain tony postcodes in Manhattan, or say, the 4 counties in Sweden where early trials took place)...... should every 'interval cancer', that is a cancer that pops up between screening intervals and is identified as a lump by the woman or detected during an incidental examination, be considered to be: a) a false-negative or b) an aggressive, rapidly growing type that just was not there in the first round of screening and ergo likely to do very badly with whatever treatment modality one throws at it. I am told, and am unsure how reliable this is, some breast cancer surgeon's practices in upper Manhattan comprise virtually all such women, i.e. those who have been told not so long ago as the screening interval is 1 year there, that they are screen negative and are utterly shocked and dumbfounded at the news as those two possibilities mentioned above sink in. Neither are easy to grapple with when on the receiving end of such news. Comments?

I think family history should be a big consideration since that does greatly increase one's risk. Yearly mammograms are recommended for all women starting at around 35-40, but if you have one or more family members who have had breast cancer or ovarian cancer you should start sooner. Monthly self exams should really start at puberty if for no other reason than to just get to know what is normal for your body and because many young women develop cysts. mesa senior retirement living

To the people that don’t think these “pink promotions” are doing any good for breast cancer: I agree with you that breast cancer is being employed as a cheap means of gaining sympathy and is used by most companies as nothing more than a marketing strategy for their other crap products (a lot like selling promotional items at a loss, except most places are actually making profits off of these “charity” promotions). I used to denounce these companies, too, but the reality is that most people have no interest/desire to care about breast cancer research unless they or someone close to them has suffered from it. I’d probably be guilty of the same thing… the only reason I even found this page is because I was searching for info about complications I had from a removal of a malignant node (and yes, men can have breast cancer, too - you can see for yourself what happened… bad breast reconstruction pics, but make sure you didn’t just eat). As shady as these companies are, with most giving maybe a penny to actual breast cancer research off of every pink nic nac they sell, the reality is that their “contribution,” as disingenuous as it is, is better than nothing at all. If it wasn’t for greedy, shady corporations trying to exploit ppl’s emotions, I don’t see any other way that we can raise awareness and garner support for this cause. And let’s face it, interest groups don’t work when the only money coming in is from the small group of ppl that are actually motivated enough to join. People just simply don’t care unless it’s affecting them directly…