False Positives

When I was in high school, every once in a while a suspicious looking truck would park outside the school. One by one, female employees would slip in and out of this truck throughout the day. The truck, which looked like some kind of mobile spy headquarters complete with satellite uplink turned out to be a local effort to improve women's health. It was a Mobile Mammography Van sponsored by a local hospital. My friends and I thought more than once about hijacking that van and parking it outside the local mall. Hey, we were teenagers.

Fast forward to the present, when the American College of Physicians has released new recommendations regarding preventative mammograms. They argue that women under 50 with no medical history of cancer or other high risk factors need not be subjected to yearly mammograms. The current recommended age is 40, supported by the American Cancer Society. This is a case where mathematics must influence our decision making process. More and more, the medical profession seeks to back up its dogma with statistics. This is a good thing if it is done correctly. Unfortunately, most doctors do not understand the math themselves and certainly can't explain it to their patients. Let's look at the numbers for mammography.

The rate of false positives for this test is estimated to be between 7-15%. This is higher than in most other first-world countries. Why? What is a false positive rate? A false positive, or Type I error, is a positive an erroneous positive result. The patient does not have cancer, but the test shows that she does. No test is perfect. All medical tests give a certain amount of false positives. The rate is calculated by dividing the number of false positives by the number of total negative instances.

false positive rate = number of false positives/ number of negative instances

This means that out of 100 non-cancerous women receiving test results for a mammogram, between 7-15 of them will be told they have cancer. Imagine getting that news. To most, cancer equals death. The anxiety alone could contribute to a host of actual medical issues. Then there is the added cost and frustration of additional tests, which will now include biopsies. This high rate also virtually guarantees that over the course of a decade, or ten yearly tests, women will receive at least one false positive.

Then there is the problem of over-diagnosis.

The widespread and virtually unchallenged acceptance of screening has resulted in a dramatic increase in the diagnosis of ductal carcinoma-in-situ (DCIS), a pre-invasive cancer, with a current estimated incidence of about 40,000 annually. DCIS is usually recognized as micro-calcifications and generally treated by lumpectomy plus radiation or even mastectomy and chemotherapy. However, some 80 percent of all DCIS never become invasive even if left untreated. Furthermore, the breast cancer mortality from DCIS is the same— about 1 percent— both for women diagnosed and treated early and for those diagnosed later following the development of invasive cancer. That early detection of DCIS does not reduce mortality is further confirmed by the 13-year follow-up results of the Canadian National Breast Cancer Screening Study.

These are the facts. So before you decide to get a test that is embarrassing, uncomfortable, or even painful for some, do the math. Decide for yourself if it is necessary for you. Ask your doctor for his/her false positive and false negative rates. If your doctor stares at you with a blank expression, you may want to look for another physician.