Statistics and Risk

Almost daily we are bombarded with statistics about risk factors for disease, side effects from medications and chances for dying! The concept of "risk" is difficult to understand and difficult to explain. Statistics are also difficult to understand and thus can be and are manipulated to make a point or generate a sexy headline.

Scientific studies are an attempt to answer a question. The question may be an effect of a drug on a disease or perhaps looking for an association between a behavior and the development of a disease. Some associations or effects occur by chance or coincidence; hence the occurrence of "miracle cures." Statistical analysis of the data from a scientific study asks the question "is this association real or due to chance." An association that is real is considered "statistically significant" and not due to chance alone.

Statistical significance does not necessarily mean that the association will benefit you as a patient. For example, in his book "Innumeracy, Mathematical Illiteracy and its Consequences" John Paulos gives the example of a medication that has been statistically proven to alleviate 3% of all migraine headaches. The medication would be advertised as providing relief in a "significant" percentage of cases. But, how much money would you spend on it?

When evaluating a statistical phenomenon it is important to understand exactly what the numbers mean. " Birth control pills triple your risk of a blood clot." This is a true statement. Why, if true, would any competent physician prescribe birth control pills? Well the absolute risk rises from 1 in 10,000 (0.01%) to 3 in 10,000 (0.03%). For comparison purposes the risk of developing a blood clot during pregnancy is 6 in 10,000 (0.06%). I call this the numerator without a denominator phenomenon. The numerator does indeed increase, but the denominator is so large the absolute risk is very small.

Another factor to keep in mind is the age specific risk of developing a disease. The oft-quoted 1 in 8 risk of developing breast cancer is true, for a 90-year-old woman. The age related risk of developing breast cancer is 1 in 217 for a 40-year-old woman and 1 in 50 for a 50-year-old woman. This is not to diminish efforts to reduce risks of breast cancer or discourage women to have mammograms. However some women are unduly alarmed by the 1 in 8 statistic. There is a computer program available, called the Gail Model, which allows us to derive an individual’s specific risk for developing breast cancer over the next five years and a lifetime risk. I have found that most women are surprised to learn their risk of developing breast cancer is lower than they think.

Now lets look at the use of percentages when evaluating the effect of a drug or lifestyle choice on diseases. Estrogen replacement therapy for postmenopausal women increases the risk of breast cancer by 30%! This sound like 30%, or 1 in 3 women, who take estrogen will develop breast cancer. On the contrary, even if the studies are reliable, it means that the age related risk increases by 30%. If a woman lives to her 90’s her lifetime risk of developing (but not necessarily dying from) breast cancer is about 1 in 8. Thus for those women who are on hormone replacement therapy the lifetime risk may increase by 30% to 1.3 in 8 women. Contrast this to the risk of developing lung cancer in smokers as opposed to non-smokers. According to the American Cancer Society female smokers are 13 times as likely to die from lung cancer compared to non-smokers. That means that cigarette smoking increases the chances of dying from lung cancer by 1300%!

When evaluating a study about a lifestyle or drug related risk to health it is important to ask, "Does this study relate to me? What does the percentage mean? What is the denominator?" Remember that eye-catching headlines about health are designed to grab your attention. It is up to you to carefully review the information and understand what the numbers mean. If you are still confused, ask your physician for his or her opinion of the study.