By Lisa Martinez.  When I was in college, I would ask my math professors how I could apply what I had learned in my math courses to the real world of problems that I would encounter. I didn’t get much of an answer. However, if they had said math may save your life and help you make good health decisions, I would have said show me what you mean. Well here is how understanding a couple of math principles can make a huge difference in our healthcare decision-making.

Most likely you will know someone who has been diagnosed with cancer: family, friend or yourself. It can be a daunting task to understand recommended treatments and what those treatments may mean in terms of preventing a recurrence of cancer or a cure. For example, the media reports a 50% increase in survivorship. Pretty impressive and sounds like the latest miracle drug. However, when evaluating a treatment you should ask if the percentages you are being provided are the relative risk reduction or the absolute risk reduction percentages so that a fully informed decision can be made. In one study, 56.8% of patients chose the medication whose benefit was presented in relative terms and 14.7% chose the medication whose benefit was in absolute terms.*   The patients in this study thought that the true benefit was much greater than it actually was when relying on the relative risk.

Here is an example of relative versus absolute risk reduction:

100 women took ABC pill and 100 women took a placebo, which is not an actual medication. Of the 100 women who took ABC pill, 2 developed cancer and of the 100 women in the placebo group, 4 got cancer. It is reported that this clinical trial showed a 50% reduction in cancer and another report states that the same clinical trial showed a 2% decrease in cancer. Both percentages are accurate and that is because the data are being reported in two different ways.

The 50% reduction was reported using relative risk reduction. The 2% decrease was reported using absolute risk reduction. It is extremely important that you understand the difference between the two when making decisions about your care.

In the relative risk reduction report, 2 women who took the ABC pill out of 100 developed cancer and 4 women out of 100 who took the placebo got cancer. Two cancers in the ABC group are half as many as the four in the placebo group.

Thus the 50% increase in survivorship or calculate 2%/4% = 50%.

To calculate the absolute risk percentage, do the following calculation:

4% (placebo) – 2% (ABC pill) = 2% absolute difference.

Here are some other examples that should make the difference between absolute versus relative risk reduction even more clear.   

Group 1 Group 2 Absolute Difference(Group 1 – Group 2) Relative Difference(Group 2/Group 1)
40%   (4/10)      20%  (2/10) 20%     50%
4%   (4/100) 2%  (2/100)                  2%                                 50%
0.4%  (4/1000)           0.2% (2/1000)              0.2%                                50%

So when presented with options for chemotherapy or any treatment, make sure you ask your healthcare provider to give you the relative and the absolute risk reduction percentages. For the absolute risk reduction number, just ask your healthcare provider, “What is the actual number of patients out of 100 who benefited from the treatment?”

If your provider cannot answer that question, then ask that she or he find out for you. To be a savvy health advocate you must become statistically literate, and understanding the difference between relative risk versus absolute risk reduction moves you towards the head of the class.

To learn more about health statistics consider reading Know Your Chances: Understanding Health Statistics  by Steven Woloshin M.D.M.S.,Lisa M. Schwartz M.D.M.S., and H. Gilbert Welch M.D. M.P.H.

*Malenka DJ, Baron JA, Johansen S, Wahrenberger JW, Ross JM. The Framing Effect of Relative and Absolute Risk. J Gen Intern Med. 1993 Oct;8(10):543-8.

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