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Seventy-five Percent More Radiation?

I’ve certainly noticed this trend before, but it wasn’t until I was emailing with an individual who had questions about radiation exposures that I realized the impact. The trend is the increasing regularity with which small changes on top of something already small is reported in big percentages to make headlines.
Here’s what I mean. If a headline states “Risk of Accident 75 Percent Higher On Highway” and they make the point that your risk of an accident is increased by 75 percent if you are driving a busy highway versus a rural road – that sounds frightening.
But is it? What are the numbers? What is the baseline? If the baseline rate of a highway traffic accident is one chance in 1,000 - one chance in 1,000 equates to 0.1 percent. A 75 percent increase in 0.1 percent is 0.075 percent for a total of 0.175 percent. So instead of one chance in 1,000, the risk is now 1.75 chances in 1,000. Yes, it is riskier to take the highway – almost twice the risk – but on a small risk to begin with, one must decide whether they want to burn more gas and time to take back roads (although maybe more scenic) rather than the highway.
The topic that the individual and I were emailing about was that a friend of hers had just taken her 4 year old to the doctor where they said they did not want to do x rays because it would raise the daughter’s cancer risk 4 percent. Not only was the mom frantic about her daughter’s health, now she’s told that a procedure that might diagnose an internal head injury won’t be done because of, what appears to be, a big cancer risk.
Although I strongly believe that imaging exams involving radiation must only be done when there is medical necessity, I found this conversation between the physician and the mom to be insensitive and very misleading. What we don't realize is that an increase of 4 percent when our background risk of cancer is 1 in 3 does nothing.  We have a 33 percent chance (1 in 3) of getting cancer with no additional radiation exposure. The 4 percent (which is a quote that is on the high side assuming they may simply have been talking about skull x rays or a head CT) increase would raise the normal incidence from 33 percent to 33.0132 percent. That would mean that our lifetime risk of cancer is 1 in 33.01 instead of 1 in 33 because we had the head imaging exam the doctors above were reluctant to perform.
Whether the physicians were correct about the 4 percent or not (and we don't know because we don't know what they were planning to do), what they failed to mention is that the amount is neglible given our normal incidence. In my opinion, this was a terrible and misinformed reason for not doing the exam. If, on the other hand, they felt that the exam would offer no additional evidence for treating the 4 year old, they should have stated such, and avoided alarming her mother unnecessarily.
The bottom line is to ask ourselves “4 percent of what?” or “75 percent of what?” What are the real numbers? If we were playing the lottery and my original chance of winning was 1 in 50 and that was increased 10 times to 10 in 50, I’d probably bet more money. If my chance of winning was 1 in a million and that was increased 10 times to 10 in a million, I probably wouldn’t play.
Remember to ask, what are the numbers?