Medical Statistics Don't Always Mean What They Seem to Mean columnist John Allen Paulos offers a few pointers on understanding the often confusing world of medical statistics.

Medical statistics are often misunderstood (perhaps up to 72.381672 percent of the time).

Sometimes they're consciously spun. More often they're just phrased in an opaque way.

Given all the stories in recent weeks on cancer screening (mammograms, psa tests, pap tests), the effectiveness of medicines, drugs and supplements (statins, tamoxifen, vitamin D), not to mention the focus on the health care bill, it is a good time to briefly discuss a few better ways to present medical results.

Relative Risk vs. Absolute Risk

To make my points general, I'll refer to an abstract cancer X rather than any particular real cancer, which is anything but abstract.

That being said, imagine that a headline announces that screening for cancer X reduces deaths from it by 25 percent. Imagine as well that another headline announces that screening cuts deaths from cancer X by about 1 in 1,000, reducing the rate from 4 in 1,000 to 3 in 1,000.

These two headlines can describe the same result, the first expressing relative risk and the second absolute risk. All things being equal, describing results in terms of absolute risk gives a more informative picture than does describing them in terms of relative risk.

Absolute risk allows you to see the magnitude of the benefit, which sometimes is not all that great, especially if the downside of the screening (false positives, over-treatment and the debilitating and disfuguring effects of radiation, chemotherapy and the like) is not immediately apparent.

We should always ask for the reduction in absolute risk and not just for the reduction of the relative risk. If cutting out an occasional portion of pork rinds, say, reduces your risk of some cancer by 67 percent, you may decide they're worth it if you know your absolute risk will decline from three in a million to one in a million.

Survival Rate vs. Mortality Rate

Now consider two different countries that treat the same disease, cancer Y, quite differently. The first country touts the fact that its five-year survival rate for Y is 100 percent, seemingly a great success. The other country admits that its 5-year survival rate for Y is 0 percent, seemingly a debacle.

But let's look at the mortality rates instead of the survival rates. It might be that in both countries there are approximately 45 cancer Y deaths per 100,000 people. How could this be? Simplifying to make the point, let's assume that if people in either country contract Y, they always get cancer in their mid 60s and live to the age of 75.

In the first country, there is an early screening program that identifies people with cancer Y in their mid-to-late 60s. Because these people live to 75, the five-year survival rate is 100 percent. The second country has no screening program at all, and people with Y are not diagnosed until they experience actual clinical symptoms in their early 70s. Their five-year survival rate is thus 0 percent.

The example is unrealistic and extreme, but a situation similar to it explained why Rudy Giuliani's superficially convincing claim a few years ago that American medicine was so much better than British medicine was wrong.

The five-year survival rate for prostate cancer is higher here, but mortality rates in the two countries do not differ that much. Because of the so-called lead time bias associated with survival rates, mortality rates often provide a clearer picture of a cancer.

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