`I quite agree with you,’ said the Duchess; `and the moral of that is–Be what you would seem to be–or if you’d like it put more simply–Never imagine yourself not to be otherwise than what it might appear to others that what you were or might have been was not otherwise than what you had been would have appeared to them to be otherwise.’

`I think I should understand that better,’ Alice said very politely, `if I had it written down: but I can’t quite follow it as you say it.’

Lewis Carroll

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Virtually all of the results presented in medical studies are displayed as ‘average’ or ‘mean’ values. I’m sure everyone knows how to come up with an average or mean (the two are synonymous) value for a group of data points is to add them and divide the sum by the number of data points analyzed. For example, if you are a teacher, and you want to find out the average score on a test you gave to 30 students, you would add all the test scores together and divide by 30. You would then have the ‘mean’ or ‘average’ score of the students in your class.

Most medical papers list the mean values of whatever is being studied. If the researchers are trying to determine whether or not an experimental weight-loss therapy works, they add the weight lost by all the subjects participating in the study then divide by the number of subjects. The number they get is the ‘mean’ or ‘average’ weight loss brought about by the therapy being tested. It all sounds pretty reasonable and scientific, but is it really?

It would be realistic if we were all average people. But we’re not. And averages don’t represent us all that well. In fact, if you think about it, the average American would have one breast and one testicle.

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I’m throwing up this post on the concept of relative risk as a time saver. I’m going to be doing some posting soon in which relative risk plays a role as it has in many of the postings in the past. Instead of taking time in each post to explain relative risk, I will simply be able to link to this one and get on with it.

Let’s say we are studying the rate at which people taking a particular medication get cancer. If we randomize our study population into two groups and give one group the drug and the other group a placebo, we can wait around for 5 years (or 10 years or 20 or whatever our protocol is) to see how many develop cancer in each group. Then we can compare.

If after 5 years we find that 10 of the subjects taking the drug develop cancer and only 5 of the subjects taking the placebo get cancer, we can say (assuming there were equal numbers of people in both study groups to start) that twice as many people taking the drug got cancer. We can then say that the relative risk (usually written as RR) of getting cancer from taking the drug is 2.

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A paper appeared in last weeks JAMA that I just now got around to reading, but had already read about in a number of other publications. The study looked at the effect early-in-life obesity has on death from heart disease decades later. The paper is a real treasure trove of information worthy of a longer, more comprehensive blog later on. For now I want to use it as an example of how statistics can be used to humbug the non-statistically inclined.

In brief the JAMA study was done with data pulled from the monster-sized Chicago Heart Association Detection Project in Industry that was begun in 1967. Subjects who were at least 31 years old were evaluated for a number of parameters including BMI, blood pressure, elevated cholesterol, and history of smoking. The researchers re-evaluated these subjects over the next several decades.

Researchers divided the subjects into five groups: low risk, moderate risk, intermediate risk, elevated risk, and highest risk. It’s not important to the point of this post to get into what specifically constituted these varying levels of risk, but in general, the greater the number or the more severe the risk factors, i.e., elevated cholesterol, high blood pressure, etc., the more high-risk the category. The researchers then divided the subjects into three other groups based solely on BMI: normal weight, overweight, and obese. Within each of these three weight-related groups were spread subjects with varying degrees of risk. In other words, the normal weight group contained subjects who were low risk, moderate risk, intermediate risk, elevated risk and highest risk as a function of their cholesterol levels, blood pressures, smoking history, etc. It was the same for all the groups. The obese group was composed of obese subjects who ranged from low-risk to highest risk. The object of the study was to follow these subjects for many years to see if obesity was truly a risk factor for death from heart disease or if obesity led to elevated cholesterol, high blood pressure, and all the rest, which in turn caused the heart disease mortality.

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