Black Boxes and the Cochran-Mantel-Haenszel Equation

Take a look under the hood of those computer programs that make your life easier just to make sure they’re working correctly

There’s this funny thing that happens in biostatistics where not being careful in how you collect and analyze your data may lead to this effect called confounding. Confounding happens when you see an association between X and Y, but it’s actually Z that is the real cause for Y. I often explain it with a quick example with coffee drinking.

In a study of pancreatic cancer, it is found that coffee drinkers have higher odds of pancreatic cancer than those who don’t drink coffee. However, if you account for the fact that smokers are also more likely to drink coffee, you find out that coffee drinkers who smoke are at highest risk, followed by smokers who don’t drink… Drinking coffee is not what’s causing the cancer. It’s the smoking.

To figure out the exact odds of cancer in coffee drinkers versus non-drinkers, and drinkers who smoke and drinkers who don’t smoke, etcetera, etcetera, we use the Cochran-Mantel-Haenszel equation. It answers the question: What are the odds of disease given the exposure, adjusting for all confounding variables?

Frankly, a logistic regression is easier — in my opinion — but this is how we learn biostatistics, by doing the tough math first. Anyway, I’m going to use some data from North Carolina to show you how the…