Statistics Done Wrong: The Woefully Complete Guide by Alex Reinhart

Author:Alex Reinhart [Alex Reinhart]
Language: eng
Format: epub, mobi, pdf
Tags: MATHEMATICS / Probability & Statistics / General
ISBN: 9781593276737
Publisher: No Starch Press
Published: 2015-03-15T16:00:00+00:00

Correlation and Causation

When you have used multiple regression to model some outcome—like the probability that a given person will suffer a heart attack, given that person’s weight, cholesterol, and so on—it’s tempting to interpret each variable on its own. You might survey thousands of people, asking whether they’ve had a heart attack and then doing a thorough physical examination, and produce a model. Then you use this model to give health advice: lose some weight, you say, and make sure your cholesterol levels fall within this healthy range. Follow these instructions, and your heart attack risk will decrease by 30%!

But that’s not what your model says. The model says that people with cholesterol and weight within that range have a 30% lower risk of heart attack; it doesn’t say that if you put an overweight person on a diet and exercise routine, that person will be less likely to have a heart attack. You didn’t collect data on that! You didn’t intervene and change the weight and cholesterol levels of your volunteers to see what would happen.

There could be a confounding variable here. Perhaps obesity and high cholesterol levels are merely symptoms of some other factor that also causes heart attacks; exercise and statin pills may fix them but perhaps not the heart attacks. The regression model says lower cholesterol means fewer heart attacks, but that’s correlation, not causation.

One example of this problem occurred in a 2010 trial testing whether omega-3 fatty acids, found in fish oil and commonly sold as a health supplement, can reduce the risk of heart attacks. The claim that omega-3 fatty acids reduce heart attack risk was supported by several observational studies, along with some experimental data. Fatty acids have anti-inflammatory properties and can reduce the level of triglycerides in the bloodstream—two qualities known to correlate with reduced heart attack risk. So it was reasoned that omega-3 fatty acids should reduce heart attack risk.5

But the evidence was observational. Patients with low triglyceride levels had fewer heart problems, and fish oils reduce triglyceride levels, so it was spuriously concluded that fish oil should protect against heart problems. Only in 2013 was a large randomized controlled trial published, in which patients were given either fish oil or a placebo (olive oil) and monitored for five years. There was no evidence of a beneficial effect of fish oil.6

Another problem arises when you control for multiple confounding factors. It’s common to interpret the results by saying, “If weight increases by one pound, with all other variables held constant, then heart attack rates increase by . . .” Perhaps that is true, but it may not be possible to hold all other variables constant in practice. You can always quote the numbers from the regression equation, but in reality the act of gaining a pound of weight also involves other changes. Nobody ever gains a pound with all other variables held constant, so your regression equation doesn’t translate to reality.

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