Willing the data to fit your model

It strikes me that in medicine, we are stuck with simplistic models - models that use one variable only, and are linear in the response. In short, we are told X results in Y, and the more X, the more Y. Real life often does not cooperate, but many people in medical research hold on to their models for dear life.

Exhibit 1 is the disappearing of unhelpful data used to reject the non-linear relationship between BMI and mortality, which I discussed here. There are many myths associated with the obesity epidemic. It is a surprise for me to learn that how inefficient physical exercise is for weight loss.

Exhibit 2 is the case of vitamin overload, as described in this NYTimes column. Here are the juicy bits:

In December 1972, concerned that people were consuming larger and larger quantities of vitamins, the F.D.A. announced a plan to regulate vitamin supplements containing more than 150 percent of the recommended daily allowance. Vitamin makers would now have to prove that these “megavitamins” were safe before selling them. Not surprisingly, the vitamin industry saw this as a threat...

Industry executives recruited William Proxmire, a Democratic senator from Wisconsin, to introduce a bill preventing the F.D.A. from regulating megavitamins.

A little more than a month later, Mr. Proxmire’s bill passed by a vote of 81 to 10. In 1976, it became law. Decades later, Peter Barton Hutt, chief counsel to the F.D.A., wrote that “it was the most humiliating defeat” in the agency’s history.

The studies cited in the article show that too much of a good thing kills.

Exhibit 3 is the demonization of salt. It's completely ingrained in our brains that salt is bad for us. However, the evidence is decidedly mixed. New York Times has a summary recently (link). Years ago, I remember reading the late David Freedman's article coming to the same conclusion. (D.A. Freedman and D.B. Petitti. “Salt and blood pressure: Conventional wisdom reconsidered.” 2001.)

A key sentence in the NYT's article is this:

Until about 2006, almost all studies on salt and health outcomes relied on the well-known fact that blood pressure can drop slightly when people eat less salt. From that, and from other studies linking blood pressure to risks of heart attacks and strokes, researchers created models showing how many lives could be saved if people ate less salt.

This is also typical of medical studies, the assumption of transitivity between studies. Anyone trained in statistics would have left transitivity at the door. When each number is not precisely estimated but has an error bar around it, transitivity is not automatic. Notice that the data did not prove the health benefit of less salt; it's the models that assume such benefits.