CDC obesity stats confusion

[lightingtool]

Here’s a link to a CNN report on the CDC’s new obesity study, and here’s a quote to kind of sum up the article:

@CNN

The Centers for Disease Control and Prevention reported that obesity accounts for 25,814 deaths a year in the United States. As recently as January, the CDC came up with an estimate 14 times higher: 365,000 deaths.

My confusion comes from a paragraph near the end.

@CNN again

The new study attributes 111,909 deaths to obesity, but then subtracts the benefits of being modestly overweight, and arrives at the 25,814 figure.

How does that work? Does that mean the 111,909 figure includes people who didn’t really die from being overweight?

[Trunk]

Here’s what I wrote in The Pit. . .this is what I think is going on.

Here’s the analogous quote from the NYT. . .it’s a little clearer.

@NYT

Now the new study says that obesity and extreme obesity are causing about 112,000 extra deaths but that overweight is preventing about 86,000, leaving a net toll of some 26,000 deaths in all three categories combined, compared with the 34,000 extra deaths found in those who are underweight.

I believe we’re talking about “modelled” vs. “actual” causes of death here.

I THINK what’s going on is they originally said something like, “through our models of the risk of obesity, we predict 112,000 deaths per year.”

What they failed to take into account are the safety factors associated with being a little overweight.

They either didn’t take them into account, or they applied the “obesity” model to “overweight” people. Notice in your CNN quote, they’re making a distinction.

Mathematically (if this helps), there was possibly a “survival model” with a term like. . .

Survival Probability = K^(-a(w-w0)) 

where K is a constant (or depends on things except weight), a>0, w is weight, and w0 is some "baseline" weight. 

when in fact it should have been 
S.P. = K^(-a1w*I(w > w0) + a2w*I(w <= w0))

where I is an indicator function, and the a's are appropriate multipliers.