What does "by" mean?

You study some really weird texts.

"Inverse association" seems to be the key phrase in understanding this.

"Residual confounding by smoking" is not easily understood, and is not standard English, but it seems to mean what you think it means.

What is residual confounding

http://www.pmean.com/10/ResidualConfounding.html

Ah. A phrase in "professional jargon" which needs seven paragraphs and about 500 words to explain it.

I don't feel so bad about not getting it straight away, then.

It's pretty clearly established that smoking causes lung cancer. They're researching the effect of other things on lung cancer, in particular BMI (presumably Body Mass Index, which rather simplisitically speaking is a measure of how fat you are). They find that higher BMI means lower incidence of lung cancer. I think by "residual confounding" they mean that it doesn't seem to correlate with smoking,, or that when you can statistically factor out the effect cigarette smoking has on lung cancer, you still find a correlation, and they're not sure why it's there. In other words, cigarette smoking is going to have a large effect on anything dealing with lung cancer, and statistically you have to control for that in your calculations and your conclusions to get anything validm, and when they do that they have a result whose reasons they can't fully explain