The OP’s assertion is true. Stratifying on certain variables can introduce bias.
Consider that you have a cohort of initially healthy men, and you are trying to quantify the causal relationship between an exposure (eg eating hamburgers) and an outcome (eg death). You have also measured a third variable, which is angina pectoris (cardiovascular disease).
Assume that the true underlying causal structure, which you are unaware of, is that hamburgers cause cardiovascular disease, which subsequently causes death.
Now look at what happens if you stratify on cardiovascular disease: In the strata consisting of men who don’t have cardiovascular disease, you will find no cases of death. This will lead you to conclude that in men who don’t have cardiovascular disease, eating hamburgers does not cause death. This is false, as eating hamburgers will cause them to develop cardiovascular disease and then die.
What you have done in this situation, is stratify on a mediator, thereby “blocking” the pathway running through it. There are also many other situations in which adjusting for a variable introduces bias, but it gets more complicated from here.
The OP’s assertion is true. Stratifying on certain variables can introduce bias.
Consider that you have a cohort of initially healthy men, and you are trying to quantify the causal relationship between an exposure (eg eating hamburgers) and an outcome (eg death). You have also measured a third variable, which is angina pectoris (cardiovascular disease).
Assume that the true underlying causal structure, which you are unaware of, is that hamburgers cause cardiovascular disease, which subsequently causes death.
Now look at what happens if you stratify on cardiovascular disease: In the strata consisting of men who don’t have cardiovascular disease, you will find no cases of death. This will lead you to conclude that in men who don’t have cardiovascular disease, eating hamburgers does not cause death. This is false, as eating hamburgers will cause them to develop cardiovascular disease and then die.
What you have done in this situation, is stratify on a mediator, thereby “blocking” the pathway running through it. There are also many other situations in which adjusting for a variable introduces bias, but it gets more complicated from here.
For further information on this I suggest reading an upcoming book called “Causal Inference”, by James Robins and Miguel Hernan, who taught me this material. The first ten chapters are available for free online at http://www.hsph.harvard.edu/faculty/miguel-hernan/files/hernanrobins_v1.10.9.pdf .