Confounding bias occurs when a variable influences both who is selected for the treatment and the outcome of the experiment. If a possible confounding variable is known, it is possible to control for the possible confounding variable. Researchers tend to control for all possible variables, which leaves the possibility of controlling for the thing you are trying to measure (e.g. controlling for mediators).
Confounding needs a causal solution, not a statistical one and causal diagrams provide a complete and systematic way of finding that solution. If all the confounders are controlled for, a causal claim can be made. However, it is not always sure whether all confounders are controlled for.
Randomization has two clear benefits. It eliminates confounder bias and it enables the researcher to quantify his uncertainty. Randomization eliminates confounders without introducing new confounders. In a non-randomized study, confounders must be eliminated by controlling for them, although it is not always possible to know all the possible confounders.
It is not always possible to conduct a randomized controlled experiment because of ethical, practical or other constraints. Causal estimates of observational studies can provide with provisional causality. This is causality contingent upon the set of assumptions that the causal diagram advertises.
Confounding stands for the discrepancy between what we want to assess (the causal effect) and what we actually do assess using statistical methods. A mediator is the variable that explains the causal effect of X on Y (X>Z>Y). If you control for a mediator, you will conclude that there is no causal link, when there is.
There are several rules for controlling for possible confounders:
- In a chain junction (A -> B -> C), controlling for B prevents information from A getting to C and vice versa.
- In a fork or confounding junction (A <- B -> C), controlling for B prevents information from A getting to C and vice versa.
- In a collider (A -> B <- C), controlling for B will allow information from A getting to C and vice versa.
- Controlling for a mediator partially closes the stream of information. Controlling for a descendant of a collider partially opens the stream of information.
A variable that is associated with both X and Y is not necessarily a confounder.
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