2
$\begingroup$

I wonder if case-control matching will bring a new confounding bias into the matched design. In the following figure, $L$ is a confounder, $E$ is the exposure, D is the disease outcome. In the matched design, $L$ can be correlated with $D$ through 1) $L\rightarrow E\rightarrow D$; 2) $L\rightarrow D$ (initial confounding); 3) $L\leftarrow S\rightarrow D$ (selection bias). Since L and D are marginally unassociated, so the overall effect over 1)+2)+3) must be 0. However, when we assess the effect of $E$ on $D$, $E$ is controlled for relative to $L$. So 1) is blocked for $L$. 2)+3) is not zero. Thus, $L$ and $D$ are correlated via paths 2)+3) in the matched design. Not adjusting for $L$ will lead to biased estimate of the exposure effect. (Mansournia et al IJE, 2013).

I understand 2) is the initial confounding effect of $L$; 3) is the selection effect by $L$. Why 3) can not be seen as a new confounding effect also? $L$ is a confounder and it is connected to $Y$ via path 3), which is a criteria for being a confounder.

So the general question is: can we see the backdoor selection bias path by matched confounders as a confounding bias path also? matched confounders are still correlated with $Y$ and $E$ in the matched design and the resulting bias is a confounding bias, right?

case-control design

$\endgroup$

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.