Regression discontinuity design can return a causal effect by
shielding the exposure of interest from (unobserved) confounding. It
does so through a forcing variable, a score or alike with a threshold
that is the sole cause of exposure. For an epidemiology overview see here.
As always a DAG
better expresses this.

For DAG aficionados, this looks a bit front doory? Front door
criterion is sort of akin to a reverse instrumental variable. This is
where a mediator of a confounded exposure acts as the instrument for the
exposure. Examples are hard to find. The regression discontinuity
example is a bit different, here the exposure rather than the mediator
is the shielded variable. Also the shielding variable does effect the
outcome. But does it have the property of the front door criterion? The
forcing variable / exposure relationship is identifiable as the outcome
(a collider) blocks the open path. Exposure / outcome relationship is
identifiable by backdoor adjustment for the forcing variable.

There are different flavours of regression discontinuity design. What
we might call the randomized is based on a slightly different DAG
(below). Analysis focuses entirely on the threshold of the forcing
variable. Here forcing variable measurement error means that exposure is
effectively randomized and adjustment isn’t needed.

Caveat time. This is just my drawing of the design, others exist. and
this is a blog, so my language is imprecise, and mistakes even more
likely. To read more about the front door criterion see The Book of Why.

### Citation

For attribution, please cite this work as

Popham (2019, April 18). Frank Popham: Knock knock. Who’s there? It’s regression discontinuity! But which door?. Retrieved from https://www.frankpopham.com/posts/2019-04-18-knock-knock-whos-there-its-regression-discontinuity-but-which-door/

BibTeX citation

@misc{popham2019knock,
author = {Popham, Frank},
title = {Frank Popham: Knock knock. Who’s there? It’s regression discontinuity! But which door?},
url = {https://www.frankpopham.com/posts/2019-04-18-knock-knock-whos-there-its-regression-discontinuity-but-which-door/},
year = {2019}
}