When is the frontdoor criterion useful?

hard

Answer

$When unmeasured confounders make backdoor impossible, but a fully-mediating variable M exists.$
$E.g.$
$T \to M \to Y where all T-Y effect goes through M and no confounder acts on M.$
$P(Y\; \mid \;\mathrm{do}(T))\; = \;{\Sigma}_{m}$
$Classic example: smoking \to tar \to cancer, if we could measure tar but not the unobserved 'smoking-gene' confounder.$
$Rarely applicable in practice but a landmark result in causal inference theory.$

Check yourself — multiple choice

Random
Uses fully-mediating M: $P(Y \mid \mathrm{do}(T))\; = \;{\Sigma}$ $P(m \mid T)$ Σ $P(Y \mid m, t)$ P(t'); works even with unmeasured confounders on T; rare in practice
Same as backdoor
Not real

Frontdoor: mediating M identifies do(T) despite unmeasured T-Y confounders.

#causal-inference

Practise Statistics Fundamentals

215 interview questions in this topic.

Read the lesson Flashcards Take the quiz

Related questions