The Front Door

Smoking, tar and cancer with a hidden genotype: the front-door formula recovers the effect until its assumptions are broken.

Day 54: The Front-Door Criterion

Genotype → smoking0.60Genotype → cancer0.30Smoking → tar0.80Tar → cancer0.10Violation: direct smoking → cancer0.00Violation: genotype → tar0.00

naive bias

0.180

front-door bias

0.000

Smoking (X), tar (M), cancer (Y) and an unobserved genotype (U). All probabilities are exact. The front-door formula uses only X, M and Y; it matches the truth as long as there is no direct X → Y arrow and U does not affect M. Turn those on to watch it fail.

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