the front door is the direct causal path Smoking → Tar → Cancer, for which we do have data on all three variables. Intuitively, the reasoning is as follows. First, we can estimate the average causal effect of Smoking on Tar, because there is no unblocked back-door path from Smoking to Tar, as the Smoking ← Smoking Gene → Cancer ← Tar path is already blocked by the collider at Cancer. Because it is blocked already, we don’t even need back-door adjustment. We can simply observe P(tar | smoking) and P(tar | no smoking), and the difference between them will be the average causal effect of Smoking
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