In Lesson 3, Chapter 3 of Miguel Hernán's edX course on causal diagrams, he presents this DAG:

It represents a study on the effect of hormone therapy on lung cancer. Among women with lung cancer in Boston, a random sample of 1,000 has been selected for the study. Among women without lung cancer in Boston, a random sample of 1,000 has also been selected for the study. This accounts for the arrow between lung cancer and selection (i.e. outcome-based selection).

Then he adds that only women with hip fractures were surveyed ("they can't run away from you"), which accounts for the arrow between hip fracture and selection.

Finally, he says that hormone therapy actually reduces the risk of hip fracture, so the final arrow between hormone therapy and hip fracture is added, creating an open backdoor path.

My question is, if only women with hip fractures were surveyed, doesn't that mean we are conditioning on hip fractures? If so, there should be a square around hip fracture, the backdoor path is actually blocked, and there is no selection bias.

In Lesson 3, Chapter 3 of Miguel Hernán's edX course on causal diagrams, he presents this DAG:

It represents a study on the effect of hormone therapy on lung cancer (whether hormone therapy causes lung cancer). Among women with lung cancer in Boston, a random sample of 1,000 has been selected for the study. Among women without lung cancer in Boston, a random sample of 1,000 has also been selected for the study. This accounts for the arrow between lung cancer and selection (i.e. outcome-based selection).

Then he adds that only women with hip fractures were surveyed ("they can't run away from you"), which accounts for the arrow between hip fracture and selection.

Finally, he says that hormone therapy actually reduces the risk of hip fracture, so the final arrow between hormone therapy and hip fracture is added, creating an open backdoor path.

My question is, if only women with hip fractures were surveyed, doesn't that mean we are conditioning on hip fractures? If so, there should be a square around hip fracture, the backdoor path is actually blocked, and there is no selection bias.

In Lesson 3, Chapter 3 of Miguel Hernán's edX course on causal diagrams, he presents this DAG:

It represents a study on the effect of hormone therapy on lung cancer. Among women with lung cancer in Boston, a random sample of 1,000 has been selected for the study. Among women without lung cancer in Boston, a random sample of 1,000 has also been selected for the study. This accounts for the arrow between lung cancer and selection (i.e. outcome-based selection).

Then he adds that only women with hip fractures were surveyed ("they can't run away from you"), which accounts for the arrow between hip fracture and selection.

Finally, he says that hormone therapy actually reduces the risk of hip fracture, so the final arrow between hormone therapy and hip fracture is added, creating an open backdoor path.

My question is, if only women with hip fractures were surveyed, doesn't that mean we are conditioning on hip fractures? If so, then there should be a square around hip fracture, the backdoor path is actually blocked, and there is no selection bias.

In Lesson 3, Chapter 3 of Miguel Hernán's edX course on causal diagrams, he presents this DAG:

It represents a study on the effect of hormone therapy on lung cancer. Among women with lung cancer in Boston, a random sample of 1,000 has been selected for the study. Among women without lung cancer in Boston, a random sample of 1,000 has also been selected for the study. This accounts for the arrow between lung cancer and selection (i.e. outcome-based selection).

Then he adds that only women with hip fractures were surveyed ("they can't run away from you"), which accounts for the arrow between hip fracture and selection.

Finally, he says that hormone therapy actually reduces the risk of hip fracture, so the final arrow between hormone therapy and hip fracture is added, creating an open backdoor path.

My question is, if only women with hip fractures were surveyed, doesn't that mean we are conditioning on hip fractures? If so, there should be a square around hip fracture, the backdoor path is actually blocked, and there is no selection bias.