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3. (BoptsJ Suppose you are interested in the causal effect of smoking (A) on lung cancer (Y). but you are worried about confounding by parents'
3. (BoptsJ Suppose you are interested in the causal effect of smoking (A) on lung cancer (Y). but you are worried about confounding by parents' smoking (U): Children of parents who smoke are more likely to smoke. and are also more likely to develop lung cancer because of secondhand smoking. However, you believe that you can nd a genetic factor (Z) that are (i) causally associated with smoking; iii) independent of parents' smoking behavior; {iii} has no direct effect on lung cancer except for the effect that goes through smoking. {a} (4pts) Draw a DAG that represents this study. {b} (4pts) Find all the ancestors of A in alphabetical order (c) [4pts] Find all the children of A in alphabetical order {d} (4pts) Find all the paths between Z and Y. Which of them are causal paths? Noncausal paths? (e) (4pts) If we want to estimate the causal effect of E on Y, which set of variables shall we adjust for? if} [4pts] Given your DAG. if you know that the association between Z and Y is nonzero. can you use that information to decide if the causal effect of A on Y is zeroinonzero? {g} [4pts] Under your DAG. is it true that the genetic factor (Z) is independent of lung cancer {Y}, conditional on the smoking status (A)? Explain. {h} {3pts} Your collaborator is concerned that the genetic factor may have an direct effect on lung cancer. Draw a DAG to represent their concern. ii} [Spts] Find a statistical test to tell if your collaborator is correct. Hint: nd a set of conditional independence relationship that holds under your DAG. but not under your oollaborator's DAG
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