Topic 4 d-separation (Part 2)

Learning Goals

  1. Practice d-separation ideas with more examples





Why care?

In adjusting for variables in our analysis, we want to “do no harm”:

  • Block non-causal paths that generate unwanted associations
  • Do not accidentally create non-causal paths that generate unwanted associations
  • Leave causal paths (chains) alone





Example: Folic Acid and Birth Defects

Does maternal folic acid supplementation reduce the risk of birth defects? Or could associations be due to confounding factors? What should we adjust for in our analysis?





Example: Selection Bias

See handout!





Example: Estrogens and Uterine Cancer

Does postmenopausal estrogen supplementation (hormone replacement therapy) cause uterine cancer?

  • Consistent association between estrogen use and uterine cancer was noticed in the 1970s
  • Two hypotheses:
    1. Estrogens do cause cancer
    2. Estrogens don’t cause cancer but lead to uterine bleeding, leading to more frequent doctor visits, leading to increased diagnosis of existing cancer
  • Proposal for a study: restrict the study only to those with uterine bleeding and compare cancer rates in estrogen-users and non-users
    • In this way, all participants have the same chance of being diagnosed.
    • What could be wrong about this approach?
    • Can we design a better study?

Causal diagrams corresponding to the two hypotheses:

Work through the following questions in your groups:

  1. Consider the study proposal: restrict analysis to those with uterine bleeding.
    • Argue that under DAG 1, estrogens and diagnosed cancer will be associated.
    • Argue that under DAG 2, estrogens and diagnosed cancer will be associated.
    • Thus conclude that this study proposal cannot distinguish between the two competing hypotheses.
  2. Consider another study proposal: ensure that everyone is screened frequently, and we don’t restrict our analysis to only those with uterine bleeding.
    • What arrow (in either DAG 1 or 2) can be removed as a result of this study design?
    • In this study, say that we don’t find an association between estrogens and diagnosed cancer? What does this mean about paths from estrogens to diagnosed cancer?
    • In this study, say that we do find an association between estrogens and diagnosed cancer? What does this mean about paths from estrogens to diagnosed cancer?
    • Based on these investigations, make a conclusion about the quality of this study proposal as compared to the first.





Principles of building causal diagrams

A DAG is a causal DAG if it is common cause-complete: for any two variables in the DAG, common causes (whether measured or unmeasured) of those variables are shown.

  • A causal DAG does NOT need to be cause-complete (infeasible due to infinite regress of causes).
  • It should contain variables that are selected on, and subsequently common causes between those variables and existing variables.