POPH90014 Chap.6 Causal Questions, Counterfactuals and DAGs

Causal Questions, Counterfactuals and DAGs

Define causal contrast

The course material gives this chapter a concrete anchor: Week 6 links counterfactual reasoning, exchangeability and graphical assumptions.

That causal contrast anchor controls how exchangeability is explained and how directed acyclic graph is tested in changed practice.

Causal Questions, Counterfactuals and DAGs is a quantitative decision problem built from causal contrast, exchangeability and directed acyclic graph.

The aim is to frame PICOT questions and use DAGs to identify confounding control; a numerical result earns meaning only when the variables, units, assumptions and comparison are all explicit.

Begin with causal contrast: state what quantity it represents, the scale on which it is measured and the condition under which it changes.

Then map every symbol in the Causal Questions, Counterfactuals and DAGs formula checkpoint to causal contrast before calculation begins.

Next connect exchangeability to the calculation. Show the exchangeability transformation line by line, preserve units and signs, and make any denominator or baseline visible.

A exchangeability calculator output is not a method; the reader must be able to reconstruct why that operation answers the question.

Trace exchangeability

Use directed acyclic graph to interpret or stress-test the result.

Ask whether the directed acyclic graph magnitude is plausible, whether a boundary case behaves as expected and which conclusion would reverse if an assumption changed. This is where computation becomes analysis rather than arithmetic.

When the task is to frame PICOT questions and use DAGs to identify confounding control, separate inputs supplied by the problem from quantities you derive.

Then report the directed acyclic graph result in the language of the course and attach the relevant uncertainty, limitation or decision consequence.

Build a representation check before solving. Put causal contrast, exchangeability and directed acyclic graph into a small symbol-and-units table, mark which values are observed and which are calculated, and predict the direction of the result before doing arithmetic.

A sign, scale or unit mismatch in causal contrast then becomes visible at setup instead of being hidden inside a polished final number.

Run one sensitivity test after the baseline answer. Change the input most closely connected to exchangeability, hold the remaining assumptions fixed and recompute only the affected steps. Explain whether the movement in directed acyclic graph matches the mechanism.

This exchangeability sensitivity shows which assumption controls the conclusion and prevents a single scenario from being presented as universal.

Test with directed acyclic graph

Use a three-column causal contrast error log for POPH90014: translation error, calculation error and interpretation error.

Record the exact line where the exchangeability solution first diverged, rewrite that line, and check it with a limiting case or an independent calculation.

Correcting the first failed exchangeability move is more useful than copying the complete solution again.

A complete response should make the task visible before the detail: identify what must be decided, define the relevant terms, connect the evidence to exchangeability, and use directed acyclic graph to test the result.

The final sentence about directed acyclic graph should answer the question actually asked rather than merely repeat the topic.

The controlling limit is specific: adjusting for colliders or mediators can introduce bias.

Keep that directed acyclic graph limit beside the worked example, because it separates a careful POPH90014 answer from one that sounds confident but claims more than the task or evidence supports.

For revision, retrieve causal contrast, exchangeability and directed acyclic graph without notes, explain their relationship aloud, then complete a changed version of the application: frame PICOT questions and use DAGs to identify confounding control.

Record the first failed exchangeability reasoning move and repair it before attempting another case.

What this chapter covers

• 01

  Causal contrast

• 02

  Exchangeability

• 03

  Directed acyclic graph

• 04

  Applying causal contrast

• 05

  Limits of exchangeability and directed acyclic graph

Choose an adjustment set

Key terms

Causal contrast

Comparison between potential outcomes under alternative exposure states. This chapter uses the concept when students frame PICOT questions and use DAGs to identify confounding control. Use this definition when the task is to frame PICOT questions and use DAGs to identify confounding control.

Exchangeability

Condition under which compared groups represent the relevant counterfactual outcomes. It helps explain the reasoning required to frame PICOT questions and use DAGs to identify confounding control. Use this definition when the task is to frame PICOT questions and use DAGs to identify confounding control.

Directed acyclic graph

Directed graph encoding assumed causal relations without directed cycles. Its limit matters because adjusting for colliders or mediators can introduce bias. Use this definition when the task is to frame PICOT questions and use DAGs to identify confounding control.

Causal Questions, Counterfactuals and DAGs FAQ

Exam move

Reconstruct the relationship among causal contrast, exchangeability and directed acyclic graph; complete the chapter application without notes; then test the result against this limit: adjusting for colliders or mediators can introduce bias.

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