Statistics + causal inference¶

Open Frontier

What you will develop¶

Define estimands; separate prediction from intervention; identify confounding, selection and measurement bias; estimate and stress-test effects.

Before you begin¶

Recorded prerequisites:

• Probability

Study and practice¶

Progress by the work you can do, not by a fixed calendar.

Practice sequence 25¶

Spine: Hernán & Robins, Causal Inference: What If (2024 revision)

Reading: Part I Ch. 1-3, approx. pp. 3-42: causal effects; randomized experiments; observational studies

Know: Define counterfactual causal effects and target trials; separate identification from association.

Reconstruct: Write potential-outcome estimands for a binary intervention and derive randomized identification by exchangeability.

Do: Take an observational claim about an AI tutoring intervention and write the target trial you wish had been run.

Defend: What exactly is the causal quantity you claim to estimate?

Gate: every claim must name intervention, population, outcome, horizon, estimand and identification assumptions.

Source: source

Practice sequence 26¶

Spine: Hernán & Robins

Reading: Part I Ch. 6-9: causal diagrams; confounding; selection bias; measurement bias

Know: Build DAGs; identify backdoor paths, colliders, selection and measurement structures.

Reconstruct: Regenerate why conditioning on a common effect can create association; derive one adjustment set from a DAG.

Do: Construct two plausible DAGs for the same platform metric where the correct adjustment decisions differ.

Defend: Can data alone choose between causally different DAGs with the same observational distribution?

Gate: diagnose three intentionally misleading regression specifications.

Source: source

Practice sequence 27¶

Spine: Hernán & Robins

Reading: Part II Ch. 11-16, approx. pp. 147-216: modeling, IP weighting, g-formula, outcome regression, propensity, IV

Know: Connect estimands to model-based estimators; understand IPW, standardization, outcome models, propensity and IV assumptions.

Reconstruct: Derive inverse-probability weighting intuition from pseudo-population balancing; derive standardization as averaging conditional outcomes.

Do: Estimate one synthetic treatment effect with outcome regression, weighting and standardization; compare sensitivity to misspecification.

Defend: Why can three estimators agree and all be wrong?

Gate: defend estimator choice by assumptions, not by lowest standard error.

Source: source

Practice sequence 28¶

Spine: Hernán & Robins

Reading: Ch. 22 Target trial emulation, pp. 299-316; selected Ch. 23 mediation, pp. 317-325

Know: Design observational analyses as explicit trial emulations; align eligibility, treatment, time zero and follow-up.

Reconstruct: Reconstruct the target-trial protocol template from memory.

Do: Turn a longitudinal product/health dataset into a target-trial specification and identify immortal-time/selection traps.

Defend: Why is time zero a causal-design decision rather than a data-cleaning detail?

Gate: Module defense: critique a published/constructed observational study and redesign it before touching estimation.

Source: source

Exit gate¶

Closed-book: 120 min: define 4 estimands; draw DAGs; identify adjustment sets; diagnose collider/selection/measurement bias.

Novel problem: Turn an observational product/health claim into a target trial and defend identification assumptions.

Artifact: Estimate one synthetic effect three ways and perform sensitivity/model checks.

Defend: Defend intervention, time zero, population, estimand, assumptions, estimator and failure modes.

Pass criterion: Pass if causal claim can be stated independently of the regression/model used to estimate it.

Transfer problems¶

Try these before consulting solutions or asking for the complete answer.

1. Estimand: Define the exact causal effect of 'AI tutor use' on exam score for a specified population/time horizon.

2. Target trial: Write eligibility, treatment strategies, assignment, follow-up, outcome, contrast and analysis for an observational claim.

3. DAG: Draw two causally distinct DAGs compatible with the same pairwise correlations.

4. Confounding: Construct a confounder that reverses the sign of a naive association.

5. Collider: Show numerically how conditioning on a common effect creates spurious association.

6. Selection: Model attrition that creates a misleading treatment effect among completers.

7. Measurement: Show how differential measurement error can create or erase an apparent effect.

8. IPW: Build stabilized weights in a toy dataset and inspect balance/extreme-weight problems.

9. Standardization: Estimate a causal mean by g-formula/standardization and compare to naive mean.

10. Robustness: Create an unmeasured-confounding sensitivity scenario and state what conclusion survives.

Textbooks¶

See the five-book resource page.

Reading options¶

Assigned readings, where available, appear in the practice sequence above. These additional recommendations are not all required reading.

• Causal Inference: What If

Applications¶

These are editorial study connections, not compulsory prerequisites.

• AI scientist / artificial scientific intelligence: Distinguish causal evidence from correlations when evaluating an automated scientific claim.
• Regenerative medicine: Evaluate evidence of treatment effects without confusing observed change with causal efficacy.

Continue¶

Connections above reflect recorded prerequisites, not a compulsory calendar.

Integrated practice | Choose a study route