Add causal inference chapter

[Copilot]

• Create causal-inference.qmd chapter file
• Create _subfiles/causal-inference/ directory with subfiles
• Add chapter to _quarto-book.yml and _quarto-website.yml (positioned before predictor-selection)
• Add references and update inst/WORDLIST
• Render, lint, spellcheck — all pass
• Address review comments:
  • Fix hat notation: \widehat{\E{Y(a)}} instead of \widehat{\E}{Y(a)} (regression adjustment and propensity score subfiles)
  • Fix citation locator syntax: [@vittinghoff2e, Chapter 9] instead of @vittinghoff2e [Chapter 9]
  • Remove unused smoking mutate from the HERS LDL regression adjustment example
  • Move causal-inference before predictor-selection in book and website navigation; move DAG definitions (_sec-pred-sel-dag.qmd) into the causal inference chapter so they are defined in the chapter that appears first; predictor-selection now links back to those definitions
  • Add hidden hers-data-setup chunk in predictor-selection.qmd so its analysis sections retain access to hers_ldl after the DAG include was removed
  • Merge the former "Causal Thinking and DAGs" and "Observational Studies" sections into a single Observational Studies section with straightforward narrative flow: observational studies intro → confounding (formal definition) → DAGs introduced as a tool to identify confounders and sufficient adjustment sets (including confounder, mediator, collider, and backdoor criterion definitions) → HERS DAG example → WCGS confounded observational study example
  • Add "Narrative Flow" guideline to .github/copilot-instructions.md instructing contributors to introduce concepts before use and avoid forward references

[Copilot]

Pull request overview

Adds a new self-contained causal inference chapter to the Quarto book/website, adapting and integrating material around potential outcomes, identification assumptions, and practical estimators using existing course datasets.

Changes:

• Adds new chapter causal-inference.qmd plus supporting subfiles under _subfiles/causal-inference/.
• Registers the new chapter in the book and website render/navigation YAMLs.
• Extends references.bib and inst/WORDLIST for new citations and terminology.

Reviewed changes

Copilot reviewed 12 out of 12 changed files in this pull request and generated 5 comments.

Show a summary per file

File	Description
references.bib	Adds causal inference references (Hernán & Robins; Rubin; Holland; Rosenbaum & Rubin).
inst/WORDLIST	Adds causal-inference-related spellcheck terms (ATE/ATT/ATU, IPW, exchangeability, etc.).
causal-inference.qmd	New chapter scaffold; includes subfiles and shared DAG section; adds learning objectives and summary.
_subfiles/causal-inference/_sec_potential_outcomes.qmd	Introduces potential outcomes and core definitions.
_subfiles/causal-inference/_sec_causal_estimands.qmd	Defines ATE/ATT/ATU with formal definitions.
_subfiles/causal-inference/_sec_assumptions.qmd	Defines consistency, exchangeability, and positivity.
_subfiles/causal-inference/_sec_rct.qmd	Explains why randomization identifies causal effects; HERS example.
_subfiles/causal-inference/_sec_observational.qmd	Defines confounding/backdoor criterion; WCGS observational framing.
_subfiles/causal-inference/_sec_regression_adjustment.qmd	Introduces G-computation/regression adjustment; HERS LDL example with code/table.
_subfiles/causal-inference/_sec_propensity_scores.qmd	Defines propensity score and IPW; WCGS example with code/diagnostic plot.
_quarto-website.yml	Adds the chapter to website render list and navbar.
_quarto-book.yml	Adds the chapter to the book chapter list.

[d-morrison]

address open comments

[Copilot]

address open comments

Addressed all open review comments in 9e7f939:

1. Hat notation — Changed \widehat{\E}{Y(a)} → \widehat{\E{Y(a)}} and \hat{\E}{...} → \widehat{\E{...}} throughout _sec_regression_adjustment.qmd and _sec_propensity_scores.qmd so the widehat covers the full expectation expression.
2. Citation locator — Changed @vittinghoff2e [Chapter 9] → [@vittinghoff2e, Chapter 9] in causal-inference.qmd.
3. Unused smoking mutate — Removed the smoking factor conversion from the HERS LDL setup chunk since smoking is not included in the model or table.

[Copilot]

Pull request overview

Copilot reviewed 12 out of 12 changed files in this pull request and generated 1 comment.

[Copilot]

@copilot apply changes based on the comments in this thread

Done in 77e834d. Replaced the {{< include _sec-pred-sel-dag.qmd >}} with prose links to the existing sections in predictor-selection.qmd, so the DAG section/definition IDs are only emitted once across the book.

[d-morrison]

@copilot the causal inference section should come before predictor selection, like in RMB; adjust where definitions are placed accordingly

[Copilot]

@copilot the causal inference section should come before predictor selection, like in RMB; adjust where definitions are placed accordingly

Done in c1159a8:

• Swapped order in _quarto-book.yml and _quarto-website.yml so causal-inference now precedes predictor-selection
• Moved the {{< include _sec-pred-sel-dag.qmd >}} from predictor-selection.qmd into causal-inference.qmd (so the definitions live in the chapter that appears first)
• predictor-selection.qmd's "Causal Thinking and DAGs" section now links back to the definitions in the causal inference chapter
• Added a hidden hers-data-setup chunk in predictor-selection.qmd so its analysis sections still have hers_ldl available without re-displaying the data loading code

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[Copilot]

Pull request overview

Copilot reviewed 13 out of 13 changed files in this pull request and generated no new comments.

[d-morrison]

@copilot consolidate #sec-causal-observational and #sec-causal-dags-chapter and make the narrative flow straightforward;

make a note in copilot-instructions to strive for straightforward narrative flow

[Copilot]

@copilot consolidate #sec-causal-observational and #sec-causal-dags-chapter and make the narrative flow straightforward;

make a note in copilot-instructions to strive for straightforward narrative...

Done in 106d23c.

Consolidation (causal-inference.qmd): Moved # Causal Thinking and DAGs to precede # Observational Studies — foundational DAG concepts (confounder, mediator, collider) are now introduced before the observational studies section applies them to confounding. The forward reference in _sec_observational.qmd ("See @sec-causal-dags-chapter") is now a backward reference ("As introduced in @sec-causal-dags-chapter"), and the redundant inline re-explanation of confounder/mediator/collider is removed.

The chapter now flows: Potential Outcomes → Estimands → Assumptions → Randomized Experiments → Causal Thinking and DAGs → Observational Studies (applying DAGs to confounding) → Regression Adjustment → Propensity Scores.

Copilot instructions: Added a "Narrative Flow" section under General Development Principles covering: introduce concepts before use, avoid forward references when the concept is needed to understand current content, and place foundational sections before applied sections.

[d-morrison]

@copilot merge #sec-causal-observational and #sec-causal-dags-chapter into a single Observational Studies section; introduce observational studies first, then confounding, then introduce DAGs as a tool to help to identify confounders and sufficient adjustment sets

[Copilot]

@copilot merge #sec-causal-observational and #sec-causal-dags-chapter into a single Observational Studies section; introduce observational studies first, then confounding, then introduce DAGs as a too...

Done in a40a6d7.

The two sections are now merged into a single # Observational Studies {#sec-causal-observational} section with this narrative order:

1. Intro — what an observational study is, and that confounding arises because treatment groups differ systematically
2. ## Confounding — formal definition of confounding in the potential outcomes framework
3. Bridge sentence — "DAGs provide a formal graphical tool for representing causal assumptions and identifying confounders, mediators, colliders, and sufficient adjustment sets"
4. ## Directed Acyclic Graphs — what a DAG is and how to use it
5. ## Key concepts — formal definitions of confounder, mediator, collider, and backdoor criterion (moved here from the old "DAGs for identifying confounding" subsection, so it precedes the examples that use it)
6. ## HERS study DAG — applying DAGs in a randomized trial context
7. ## An observational study example: WCGS — applying DAGs and the backdoor criterion to the confounded observational study

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_{2026-04-28 23:27 UTC}