Add Chapter 2 Documentation: Extending Hierarchical Model to Correlated Biomarkers

[Kwan-Jenny]

This PR adds a new Quarto (.qmd) presentation file titled "Extending the Hierarchical Model for Antibody Kinetics" to the serodynamics documentation.
Key features:

• Model Focus:

  • Incorporates feedback from Dr. Morrison and Dr. Aiemjoy to focus exclusively on the Teunis (2016) within-host antibody kinetics model.

  • Clarifies model dynamics, parameter definitions, and the distinction between estimated vs. derived quantities.

  • Updates notation for consistency across project documentation.

• Covariance Structure Extension:

  • Reviews current block-diagonal covariance assumption (Σ_K ⊗ I_J) that treats biomarkers as independent.

  • Proposes extended model with full biomarker covariance matrix (Σ_K ⊗ Σ_J) to capture correlation across antigen–isotype combinations.

  • Includes Kronecker product examples and expanded matrix forms for clarity.

• Simulation & Validation Plan:

  • Outlines steps to simulate individuals with correlated biomarkers.

  • Compares independence model (I_J) vs. correlated model (Σ_J) via DIC/WAIC and posterior predictive checks.

  • Forms the basis for Chapter 2’s methodological framework and simulation study.

• Next Steps:

  • Implement full Σ_J prior in JAGS.

  • Run simulation experiments to test model recovery of known correlation.

  • Apply extended model to Shigella longitudinal dataset once validated.

This .qmd file will serve as both a reproducible Beamer slide deck and internal reference for model development in Chapter 2.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ All tests successful. No failed tests found.

[github-actions]

📖 https://ucd-serg.github.io/serodynamics/preview/pr129
Preview documentation for this PR (at commit 9c82e87)

[Kwan-Jenny]

Hi @d-morrison — as we talked about in our last meeting, could you review the notation here and share any overall feedback on this .qmd file? Thanks!

[d-morrison]

Suggested change

	* Added Chapter 2 documentation on correlated biomarker model (#129)
	* Added documentation on correlated biomarker model (#129)

[d-morrison]

(@Kwan-Jenny I'm taking a look at this PR this afternoon and posted this edit early by accident; you can ignore it until I finish the full review)

[d-morrison]

@Kwan-Jenny coming along! see notes in docx version on Teams

[d-morrison]

remove progress notes from document; comments like this should go into the PR description on Github instead

[d-morrison]

(@Kwan-Jenny I'm taking a look at this PR this afternoon and posted this edit early by accident; you can ignore it until I finish the full review)

[Kwan-Jenny]

@copilot,
could you review my conversation above with d-morrison and update my files accordingly? In particular, please revise and enhance chapter2_correlated_biomarkers.qmd based on the images and feedback suggested by d-morrison. Additionally, please use the attached images and the Word file (which d-morrison reviewed) to further revise chapter2_correlated_biomarkers.qmd.
chapter2_correlated_biomarkers.docx

Also, please review the .qmd file thoroughly and carefully to improve it, and align the revisions with d-morrison’s approach and way of thinking.

[Copilot]

@Kwan-Jenny I've opened a new pull request, #187, to work on those changes. Once the pull request is ready, I'll request review from you.