Feedback on Hodges' model in 'mathematical' terms

Through HIFA, I noticed an introduction by a new subscriber - Mr James Twahirwa; and noted a maths-oriented skillset:

'HIFA profile: James Twahirwa works on Research and data analysis in Rwanda. He is deeply interested in contributing to the global effort to improve health equity through reliable, accessible information. His background in statistics, data analysis, and research methods equips him to support evidence-based decision-making and strengthen health systems.

By email, I got in touch seeking an independent reading of the draft h2cm-maths paper (part 1).

Prior to this, Mr Twahirwa kindly made the following observations on Hodges' model which he is happy for me to post here:

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Dear Peter Jones 

I find your work interesting and really well-positioned.

Overall impression

Your work is intellectually ambitious and unusually well-positioned. You are attempting something that many disciplines struggle with: creating a unifying conceptual framework that can bridge practice, theory, and abstraction without collapsing into reductionism. The fact that Hodges’ model originates in nursing and has sustained relevance across decades already gives it credibility as a practice-informed epistemic structure, not just a diagram.

Your effort to reinterpret it through mathematics and category theory is especially interesting, because health economics often suffers from exactly the fragmentation your work seeks to address: disconnected models of behavior, outcomes, ethics, and systems.

1. The 2x2 structure aligns naturally with health systems thinking

Health economics constantly balances dualities such as:

• Individual vs population
• Clinical outcomes vs social value
• Quantitative evidence vs lived experience
• Efficiency vs equity

A 2x2 framework provides a powerful way to hold these tensions without collapsing them into a single metric. This is one reason cost-effectiveness frameworks often feel incomplete. Hodges’ model appears capable of holding multiple dimensions of value simultaneously.

2. Conceptual clarity over mathematical dominance

Health economics has increasingly recognized that mathematical rigor alone does not guarantee insight. Your attempt to treat Hodges’ model as a conceptual object rather than a predictive algorithm is aligned with modern critiques of over-formalization in economics and health policy.

Where your work could be strengthened

1. Clarify the “mathematical” claim carefully

From a health economist’s perspective, the risk is not that the model lacks mathematics, but that readers may misunderstand what kind of mathematics is being invoked.

You may want to explicitly distinguish between:

• Mathematics as computation or formal proof
• Mathematics as structural reasoning (relations, mappings, constraints)

Making this distinction early will help avoid criticism that the model is “not really mathematical,” while still defending its rigor.

2. Connect to applied decision-making

To attract health economists and policy researchers, it may help to show how Hodges’ model could:

• Frame health technology assessment decisions
• Structure evaluations of complex interventions
• Support mixed-methods research designs

Even one concrete example (e.g., health service redesign, chronic disease management, or resource allocation) would strengthen its practical relevance.

3. Position the work in relation to existing frameworks

Your work resonates with, but is distinct from:

• Systems thinking in health
• Capability approach (Sen, Nussbaum)
• Complex adaptive systems
• Multi-criteria decision analysis

Explicitly stating how Hodges’ model complements or improves upon these will help readers locate it intellectually.

I hope this feedback may be of help

Happy festive season.

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Thank you Mr James Twahirwa. These comments are very helpful. You have identified the many strengths of Hodges' model and its uses. On the mathematics, you make many points for me to address and balance in terms of the overall intent and content of this 'project'.

Mr Twahirwa is now in possession of the draft paper. Any further thoughts are always welcome. While rather remote from clinical practice (a debate in itself) health economics is ultimately grounded in health services and health systems development. So this perspective provides a critical counterbalance to my clinical (business) as usual approach.

Point #1 is a primary motivating factor for this 'project'. I'm sure I can use structure as an anchor, while acknowledging that Hodges' model is a conceptual model, an idealisation. Additional feedback regards reasoning, decision making and Bayes also apply here:
[ ii Learn your lines and the hyperplanes will follow ].

In Point #2 I may be able to leverage research, drawing from #1:

'Mathematics as structural reasoning (relations, mappings, constraints)'.

Point #3 will be considered in-part through April's complexity conference; and revisiting former work on systems.

Both points #2 and #3 may find their home in a second paper (part 2), but this is fine, as it may support a step-wise workflow, and something akin to a logical progression(?).

As posted before any assistance greatly appreciated.