One metric for savings opportunity and supply risk — in quality-adjusted hours
2026-07-12
2017 — Hurricane Maria knocks out three Baxter plants in Puerto Rico — ~50% of US small-volume saline bags. Nurses go back to pushing drugs by syringe.
2022 — A COVID lockdown shuts a single GE plant in Shanghai. Hospitals ration contrast media — triaging which patients get CT scans.
2024 — A national shortage of blood culture bottles (CDC HAN-00512).
Materiality is measured to the penny. Criticality is tracked in adjectives. When the two argue, dollars win every time — not because they matter more, but because they have units.
What happens if this specific thing vanishes and the slot is filled from the open market?
Measure vs. zero
Inflates everything — every product looks priceless.
Measure vs. average
Punishes solid performers, rewards mediocrity.
Measure vs. replacement ✓
The decision-relevant counterfactual: what do I lose, given the freely available alternative?
Normal market
Saline has a deep substitute pool. Its value above replacement is ~zero — which is exactly why it’s cheap.
Stressed market
A hurricane, a lockdown, a recall. The pool collapses and the same product’s value above replacement explodes — without the product changing at all.
The output of a hospital supply chain is patient health. Health economics already has a unit for it: the QALY — a quality-adjusted life year.
\[ \frac{\$100{,}000 \text{ per QALY}}{8{,}766 \text{ hours per year}} \;\approx\; \$11.40 \text{ per quality-adjusted hour} \]
That exchange rate — call it v — is what lets a $2M savings opportunity and a supply-disruption scenario be compared as quantities, not argued as a spreadsheet vs. an anecdote.
1. It isn’t settled. Supply-side (~£13k/QALY, NHS marginal productivity) vs. demand-side ($100–150k/QALY, willingness-to-pay) disagree 3–5×. For procurement savings, supply-side is causally correct.
2. It crosses asymmetrically. Risk is born in hours — no valuation step. Savings is born in dollars and only becomes hours through v. So v is a weighting knob between channels, not a shared unit conversion.
Mandatory phrasing rule Externally, dollars are “valued at the standard cost-effectiveness threshold.” Never “lives saved.”
\[ \mathrm{HAR}(p) = \mathrm{HAR}_{\mathrm{savings}}(p) + \mathrm{HAR}_{\mathrm{risk}}(p) \qquad \mathrm{risk\_share} = \frac{\mathrm{HAR}_{\mathrm{risk}}}{\mathrm{HAR}} \]
HAR_savings — the money channel
Well-measured, high-resolution, computed from millions of observed transactions.
HAR_risk — the clinical channel
Noisier, log-resolution — and the reason the composite exists at all.
The guardrail: never let the savings channel’s four-significant-figure precision lend its credibility to the risk channel. They share a unit, not an error bar.
Worked example — knee implants \(300/\text{yr} \times (\$5{,}000 - \$4{,}200) \times 0.5 \div \$11.40/\text{h} \approx \mathbf{10{,}500\ \text{hours/year}}\)
\[ \mathrm{HAR}_{\mathrm{risk}}(p) = P(\text{pool shrink}) \times \text{downstream hours at stake} \times P(\text{no viable path}) \]
Worked example — contrast media 20,000 scans/yr, log-bin terms multiplied through ≈ 10²–10³ expected h/yr — but the year it lands: 10⁴–10⁵ realized hours, at every hospital simultaneously.
Hours-at-stake aren’t owned by a product — they’re inherited from every procedure downstream of it. Complement edges propagate risk upstream; substitutes shunt it away.
Build an edge only where resolving it could change a decision.
Carve-out: high-volume, low-class consumables (saline, contrast, blood culture bottles) are assumed to gate procedures until proven otherwise — or the cheapest proxy prunes exactly the motivating examples first.
HAR recovers the Kraljic matrix — taught everywhere, quantified almost nowhere — as a scalar and a ratio.
| risk_share | Posture |
|---|---|
| ≈ 0 (savings-dominated) | Negotiate hard, commoditize |
| ≈ 1 (risk-dominated) | Secure supply — dual-source, hold inventory, stop squeezing |
| both channels large | Strategic — the metric flags it, judgment settles it |
“This category’s supply risk is worth ten times its savings opportunity, so we’re buying continuity, not discounts.”
| # | Product family | HARsavings (h/yr) | HARrisk (h/yr) | risk_share | Posture |
|---|---|---|---|---|---|
| 1 | Hip & knee implants | 10⁸ | 10⁴·⁵ | ≈ 0 | Negotiate |
| 2 | Stents & cardiac rhythm devices | 10⁷·⁵ | 10⁵·⁵ | 0.01 | Negotiate |
| 3 | IV saline & solutions | 10⁵·⁹ | 10⁷·³ | 0.96 | Secure supply |
| 4 | Iodinated contrast media | 10⁶·¹ | 10⁷·¹ | 0.91 | Secure supply |
| 5 | Platinum chemotherapies | 10⁴·⁵ | 10⁷ | ≈ 1 | Secure supply |
| 6 | Exam & surgical gloves | 10⁶·⁸ | 10⁵·² | 0.02 | Negotiate |
| 7 | Blood culture bottles | 10⁵ | 10⁶·⁸ | 0.98 | Secure supply |
| 8 | Dialysis consumables | 10⁶·³ | 10⁶·⁵ | 0.61 | Strategic |
| 9 | Infusion pumps & sets | 10⁶·⁵ | 10⁶·² | 0.33 | Strategic |
| 10 | Heparin | 10⁵·⁵ | 10⁶·⁵ | 0.91 | Secure supply |
At ~$100/hour loaded cost and v ≈ $11.40/hour, one analyst hour costs ≈ 9 health-hours — every review task must move ~10 HAR-hours per analyst-hour to be worth doing.
\[ \mathrm{queue\_score} = \frac{E[\Delta\mathrm{HAR} \mid \text{review}] \times P(\text{action}) \times \text{persistence}}{\text{expected analyst-hours to review}} \]
Items below the line are correctly declined, not backlog. Data-quality queues, enrichment targeting, and classification training data are all prioritized by the HAR at stake.
The expensive parts of HAR are all in the risk channel — shortage base rates, hours anchors, the dependency graph. The cheap part is a few hours of work on data we already have.
First computation = a falsification test Does the risk term ever move a rank?
If not — stop. Keep the sharpened savings metric (it improves the existing deliverable on its own) and retest at finer grain before spending more.
Savings eats itself (good). Median falls as everyone negotiates toward it; attention shifts from price transfers to resilience.
Correlated stockpiling. Everyone reads the same shortage data → a bank run with a dashboard. Shared inputs mean shared blind spots.
Margin compression feeds fragility. Universal squeezing is what made saline fragile — and the risk channel warns on lagging data.
Vendors Goodhart it. risk_share ≈ 1 tells suppliers, in writing, to start charging continuity premiums.
Net: the stabilizing case wins — pricing fragility creates a revenue stream for redundant capacity.
The saline bag is still a dollar — a thin margin, a spot near the bottom of every spend report ever printed, invisible until the week it’s unavailable. Now the hours behind it have units.
Full write-up: jjd.io/posts/hours_above_replacement.html · jjd@jjd.io
curvo · Better Starts Here