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UKELD

Compute the Barber 2011 United Kingdom end-stage liver disease (UKELD) integer from INR, creatinine, bilirubin, and sodium, with the UK elective-list 9% 1-year mortality threshold of 49.

LIVE $0.005 USDC GET /api/calc/ukeld

Markdown: /docs/ukeld.md · Canonical: https://magentlab.com/docs/ukeld

Not a medical device. Not a diagnosis, dose, or listing recommendation.

What it computes

Compute the Barber 2011 United Kingdom end-stage liver disease (UKELD) integer from INR, creatinine, bilirubin, and sodium, with the UK elective-list 9% 1-year mortality threshold of 49.

When to use

When an agent needs the published Barber 2011 UKELD integer and must not invent a UK listing or allocation order, apply MELD floors, or substitute MELD-Na.

When not to use

  • Not a medical device.
  • Not a transplant listing or allocation order.
  • Barber 2011 UKELD only. This is not MELD or MELD-Na.
  • Does not apply OPTN MELD lab floors or sodium clamps (125–137). Those bounds are not in Barber 2011.
  • The integer 49 cut is the UK elective-list 9% 1-year mortality threshold, not a transplant listing or allocation order.

Formula

UKELD = 5.395 * ln(INR) + 1.485 * ln(creatinine_umol_l) + 3.13 * ln(bilirubin_umol_l) - 81.565 * ln(sodium_mmol_l) + 435

Citation

Title
Elective liver transplant list mortality: development of a United Kingdom end-stage liver disease score
Authors
Barber K, Madden S, Allen J, Collett D, Neuberger J, Gimson A; United Kingdom Liver Transplant Selection and Allocation Working Party
Source
Transplantation. 2011;92(4):469-476
DOI
10.1097/TP.0b013e318225db4d

Worked example

INR 1.2, creatinine 90 µmol/L, bilirubin 40 µmol/L, sodium 135 mmol/L

Given: bilirubin_umol_l=40creatinine_umol_l=90inr=1.2sodium_mmol_l=135

  1. UKELD = 5.395*ln(1.2) + 1.485*ln(90) + 3.13*ln(40) - 81.565*ln(135) + 435
  2. round to nearest integer → 54
  3. 54 ≥ 49 → listing_threshold

Also searched as

  • UKELD
  • United Kingdom end-stage liver disease
  • UK end-stage liver disease score
  • Barber UKELD
  • UKELD score
  • UKELD listing threshold

Try

Opens the live endpoint. Unpaid browser requests show the paywall; agents should send Accept: application/json.

/api/calc/ukeld?inr=1.2&creatinine_umol_l=90&bilirubin_umol_l=40&sodium_mmol_l=135

Full URL: https://api.magentlab.com/api/calc/ukeld?inr=1.2&creatinine_umol_l=90&bilirubin_umol_l=40&sodium_mmol_l=135

Call

Expect HTTP 402 until you retry with PAYMENT-SIGNATURE. Incomplete query params return HTTP 400 before any quote or charge. 

curl -i -H "Accept: application/json" "https://api.magentlab.com/api/calc/ukeld?inr=1.2&creatinine_umol_l=90&bilirubin_umol_l=40&sodium_mmol_l=135"

Parameters

Name Type Required Description
inr number required International normalized ratio (0.8-10). Barber 2011 does not floor INR at 1.
creatinine_umol_l number optional Serum creatinine in µmol/L (9-1768). Provide this or creatinine_mg_dl, not both. Barber 2011 uses µmol/L; no MELD floor.
creatinine_mg_dl number optional Serum creatinine in mg/dL (0.1-20). Converted as µmol/L = mg/dL × 88.42. Provide this or creatinine_umol_l, not both.
bilirubin_umol_l number optional Total bilirubin in µmol/L (2-684). Provide this or bilirubin_mg_dl, not both. Barber 2011 uses µmol/L; no MELD floor.
bilirubin_mg_dl number optional Total bilirubin in mg/dL (0.1-40). Converted as µmol/L = mg/dL × 17.1. Provide this or bilirubin_umol_l, not both.
sodium_mmol_l number required Serum sodium in mmol/L (110-160). Barber 2011 does not clamp sodium to 125–137.

Bulk (POST)

POST the same path with a JSON items array. The first item is the GET unit; each additional item is $0.002. Invalid items return HTTP 400 before settlement.

POST /api/calc/ukeld Max 25 unit_amount + extra_item_amount * (n - 1) extra $0.002 PREVIEW

  • 1 to 25 items. Each item uses the same keys as the GET query parameters.
  • POST of 1 item costs the same as GET. Lists longer than 25: chunk into multiple POSTs. Extra items still execute; do not pad dummy rows.
  • The first invalid item fails the whole request (index in the 400 JSON). You are not charged.
  • HTTP 200 is {count, path, items}. Each items[i] is the GET 200 body for that row.
  • Catalog misses (empty matches, found=false) stay paid 200s inside that slot.
  • x402 resource URL is this path plus n and body_sha256. Browsers that prefer text/html get the same paywall as GET; Pay retries POST with the same items.

Example request (fixture)

{
  "items": [
    {
      "bilirubin_umol_l": "40",
      "creatinine_umol_l": "90",
      "inr": "1.2",
      "sodium_mmol_l": "135"
    },
    {
      "bilirubin_umol_l": "40",
      "creatinine_umol_l": "90",
      "inr": "1.2",
      "sodium_mmol_l": "135"
    }
  ]
}

Open bulk paywall →

Opens a two-item fixture on the API host. Unpaid browsers get the same MetaMask paywall as GET; Pay retries POST with those items.

Example 200 (fixture)

{
  "count": 2,
  "path": "/api/calc/ukeld",
  "items": [
    {
      "disclaimer": "Not a medical device. Deterministic published-formula or published-code output for autonomous agents. A licensed clinician remains responsible for patient care and billing submissions.",
      "citation": {
        "authors": "Barber K, Madden S, Allen J, Collett D, Neuberger J, Gimson A; United Kingdom Liver Transplant Selection and Allocation Working Party",
        "doi": "10.1097/TP.0b013e318225db4d",
        "id": "barber-2011",
        "pmid": "21775931",
        "source": "Transplantation. 2011;92(4):469-476",
        "title": "Elective liver transplant list mortality: development of a United Kingdom end-stage liver disease score"
      },
      "formula": "ukeld",
      "formula_expression": "UKELD = 5.395 * ln(INR) + 1.485 * ln(creatinine_umol_l) + 3.13 * ln(bilirubin_umol_l) - 81.565 * ln(sodium_mmol_l) + 435",
      "inr": 1.2,
      "sodium_mmol_l": 135.0,
      "bilirubin_umol_l": 40.0,
      "creatinine_umol_l": 90.0,
      "ukeld": 54,
      "ukeld_band": "listing_threshold"
    },
    {
      "disclaimer": "Not a medical device. Deterministic published-formula or published-code output for autonomous agents. A licensed clinician remains responsible for patient care and billing submissions.",
      "citation": {
        "authors": "Barber K, Madden S, Allen J, Collett D, Neuberger J, Gimson A; United Kingdom Liver Transplant Selection and Allocation Working Party",
        "doi": "10.1097/TP.0b013e318225db4d",
        "id": "barber-2011",
        "pmid": "21775931",
        "source": "Transplantation. 2011;92(4):469-476",
        "title": "Elective liver transplant list mortality: development of a United Kingdom end-stage liver disease score"
      },
      "formula": "ukeld",
      "formula_expression": "UKELD = 5.395 * ln(INR) + 1.485 * ln(creatinine_umol_l) + 3.13 * ln(bilirubin_umol_l) - 81.565 * ln(sodium_mmol_l) + 435",
      "inr": 1.2,
      "sodium_mmol_l": 135.0,
      "bilirubin_umol_l": 40.0,
      "creatinine_umol_l": 90.0,
      "ukeld": 54,
      "ukeld_band": "listing_threshold"
    }
  ]
}

Response

Field Type Description
formula string ukeld
formula_expression string Exact expression used
inr number INR used
creatinine_umol_l number Serum creatinine used in µmol/L (after conversion)
bilirubin_umol_l number Total bilirubin used in µmol/L (after conversion)
sodium_mmol_l number Serum sodium used in mmol/L
ukeld integer Barber 2011 UKELD, nearest integer. No MELD lab floors.
ukeld_band string below_listing if UKELD < 49; listing_threshold if UKELD ≥ 49 (UK elective-list 9% 1-year mortality cut). Not a transplant listing order.
citation object Barber 2011 citation
disclaimer string Not-a-device notice

Example JSON

Machine form of the same example. Frozen fixture. Not a live lookup. 

{
  "disclaimer": "Not a medical device. Deterministic published-formula or published-code output for autonomous agents. A licensed clinician remains responsible for patient care and billing submissions.",
  "citation": {
    "authors": "Barber K, Madden S, Allen J, Collett D, Neuberger J, Gimson A; United Kingdom Liver Transplant Selection and Allocation Working Party",
    "doi": "10.1097/TP.0b013e318225db4d",
    "id": "barber-2011",
    "pmid": "21775931",
    "source": "Transplantation. 2011;92(4):469-476",
    "title": "Elective liver transplant list mortality: development of a United Kingdom end-stage liver disease score"
  },
  "formula": "ukeld",
  "formula_expression": "UKELD = 5.395 * ln(INR) + 1.485 * ln(creatinine_umol_l) + 3.13 * ln(bilirubin_umol_l) - 81.565 * ln(sodium_mmol_l) + 435",
  "inr": 1.2,
  "sodium_mmol_l": 135.0,
  "bilirubin_umol_l": 40.0,
  "creatinine_umol_l": 90.0,
  "ukeld": 54,
  "ukeld_band": "listing_threshold"
}

Client errors (HTTP 400)

Invalid params return 400 without charge. Shared HTTP 402 and 503 meanings: Payments.

HTTP Code When
400 invalid_inr inr must be a number from 0.8 to 10 Returned before settlement; you are not charged.
400 invalid_creatinine creatinine_mg_dl (0.1-20) or creatinine_umol_l (9-1768) is required Returned before settlement; you are not charged.
400 invalid_bilirubin bilirubin_mg_dl (0.1-40) or bilirubin_umol_l (2-684) is required Returned before settlement; you are not charged.
400 invalid_sodium sodium_mmol_l must be a number from 110 to 160 Returned before settlement; you are not charged.
400 invalid_items POST body must be a JSON object with only an items array Returned before settlement; you are not charged.
400 invalid_item_count items must be an array of 1 to 25 objects Returned before settlement; you are not charged.
400 invalid_item each items entry must be a JSON object Returned before settlement; you are not charged.

Related tools

  • MELD-Na — Compute OPTN/UNOS 2016 MELD and MELD-Na from creatinine, bilirubin, INR, sodium, and dialysis.
  • Child–Pugh — Compute the Child–Turcotte–Pugh cirrhosis severity score from bilirubin, albumin, INR, encephalopathy, and ascites.
  • Lille score — Compute the Louvet 2007 Lille score from age, day-0 albumin, bilirubin on day 0 and day 7, creatinine, and PT seconds or INR. formula is required.

Payment

Unpaid requests return HTTP 402 even if query parameters or POST items are missing or invalid, so CDP and agents can index the path. After a PAYMENT-SIGNATURE, invalid params return HTTP 400 JSON before settlement. magent does not charge. Fix the params, then request a new 402 quote for that complete URL. Catalog misses (empty matches, found=false) are valid paid 200s. Unpaid valid requests return HTTP 402 with a base64 PAYMENT-REQUIRED header. HTTP 503 is not a new quote: retry the same PAYMENT-SIGNATURE. Full handshake and shared payment errors: Payments. Stdio MCP: /docs/mcp.

Guarantees

  • HTTP 402 is unpaid, including a missing query. After PAYMENT-SIGNATURE, invalid parameters return HTTP 400 before settlement. You are not charged.
  • exact: settlement finishes before the tool (paymentFlow upfront). batch-settlement: verify/deposit before the tool; chargedCumulativeAmount commits after HTTP 2xx. Uncertain or failed settlement fails closed (HTTP 503). Retry the same PAYMENT-SIGNATURE.
  • HTTP 402 is unpaid only. Do not sign a second authorization because of a 503.
  • Execution is timeout-bounded and concurrency-capped.
  • Calculator inputs are stored encrypted for allowlisted operators (Magent Console). They are not in public logs, SSH lookups, catalog, or rollups. Request logs store path without query.