# UKELD UKELD Status: LIVE Price: $0.005 USDC `GET /api/calc/ukeld` HTML: https://magentlab.com/docs/ukeld Markdown: https://magentlab.com/docs/ukeld.md 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 [Elective liver transplant list mortality: development of a United Kingdom end-stage liver disease score](https://doi.org/10.1097/TP.0b013e318225db4d) Barber K, Madden S, Allen J, Collett D, Neuberger J, Gimson A; United Kingdom Liver Transplant Selection and Allocation Working Party Transplantation. 2011;92(4):469-476 DOI: [10.1097/TP.0b013e318225db4d](https://doi.org/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=40, creatinine_umol_l=90, inr=1.2, sodium_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 ## Parameters - `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. Method: `POST /api/calc/ukeld` Max items: 25 Price: unit_amount + extra_item_amount * (n - 1) (unit 5000 atomic, extra 2000 atomic) Status: 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: ```json { "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" } ] } ``` Human paywall (two-item fixture): https://api.magentlab.com/paywall/bulk/ukeld Example 200: ```json { "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 fields - `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 Frozen fixture. Not a live lookup. ```json { "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" } ``` ## Errors - HTTP 400 `invalid_inr`: inr must be a number from 0.8 to 10 Returned before settlement; you are not charged. - HTTP 400 `invalid_creatinine`: creatinine_mg_dl (0.1-20) or creatinine_umol_l (9-1768) is required Returned before settlement; you are not charged. - HTTP 400 `invalid_bilirubin`: bilirubin_mg_dl (0.1-40) or bilirubin_umol_l (2-684) is required Returned before settlement; you are not charged. - HTTP 400 `invalid_sodium`: sodium_mmol_l must be a number from 110 to 160 Returned before settlement; you are not charged. - HTTP 400 `invalid_items`: POST body must be a JSON object with only an items array Returned before settlement; you are not charged. - HTTP 400 `invalid_item_count`: items must be an array of 1 to 25 objects Returned before settlement; you are not charged. - HTTP 400 `invalid_item`: each items entry must be a JSON object Returned before settlement; you are not charged. Shared HTTP 402 and 503: https://magentlab.com/docs/payments ## Related tools - [MELD-Na](https://magentlab.com/docs/meld-na) — Compute OPTN/UNOS 2016 MELD and MELD-Na from creatinine, bilirubin, INR, sodium, and dialysis. - [Child–Pugh](https://magentlab.com/docs/child-pugh) — Compute the Child–Turcotte–Pugh cirrhosis severity score from bilirubin, albumin, INR, encephalopathy, and ascites. - [Lille score](https://magentlab.com/docs/lille) — 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. - GET the tool with Accept: application/json (do not send Accept: text/html unless you want the human paywall). - HTTP 402 means you have not paid. Decode the base64 PAYMENT-REQUIRED header. HTTP 503 is not a new quote. - Sign accepts[0] (exact, EIP-3009) with validBefore = now + maxTimeoutSeconds (600 seconds), or accepts[1] (batch-settlement deposit/voucher) on product GET. Ping and POST {items} stay exact. Magent retries transient facilitator 429/5xx before answering. - Retry the same URL with PAYMENT-SIGNATURE (base64 JSON of accepted and payload). Magent attaches canonical extensions.bazaar on CDP verify/settle; echoing 402 bazaar is optional. - Success is HTTP 200 JSON plus PAYMENT-RESPONSE. exact settles before the tool. batch-settlement verifies (and deposit-settles) before the tool and commits the charge after HTTP 2xx. HTTP 503: retry the same PAYMENT-SIGNATURE. Mint a new exact nonce only after a new HTTP 402. - offered `exact` on eip155:8453: Fixed-price USDC on Base. The buyer authorizes the advertised amount (EIP-3009). magent settles before the tool runs (paymentFlow upfront). extra.assetTransferMethod=eip3009 extra.paymentFlow=upfront. - offered `batch-settlement` on eip155:8453: Payment-channel vouchers claimed later in batches. Exact stays accepts[0]. Same-path POST {items} is still exact. extra.assetTransferMethod=eip3009 extra.paymentFlow=authorization. - not offered `upto`: Not offered. Usage-based: buyer authorizes a ceiling, seller settles the actual amount after work. Reserved for a future metered tool. Not for current calculators or code search. Same-path POST {items} is still scheme exact: one EIP-3009 authorization for GET unit plus $0.002 per extra item. That is not x402 batch-settlement (payment channels / vouchers). Shared HTTP 402 and 503 table: https://magentlab.com/docs/payments Stdio MCP (one process per host): https://magentlab.com/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.