# MELD (Kamath 2001)

MELD

Status: LIVE
Price: $0.005 USDC
`GET /api/calc/meld`
HTML: https://magentlab.com/docs/meld
Markdown: https://magentlab.com/docs/meld.md

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

## What it computes

Compute the Kamath 2001 model for end-stage liver disease (MELD) integer from creatinine, bilirubin, INR, and cholestatic or alcoholic etiology.

## When to use

When an agent needs the published Kamath 2001 MELD integer and must not apply UNOS lab floors, add dialysis, invent a listing order, or substitute MELD-Na.

## When not to use

- Not a medical device.
- Not a transplant listing or allocation order.
- Kamath 2001 original MELD only. This is not MELD-Na (OPTN 2016) and not MELD 3.0.
- Does not floor bilirubin, INR, or creatinine at 1.0. Those floors are later UNOS/OPTN, not this paper. Kamath tables include bilirubin 0.8.
- Does not include dialysis. Dialysis is not in Kamath 2001.
- Does not include sodium. That is MELD-Na.

## Formula

```
meld = round(3.8 * ln(bilirubin_mg_dL) + 11.2 * ln(INR) + 9.6 * ln(creatinine_mg_dL) + 6.4 * etiology)
```

## Citation

[A model to predict survival in patients with end-stage liver disease](https://doi.org/10.1053/jhep.2001.22172)
Kamath PS, Wiesner RH, Malinchoc M, Kremers W, Therneau TM, Kosberg CL, D'Amico G, Dickson ER, Kim WR
Hepatology. 2001;33(2):464-470
DOI: [10.1053/jhep.2001.22172](https://doi.org/10.1053/jhep.2001.22172)

## Worked example

### Cr 1.9, bili 4.2, INR 1.2, cholestatic or alcoholic

Given: `bilirubin_mg_dl=4.2, cholestatic_or_alcoholic=true, creatinine_mg_dl=1.9, inr=1.2`

1. etiology = 0 because cholestatic_or_alcoholic is true
2. meld = round(3.8*ln(4.2) + 11.2*ln(1.2) + 9.6*ln(1.9) + 6.4*0)
3. round to nearest integer → 14


### Cr 1.9, bili 4.2, INR 1.2, other etiology

Given: `bilirubin_mg_dl=4.2, cholestatic_or_alcoholic=false, creatinine_mg_dl=1.9, inr=1.2`

1. etiology = 1 because cholestatic_or_alcoholic is false
2. meld = round(3.8*ln(4.2) + 11.2*ln(1.2) + 9.6*ln(1.9) + 6.4*1)
3. round to nearest integer → 20


## Also searched as

- MELD
- model for end-stage liver disease
- Kamath MELD
- original MELD 2001
- Mayo end-stage liver disease
- cholestatic alcoholic MELD
- MELD etiology

## Parameters

- `creatinine_mg_dl` (number, optional): Serum creatinine in mg/dL (0.1-20). Provide this or creatinine_umol_l, not both. Kamath 2001 does not floor creatinine at 1.0 and does not include dialysis.
- `creatinine_umol_l` (number, optional): Serum creatinine in µmol/L (9-1768). Converted as mg/dL = µmol/L / 88.42.
- `bilirubin_mg_dl` (number, optional): Total bilirubin in mg/dL (0.1-40). Provide this or bilirubin_umol_l. Kamath 2001 tables include bilirubin 0.8; magent does not floor at 1.0.
- `bilirubin_umol_l` (number, optional): Total bilirubin in µmol/L (2-684). Converted as mg/dL = µmol/L / 17.1.
- `inr` (number, required): International normalized ratio (0.8-10). Kamath 2001 does not floor INR at 1.0.
- `cholestatic_or_alcoholic` (boolean, required): true if the liver disease is cholestatic or alcoholic (etiology 0); false otherwise (etiology 1).

## 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/meld`
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_mg_dl": "4.2",
      "cholestatic_or_alcoholic": "true",
      "creatinine_mg_dl": "1.9",
      "inr": "1.2"
    },
    {
      "bilirubin_mg_dl": "4.2",
      "cholestatic_or_alcoholic": "true",
      "creatinine_mg_dl": "1.9",
      "inr": "1.2"
    }
  ]
}
```

Human paywall (two-item fixture): https://api.magentlab.com/paywall/bulk/meld

Example 200:

```json
{
  "count": 2,
  "path": "/api/calc/meld",
  "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": "Kamath PS, Wiesner RH, Malinchoc M, Kremers W, Therneau TM, Kosberg CL, D'Amico G, Dickson ER, Kim WR",
        "doi": "10.1053/jhep.2001.22172",
        "id": "kamath-2001",
        "pmid": "11172350",
        "source": "Hepatology. 2001;33(2):464-470",
        "title": "A model to predict survival in patients with end-stage liver disease"
      },
      "formula": "kamath_meld_2001",
      "formula_expression": "meld = round(3.8 * ln(bilirubin_mg_dL) + 11.2 * ln(INR) + 9.6 * ln(creatinine_mg_dL) + 6.4 * etiology)",
      "inr": 1.2,
      "bilirubin_mg_dl": 4.2,
      "creatinine_mg_dl": 1.9,
      "etiology": 0,
      "meld": 14,
      "cholestatic_or_alcoholic": true
    },
    {
      "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": "Kamath PS, Wiesner RH, Malinchoc M, Kremers W, Therneau TM, Kosberg CL, D'Amico G, Dickson ER, Kim WR",
        "doi": "10.1053/jhep.2001.22172",
        "id": "kamath-2001",
        "pmid": "11172350",
        "source": "Hepatology. 2001;33(2):464-470",
        "title": "A model to predict survival in patients with end-stage liver disease"
      },
      "formula": "kamath_meld_2001",
      "formula_expression": "meld = round(3.8 * ln(bilirubin_mg_dL) + 11.2 * ln(INR) + 9.6 * ln(creatinine_mg_dL) + 6.4 * etiology)",
      "inr": 1.2,
      "bilirubin_mg_dl": 4.2,
      "creatinine_mg_dl": 1.9,
      "etiology": 0,
      "meld": 14,
      "cholestatic_or_alcoholic": true
    }
  ]
}
```

## Response fields

- `formula` (string): kamath_meld_2001
- `formula_expression` (string): Exact expression used
- `creatinine_mg_dl` (number): Serum creatinine used in mg/dL (after conversion)
- `bilirubin_mg_dl` (number): Total bilirubin used in mg/dL (after conversion). Not floored at 1.0.
- `inr` (number): INR used. Not floored at 1.0.
- `cholestatic_or_alcoholic` (boolean): true if cholestatic or alcoholic disease
- `etiology` (integer): 0 if cholestatic_or_alcoholic is true, otherwise 1
- `meld` (integer): Kamath 2001 MELD, nearest integer. No UNOS lab floors or dialysis.
- `citation` (object): Kamath 2001 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": "Kamath PS, Wiesner RH, Malinchoc M, Kremers W, Therneau TM, Kosberg CL, D'Amico G, Dickson ER, Kim WR",
    "doi": "10.1053/jhep.2001.22172",
    "id": "kamath-2001",
    "pmid": "11172350",
    "source": "Hepatology. 2001;33(2):464-470",
    "title": "A model to predict survival in patients with end-stage liver disease"
  },
  "formula": "kamath_meld_2001",
  "formula_expression": "meld = round(3.8 * ln(bilirubin_mg_dL) + 11.2 * ln(INR) + 9.6 * ln(creatinine_mg_dL) + 6.4 * etiology)",
  "inr": 1.2,
  "bilirubin_mg_dl": 4.2,
  "creatinine_mg_dl": 1.9,
  "etiology": 0,
  "meld": 14,
  "cholestatic_or_alcoholic": true
}
```

## Errors

- 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_inr`: inr must be a number from 0.8 to 10 Returned before settlement; you are not charged.
- HTTP 400 `invalid_flag`: boolean clinical flags must be true or false 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.
- [UKELD](https://magentlab.com/docs/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.

## 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.