# Revised PSC model (Kim 2000)

Revised PSC model

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

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

## What it computes

Compute the Kim 2000 revised natural history model R for primary sclerosing cholangitis from age, bilirubin, AST, albumin, and variceal bleeding (no histologic stage).

## When to use

When an agent needs the published Kim 2000 revised PSC R and must not apply the original Mayo PSC biopsy model, invent survival percents or risk bands, assay labs, diagnose PSC, or treat the result as a transplant listing or biopsy order.

## When not to use

- Not a medical device. magent does not assay labs or diagnose PSC.
- Not a transplant listing or biopsy order.
- Kim 2000 revised model only (age, bilirubin, AST, albumin, variceal bleeding). This is not the original Mayo PSC model that used histologic stage.
- Returns R only. Does not look up Kim 2000 survival-table percents for the computed R and does not invent website risk bands such as low / intermediate / high.

## Formula

```
R = 0.03 * age_years + 0.54 * ln(bilirubin_mg_dl) + 0.54 * ln(ast_u_l) + 1.24 * variceal_bleeding - 0.84 * albumin_g_dl
```

## Citation

[A revised natural history model for primary sclerosing cholangitis](https://doi.org/10.4065/75.7.688)
Kim WR, Therneau TM, Wiesner RH, Poterucha JJ, Benson JT, Malinchoc M, LaRusso NF, Lindor KD, Dickson ER
Mayo Clin Proc. 2000;75(7):688-694
DOI: [10.4065/75.7.688](https://doi.org/10.4065/75.7.688)

## Worked example

### Age 55, bili 5, AST 120, albumin 3.0, variceal bleeding

Given: `age_years=55, albumin_g_dl=3.0, ast_u_l=120, bilirubin_mg_dl=5, variceal_bleeding=true`

1. variceal_bleeding = 1
2. R = 0.03*55 + 0.54*ln(5) + 0.54*ln(120) + 1.24 - 0.84*3.0
3. round to 2 decimals → 3.82


### Age 20, bili 1, AST 20, albumin 4.5, no variceal bleeding

Given: `age_years=20, albumin_g_dl=4.5, ast_u_l=20, bilirubin_mg_dl=1, variceal_bleeding=false`

1. variceal_bleeding = 0; ln(1) = 0
2. R = 0.03*20 + 0.54*ln(1) + 0.54*ln(20) + 0 - 0.84*4.5
3. round to 2 decimals → -1.56


## Also searched as

- revised PSC model
- Kim PSC score
- Mayo PSC revised
- primary sclerosing cholangitis R
- PSC natural history model
- revised Mayo PSC
- PSC variceal bleeding model

## Parameters

- `age_years` (integer, required): Age in whole years (18-120, magent clamp). Kim 2000 uses age in years in the R equation.
- `bilirubin_mg_dl` (number, required): Total bilirubin in mg/dL (0.1-40, magent clamp). Must be positive; natural log is undefined at 0. Kim 2000 uses mg/dL. magent does not assay bilirubin.
- `ast_u_l` (number, required): Aspartate aminotransferase in U/L (1-10000, magent clamp). Must be positive. magent does not assay AST.
- `albumin_g_dl` (number, required): Serum albumin in g/dL (1.0-6.0, magent clamp). Must be positive. Kim 2000 uses g/dL. magent does not assay albumin.
- `variceal_bleeding` (boolean, required): History of variceal bleeding as assigned by the caller (Kim 2000): true (1) or false (0). magent does not diagnose bleeding.

## 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/psc_revised`
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": [
    {
      "age_years": "55",
      "albumin_g_dl": "3.0",
      "ast_u_l": "120",
      "bilirubin_mg_dl": "5",
      "variceal_bleeding": "true"
    },
    {
      "age_years": "55",
      "albumin_g_dl": "3.0",
      "ast_u_l": "120",
      "bilirubin_mg_dl": "5",
      "variceal_bleeding": "true"
    }
  ]
}
```

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

Example 200:

```json
{
  "count": 2,
  "path": "/api/calc/psc_revised",
  "items": [
    {
      "r": 3.82,
      "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": "Kim WR, Therneau TM, Wiesner RH, Poterucha JJ, Benson JT, Malinchoc M, LaRusso NF, Lindor KD, Dickson ER",
        "doi": "10.4065/75.7.688",
        "id": "kim-2000",
        "pmid": "10907383",
        "source": "Mayo Clin Proc. 2000;75(7):688-694",
        "title": "A revised natural history model for primary sclerosing cholangitis"
      },
      "formula": "kim_psc_revised_2000",
      "formula_expression": "R = 0.03 * age_years + 0.54 * ln(bilirubin_mg_dl) + 0.54 * ln(ast_u_l) + 1.24 * variceal_bleeding - 0.84 * albumin_g_dl",
      "age_years": 55,
      "ast_u_l": 120.0,
      "albumin_g_dl": 3.0,
      "bilirubin_mg_dl": 5.0,
      "variceal_bleeding": true
    },
    {
      "r": 3.82,
      "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": "Kim WR, Therneau TM, Wiesner RH, Poterucha JJ, Benson JT, Malinchoc M, LaRusso NF, Lindor KD, Dickson ER",
        "doi": "10.4065/75.7.688",
        "id": "kim-2000",
        "pmid": "10907383",
        "source": "Mayo Clin Proc. 2000;75(7):688-694",
        "title": "A revised natural history model for primary sclerosing cholangitis"
      },
      "formula": "kim_psc_revised_2000",
      "formula_expression": "R = 0.03 * age_years + 0.54 * ln(bilirubin_mg_dl) + 0.54 * ln(ast_u_l) + 1.24 * variceal_bleeding - 0.84 * albumin_g_dl",
      "age_years": 55,
      "ast_u_l": 120.0,
      "albumin_g_dl": 3.0,
      "bilirubin_mg_dl": 5.0,
      "variceal_bleeding": true
    }
  ]
}
```

## Response fields

- `formula` (string): kim_psc_revised_2000
- `formula_expression` (string): Exact expression used
- `age_years` (integer): Age used, whole years
- `bilirubin_mg_dl` (number): Total bilirubin used in mg/dL
- `ast_u_l` (number): AST used in U/L
- `albumin_g_dl` (number): Albumin used in g/dL
- `variceal_bleeding` (boolean): true if variceal bleeding history is present (coefficient 1.24)
- `r` (number): Kim 2000 revised PSC R, 2 decimals. Natural log. No survival-table lookup and no invented risk bands.
- `citation` (object): Kim 2000 Mayo Clin Proc citation
- `disclaimer` (string): Not-a-device notice

## Example JSON

Frozen fixture. Not a live lookup.

```json
{
  "r": 3.82,
  "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": "Kim WR, Therneau TM, Wiesner RH, Poterucha JJ, Benson JT, Malinchoc M, LaRusso NF, Lindor KD, Dickson ER",
    "doi": "10.4065/75.7.688",
    "id": "kim-2000",
    "pmid": "10907383",
    "source": "Mayo Clin Proc. 2000;75(7):688-694",
    "title": "A revised natural history model for primary sclerosing cholangitis"
  },
  "formula": "kim_psc_revised_2000",
  "formula_expression": "R = 0.03 * age_years + 0.54 * ln(bilirubin_mg_dl) + 0.54 * ln(ast_u_l) + 1.24 * variceal_bleeding - 0.84 * albumin_g_dl",
  "age_years": 55,
  "ast_u_l": 120.0,
  "albumin_g_dl": 3.0,
  "bilirubin_mg_dl": 5.0,
  "variceal_bleeding": true
}
```

## Errors

- HTTP 400 `invalid_psc_revised`: Revised PSC model inputs must be numeric age, bilirubin, AST, and albumin plus variceal-bleeding as used in Kim 2000. 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](https://magentlab.com/docs/meld) — Compute the Kamath 2001 model for end-stage liver disease (MELD) integer from creatinine, bilirubin, INR, and cholestatic or alcoholic etiology.
- [Child–Pugh](https://magentlab.com/docs/child-pugh) — Compute the Child–Turcotte–Pugh cirrhosis severity score from bilirubin, albumin, INR, encephalopathy, and ascites.

## 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. HTTP 402 never includes the tool JSON.
- 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.