# Sampson estimated LDL-C

Sampson LDL-C

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

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

## What it computes

Estimate LDL-C from total cholesterol, HDL, and triglycerides using Sampson 2020.

## When to use

When an agent needs Sampson LDL arithmetic (including triglycerides up to 800 mg/dL) and must not apply Friedewald TG/5.

## When not to use

- Not a diagnosis and not a statin order. Direct LDL assay is out of scope.
- Triglycerides above 800 mg/dL (or 9.03 mmol/L) are rejected. Sampson 2020 is not applied above that cap.
- Sampson 2020 only. Not Friedewald 1972 and not Martin/Hopkins.

## Formula

```
LDL-C = TC/0.948 - HDL/0.971 - (TG/8.56 + TG*(TC-HDL)/2140 - TG^2/16100) - 9.44 (mg/dL)
```

## Citation

[A new equation for calculation of low-density lipoprotein cholesterol in patients with normolipidemia and/or hypertriglyceridemia](https://doi.org/10.1001/jamacardiol.2020.0013)
Sampson M, Ling C, Sun Q, et al.
JAMA Cardiol. 2020;5(5):540-548
DOI: [10.1001/jamacardiol.2020.0013](https://doi.org/10.1001/jamacardiol.2020.0013)

## Worked example

### TC 200, HDL 50, TG 150 mg/dL

Given: `hdl_mg_dl=50, total_cholesterol_mg_dl=200, triglycerides_mg_dl=150`

1. nonHDL = 200 - 50 = 150
2. TG term = 150/8.56 + 150*150/2140 - 150^2/16100
3. LDL-C = 200/0.948 - 50/0.971 - TG term - 9.44 = 123.4 mg/dL


## Also searched as

- Sampson equation
- Sampson LDL-C
- NIH LDL equation
- calculated LDL 800
- Sampson 2020
- LDL-C hypertriglyceridemia

## Parameters

- `total_cholesterol_mg_dl` (number, optional): Total cholesterol in mg/dL (50-500). Provide the full mg/dL set or the full mmol/L set, not mixed.
- `hdl_mg_dl` (number, optional): HDL cholesterol in mg/dL (5-150). Same unit system as the other lipids.
- `triglycerides_mg_dl` (number, optional): Triglycerides in mg/dL (10-800). Values above 800 are rejected; Sampson 2020 is not applied above 800 mg/dL.
- `total_cholesterol_mmol_l` (number, optional): Total cholesterol in mmol/L (1.3-12.9). Converted as mg/dL = mmol/L * 38.67. Do not mix with mg/dL keys.
- `hdl_mmol_l` (number, optional): HDL cholesterol in mmol/L (0.1-3.9). Converted as mg/dL = mmol/L * 38.67.
- `triglycerides_mmol_l` (number, optional): Triglycerides in mmol/L (0.1-9.03). Cap is the SI stand-in for 800 mg/dL (mg/dL = mmol/L * 88.57). The Sampson equation is applied in mg/dL.

## 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/sampson`
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": [
    {
      "hdl_mg_dl": "50",
      "total_cholesterol_mg_dl": "200",
      "triglycerides_mg_dl": "150"
    },
    {
      "hdl_mg_dl": "50",
      "total_cholesterol_mg_dl": "200",
      "triglycerides_mg_dl": "150"
    }
  ]
}
```

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

Example 200:

```json
{
  "count": 2,
  "path": "/api/calc/sampson",
  "items": [
    {
      "unit": "mg_dl",
      "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": "Sampson M, Ling C, Sun Q, et al.",
        "doi": "10.1001/jamacardiol.2020.0013",
        "id": "sampson-2020",
        "source": "JAMA Cardiol. 2020;5(5):540-548",
        "title": "A new equation for calculation of low-density lipoprotein cholesterol in patients with normolipidemia and/or hypertriglyceridemia"
      },
      "formula": "sampson",
      "formula_expression": "LDL-C = TC/0.948 - HDL/0.971 - (TG/8.56 + TG*(TC-HDL)/2140 - TG^2/16100) - 9.44 (mg/dL)",
      "hdl_mg_dl": 50.0,
      "ldl_c_mg_dl": 123.4,
      "ldl_c_mmol_l": 3.2,
      "total_cholesterol_mg_dl": 200.0,
      "triglycerides_mg_dl": 150.0
    },
    {
      "unit": "mg_dl",
      "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": "Sampson M, Ling C, Sun Q, et al.",
        "doi": "10.1001/jamacardiol.2020.0013",
        "id": "sampson-2020",
        "source": "JAMA Cardiol. 2020;5(5):540-548",
        "title": "A new equation for calculation of low-density lipoprotein cholesterol in patients with normolipidemia and/or hypertriglyceridemia"
      },
      "formula": "sampson",
      "formula_expression": "LDL-C = TC/0.948 - HDL/0.971 - (TG/8.56 + TG*(TC-HDL)/2140 - TG^2/16100) - 9.44 (mg/dL)",
      "hdl_mg_dl": 50.0,
      "ldl_c_mg_dl": 123.4,
      "ldl_c_mmol_l": 3.2,
      "total_cholesterol_mg_dl": 200.0,
      "triglycerides_mg_dl": 150.0
    }
  ]
}
```

## Response fields

- `formula` (string): sampson
- `formula_expression` (string): Exact Sampson 2020 expression
- `unit` (string): mg_dl or mmol_l, the unit system supplied
- `total_cholesterol_mg_dl` (number): Total cholesterol in mg/dL (converted when SI inputs are used)
- `hdl_mg_dl` (number): HDL cholesterol in mg/dL (converted when SI inputs are used)
- `triglycerides_mg_dl` (number): Triglycerides in mg/dL (converted when SI inputs are used)
- `ldl_c_mg_dl` (number): Estimated LDL-C in mg/dL, 1 decimal
- `ldl_c_mmol_l` (number): Estimated LDL-C in mmol/L, 1 decimal
- `citation` (object): Sampson JAMA Cardiol 2020 citation
- `disclaimer` (string): Not-a-device notice

## Example JSON

Frozen fixture. Not a live lookup.

```json
{
  "unit": "mg_dl",
  "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": "Sampson M, Ling C, Sun Q, et al.",
    "doi": "10.1001/jamacardiol.2020.0013",
    "id": "sampson-2020",
    "source": "JAMA Cardiol. 2020;5(5):540-548",
    "title": "A new equation for calculation of low-density lipoprotein cholesterol in patients with normolipidemia and/or hypertriglyceridemia"
  },
  "formula": "sampson",
  "formula_expression": "LDL-C = TC/0.948 - HDL/0.971 - (TG/8.56 + TG*(TC-HDL)/2140 - TG^2/16100) - 9.44 (mg/dL)",
  "hdl_mg_dl": 50.0,
  "ldl_c_mg_dl": 123.4,
  "ldl_c_mmol_l": 3.2,
  "total_cholesterol_mg_dl": 200.0,
  "triglycerides_mg_dl": 150.0
}
```

## Errors

- HTTP 400 `invalid_cholesterol`: provide all of total_cholesterol_mg_dl (50-500), hdl_mg_dl (5-150), and triglycerides_mg_dl, or all of total_cholesterol_mmol_l (1.3-12.9), hdl_mmol_l (0.1-3.9), and triglycerides_mmol_l, not mixed. Returned before settlement; you are not charged.
- HTTP 400 `invalid_sampson_triglyceride`: triglycerides_mg_dl must be 10-800; triglycerides_mmol_l must be 0.1-9.03. Sampson is not applied above 800 mg/dL. Returned before settlement; you are not charged.
- HTTP 400 `invalid_lipid_inputs`: computed LDL-C would be negative; check total cholesterol, HDL, and triglycerides. 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

- [Friedewald LDL-C](https://magentlab.com/docs/friedewald) — Estimate LDL-C from total cholesterol, HDL, and triglycerides using Friedewald 1972.

## 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 echoing accepted, payload, and extensions when present).
- 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.