# FRACTURE Index with known BMD

FRACTURE Index

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

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

## What it computes

Sum the Black 2001 FRACTURE Index with known total-hip BMD T-score from age, T-score, fracture after 50, maternal hip fracture after 50, weight ≤125 lb, current smoking, and arms to stand, then return the integer total and the printed 5-year hip, vertebral, and nonvertebral percents for that quintile.

## When to use

When an agent has caller-supplied age, total-hip T-score, and the five Black 2001 history flags and needs the published with-BMD FRACTURE Index and 5-year percents, not FRAX, not a DXA order, and not a treatment order.

## When not to use

- Not a medical device. Not a treatment order, DXA order, or osteoporosis diagnosis. magent does not DXA-scan or take a history.
- Black 2001 derivation was postmenopausal women in the Study of Osteoporotic Fractures (age 65 or older) with total-hip BMD. That is a limitation, not a sex input. magent does not restrict sex at input.
- This tool is the with-known-BMD instrument only. It is not the without-BMD score, not FRAX, not OSTA, not ORAI, and not OSIRIS.
- 5-year percents are the printed with-BMD quintile cells (1–2, 3–4, 5, 6–7, 8–13). Score 0 has no printed cell. Theoretical max is 15; scores ≥8 map to the 8–13 cell. Percents are not interpolated.

## Formula

```
FRACTURE Index (with BMD) = age (<65 0, 65-69 1, 70-74 2, 75-79 3, 80-84 4, >=85 5) + total_hip_T (>= -1 0, -2 <= T < -1 2, -2.5 <= T < -2 3, T < -2.5 4) + fracture_after_50 1 + maternal_hip_fracture_after_50 1 + weight_le_125_lb 1 + current_smoker 1 + arms_to_stand 2; Black 2001; max 15; 5-year hip/vertebral/nonvertebral percents by printed quintiles 1-2, 3-4, 5, 6-7, 8-13 (score >=8 maps to 8-13); score 0 unpublished
```

## Citation

[An assessment tool for predicting fracture risk in postmenopausal women](https://doi.org/10.1007/s001980170072)
Black DM, Steinbuch M, Palermo L, et al.
Osteoporos Int. 2001;12(7):519-528
DOI: [10.1007/s001980170072](https://doi.org/10.1007/s001980170072)

## Worked example

### Age 60, T-score −0.5, all flags false (score 0)

Given: `age=60, arms_to_stand=false, bmd_t_score=-0.5, current_smoker=false, fracture_after_50=false, maternal_hip_fracture_after_50=false, weight_le_125_lb=false`

1. Age 60 is <65 → 0; T-score −0.5 is ≥ −1 → 0; five flags false → 0
2. Score = 0 (max 15). Black 2001 with-BMD quintile table starts at 1–2; score 0 has no printed 5-year percent.


### Age 65, T-score −0.5, all flags false (quintile 1–2)

Given: `age=65, arms_to_stand=false, bmd_t_score=-0.5, current_smoker=false, fracture_after_50=false, maternal_hip_fracture_after_50=false, weight_le_125_lb=false`

1. Age 65 is 65–69 → 1; T-score −0.5 is ≥ −1 → 0; flags false → 0
2. Score = 1; printed quintile 1–2: hip 0.4%, vertebral 1.2%, nonvertebral 8.6%


### Age ≥85, T-score −3.0, all flags true (maps to 8–13)

Given: `age=85, arms_to_stand=true, bmd_t_score=-3.0, current_smoker=true, fracture_after_50=true, maternal_hip_fracture_after_50=true, weight_le_125_lb=true`

1. Age 85 is ≥85 → 5; T-score −3.0 is < −2.5 → 4; fracture 1 + maternal 1 + weight 1 + smoker 1 + arms 2
2. Score = 15 (max 15). Printed top quintile is 8–13; score ≥8 maps to that cell: hip 8.7%, vertebral 11.2%, nonvertebral 27.5%. Not a treatment order.


## Also searched as

- FRACTURE Index
- Black FRACTURE Index
- SOF fracture index
- Black 2001 fracture risk
- total hip T-score fracture
- postmenopausal fracture index
- 5-year hip vertebral nonvertebral risk

## Parameters

- `age` (integer, required): Age in years (integer 18-120). Black 2001 FRACTURE Index: <65 scores 0; 65-69 scores 1; 70-74 scores 2; 75-79 scores 3; 80-84 scores 4; >=85 scores 5. Derivation was postmenopausal SOF women age 65 or older; the published instrument still lists <65 as 0.
- `bmd_t_score` (number, required): Caller-assigned total-hip BMD T-score (number -5.0 to 4.0). Black 2001 with-BMD instrument: T >= -1 scores 0; -2 <= T < -1 scores 2; -2.5 <= T < -2 scores 3; T < -2.5 scores 4. magent does not DXA-scan.
- `fracture_after_50` (boolean, required): Any fracture after age 50 (Black 2001). true scores 1; false scores 0. true or false. magent does not take a history.
- `maternal_hip_fracture_after_50` (boolean, required): Maternal hip fracture after age 50 (Black 2001). true scores 1; false scores 0. true or false. magent does not take a history.
- `weight_le_125_lb` (boolean, required): Weight 125 pounds (57 kg) or less (Black 2001). true scores 1; false scores 0. true or false. magent does not weigh the patient.
- `current_smoker` (boolean, required): Current smoker (Black 2001). true scores 1; false scores 0. true or false. magent does not take a smoking history.
- `arms_to_stand` (boolean, required): Usually needs arms to stand from a chair (Black 2001). true scores 2; false scores 0. true or false. magent does not examine the patient.

## 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/fracture_index`
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": "60",
      "arms_to_stand": "false",
      "bmd_t_score": "-0.5",
      "current_smoker": "false",
      "fracture_after_50": "false",
      "maternal_hip_fracture_after_50": "false",
      "weight_le_125_lb": "false"
    },
    {
      "age": "60",
      "arms_to_stand": "false",
      "bmd_t_score": "-0.5",
      "current_smoker": "false",
      "fracture_after_50": "false",
      "maternal_hip_fracture_after_50": "false",
      "weight_le_125_lb": "false"
    }
  ]
}
```

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

Example 200:

```json
{
  "count": 2,
  "path": "/api/calc/fracture_index",
  "items": [
    {
      "components": [
        {
          "value": 60,
          "factor": "age",
          "points": 0,
          "present": false
        },
        {
          "value": -0.5,
          "factor": "bmd_t_score",
          "points": 0,
          "present": false
        },
        {
          "factor": "fracture_after_50",
          "points": 0,
          "present": false
        },
        {
          "factor": "maternal_hip_fracture_after_50",
          "points": 0,
          "present": false
        },
        {
          "factor": "weight_le_125_lb",
          "points": 0,
          "present": false
        },
        {
          "factor": "current_smoker",
          "points": 0,
          "present": false
        },
        {
          "factor": "arms_to_stand",
          "points": 0,
          "present": false
        }
      ],
      "age": 60,
      "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": "Black DM, Steinbuch M, Palermo L, et al.",
        "doi": "10.1007/s001980170072",
        "id": "black-2001",
        "pmid": "11527048",
        "source": "Osteoporos Int. 2001;12(7):519-528",
        "title": "An assessment tool for predicting fracture risk in postmenopausal women"
      },
      "formula": "fracture_index",
      "formula_expression": "FRACTURE Index (with BMD) = age (<65 0, 65-69 1, 70-74 2, 75-79 3, 80-84 4, >=85 5) + total_hip_T (>= -1 0, -2 <= T < -1 2, -2.5 <= T < -2 3, T < -2.5 4) + fracture_after_50 1 + maternal_hip_fracture_after_50 1 + weight_le_125_lb 1 + current_smoker 1 + arms_to_stand 2; Black 2001; max 15; 5-year hip/vertebral/nonvertebral percents by printed quintiles 1-2, 3-4, 5, 6-7, 8-13 (score >=8 maps to 8-13); score 0 unpublished",
      "max_score": 15,
      "score": 0,
      "age_score": 0,
      "arms_to_stand": false,
      "bmd_t_score": -0.5,
      "current_smoker": false,
      "fracture_after_50": false,
      "hip_risk_5y_percent": null,
      "maternal_hip_fracture_after_50": false,
      "nonvertebral_risk_5y_percent": null,
      "score_group": null,
      "t_score_points": 0,
      "vertebral_risk_5y_percent": null,
      "weight_le_125_lb": false
    },
    {
      "components": [
        {
          "value": 60,
          "factor": "age",
          "points": 0,
          "present": false
        },
        {
          "value": -0.5,
          "factor": "bmd_t_score",
          "points": 0,
          "present": false
        },
        {
          "factor": "fracture_after_50",
          "points": 0,
          "present": false
        },
        {
          "factor": "maternal_hip_fracture_after_50",
          "points": 0,
          "present": false
        },
        {
          "factor": "weight_le_125_lb",
          "points": 0,
          "present": false
        },
        {
          "factor": "current_smoker",
          "points": 0,
          "present": false
        },
        {
          "factor": "arms_to_stand",
          "points": 0,
          "present": false
        }
      ],
      "age": 60,
      "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": "Black DM, Steinbuch M, Palermo L, et al.",
        "doi": "10.1007/s001980170072",
        "id": "black-2001",
        "pmid": "11527048",
        "source": "Osteoporos Int. 2001;12(7):519-528",
        "title": "An assessment tool for predicting fracture risk in postmenopausal women"
      },
      "formula": "fracture_index",
      "formula_expression": "FRACTURE Index (with BMD) = age (<65 0, 65-69 1, 70-74 2, 75-79 3, 80-84 4, >=85 5) + total_hip_T (>= -1 0, -2 <= T < -1 2, -2.5 <= T < -2 3, T < -2.5 4) + fracture_after_50 1 + maternal_hip_fracture_after_50 1 + weight_le_125_lb 1 + current_smoker 1 + arms_to_stand 2; Black 2001; max 15; 5-year hip/vertebral/nonvertebral percents by printed quintiles 1-2, 3-4, 5, 6-7, 8-13 (score >=8 maps to 8-13); score 0 unpublished",
      "max_score": 15,
      "score": 0,
      "age_score": 0,
      "arms_to_stand": false,
      "bmd_t_score": -0.5,
      "current_smoker": false,
      "fracture_after_50": false,
      "hip_risk_5y_percent": null,
      "maternal_hip_fracture_after_50": false,
      "nonvertebral_risk_5y_percent": null,
      "score_group": null,
      "t_score_points": 0,
      "vertebral_risk_5y_percent": null,
      "weight_le_125_lb": false
    }
  ]
}
```

## Response fields

- `formula` (string): fracture_index
- `formula_expression` (string): Exact Black 2001 with-BMD FRACTURE Index expression
- `score` (integer): FRACTURE Index points with known BMD; published range 0-15
- `max_score` (integer): 15 (5 + 4 + 1 + 1 + 1 + 1 + 2)
- `score_group` (string): Black 2001 with-BMD printed quintile: 1-2, 3-4, 5, 6-7, or 8-13. Score >=8 maps to 8-13. Null when score is 0 (no printed cell).
- `hip_risk_5y_percent` (number): Black 2001 with-BMD 5-year hip fracture percent for that printed quintile; null when score is 0
- `vertebral_risk_5y_percent` (number): Black 2001 with-BMD 5-year vertebral fracture percent for that printed quintile; null when score is 0
- `nonvertebral_risk_5y_percent` (number): Black 2001 with-BMD 5-year nonvertebral fracture percent for that printed quintile; null when score is 0
- `age` (integer): Caller-supplied age in years used for age points
- `bmd_t_score` (number): Caller-supplied total-hip T-score used for T-score points
- `fracture_after_50` (boolean): Caller-supplied fracture-after-50 flag; true scores 1
- `maternal_hip_fracture_after_50` (boolean): Caller-supplied maternal hip-fracture-after-50 flag; true scores 1
- `weight_le_125_lb` (boolean): Caller-supplied weight <=125 lb flag; true scores 1
- `current_smoker` (boolean): Caller-supplied current-smoker flag; true scores 1
- `arms_to_stand` (boolean): Caller-supplied arms-to-stand flag; true scores 2
- `age_score` (integer): Age band points: 0, 1, 2, 3, 4, or 5
- `t_score_points` (integer): Total-hip T-score points: 0, 2, 3, or 4
- `components` (array): Per-factor points
- `citation` (object): Black 2001 Osteoporos Int citation
- `disclaimer` (string): Not-a-device notice

## Example JSON

Frozen fixture. Not a live lookup.

```json
{
  "components": [
    {
      "value": 60,
      "factor": "age",
      "points": 0,
      "present": false
    },
    {
      "value": -0.5,
      "factor": "bmd_t_score",
      "points": 0,
      "present": false
    },
    {
      "factor": "fracture_after_50",
      "points": 0,
      "present": false
    },
    {
      "factor": "maternal_hip_fracture_after_50",
      "points": 0,
      "present": false
    },
    {
      "factor": "weight_le_125_lb",
      "points": 0,
      "present": false
    },
    {
      "factor": "current_smoker",
      "points": 0,
      "present": false
    },
    {
      "factor": "arms_to_stand",
      "points": 0,
      "present": false
    }
  ],
  "age": 60,
  "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": "Black DM, Steinbuch M, Palermo L, et al.",
    "doi": "10.1007/s001980170072",
    "id": "black-2001",
    "pmid": "11527048",
    "source": "Osteoporos Int. 2001;12(7):519-528",
    "title": "An assessment tool for predicting fracture risk in postmenopausal women"
  },
  "formula": "fracture_index",
  "formula_expression": "FRACTURE Index (with BMD) = age (<65 0, 65-69 1, 70-74 2, 75-79 3, 80-84 4, >=85 5) + total_hip_T (>= -1 0, -2 <= T < -1 2, -2.5 <= T < -2 3, T < -2.5 4) + fracture_after_50 1 + maternal_hip_fracture_after_50 1 + weight_le_125_lb 1 + current_smoker 1 + arms_to_stand 2; Black 2001; max 15; 5-year hip/vertebral/nonvertebral percents by printed quintiles 1-2, 3-4, 5, 6-7, 8-13 (score >=8 maps to 8-13); score 0 unpublished",
  "max_score": 15,
  "score": 0,
  "age_score": 0,
  "arms_to_stand": false,
  "bmd_t_score": -0.5,
  "current_smoker": false,
  "fracture_after_50": false,
  "hip_risk_5y_percent": null,
  "maternal_hip_fracture_after_50": false,
  "nonvertebral_risk_5y_percent": null,
  "score_group": null,
  "t_score_points": 0,
  "vertebral_risk_5y_percent": null,
  "weight_le_125_lb": false
}
```

## Errors

- HTTP 400 `invalid_age`: age must be an integer from 18 to 120 Returned before settlement; you are not charged.
- HTTP 400 `invalid_t_score`: bmd_t_score must be a number from -5.0 to 4.0 (Black 2001 Fracture Index T-score). 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

- [OSTA](https://magentlab.com/docs/osta) — Compute the Koh 2001 Osteoporosis Self-Assessment Tool for Asians (OSTA) as trunc(0.2 × (weight_kg − age)) toward zero, then the published low, intermediate, or high band.
- [ORAI](https://magentlab.com/docs/orai) — Sum Cadarette 2000 ORAI (age, weight, and current estrogen use) and return the Table 4 point total with select_for_dxa (score ≥9) or do_not_select.
- [OSIRIS](https://magentlab.com/docs/osiris) — Compute the Sedrine 2002 Osteoporosis Index of Risk (OSIRIS) as (-0.2 × age) + (0.2 × weight_kg) + 2 if current HRT/estrogen use + (-2) if prior low-impact fracture, rounded to 1 decimal, then the published low, intermediate, or high band.

## 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.