# PSA doubling time (Pound 1999)

PSA doubling time

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

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

## What it computes

Compute Pound 1999 PSA doubling time from two rising PSA values and the months between them using two-point first-order kinetics, and report the 10-month prognostic split.

## When to use

When an agent already has two rising detectable PSA values and the interval in months and must not invent a 3-point least-squares slope, Gleason, time-to-recurrence tables, or treat doubling time as a treatment order.

## When not to use

- Not a medical device. magent does not measure PSA or diagnose recurrence or metastasis.
- Two-point first-order kinetics only: psadt_months = ln(2) × interval_months / ln(psa2_ng_ml / psa1_ng_ml). Does not implement 3-point least-squares, Gleason, or time-to-recurrence algorithm tables.
- Pound 1999 split is PSADT of 10 months or less versus greater than 10. Exactly 10.0 is <=10. Not a treatment order.
- Each PSA is 0.2-10000 ng/mL (Pound biochemical recurrence used detectable PSA ≥0.2 ng/mL). psa2_ng_ml must be greater than psa1_ng_ml. interval_months is 0.25-120 (magent clamp).

## Formula

```
psadt_months = ln(2) × interval_months / ln(psa2_ng_ml / psa1_ng_ml)
```

## Citation

[Natural history of progression after PSA elevation following radical prostatectomy](https://doi.org/10.1001/jama.281.17.1591)
Pound CR, Partin AW, Eisenberger MA, Chan DW, Pearson JD, Walsh PC
JAMA. 1999;281(17):1591-1597
DOI: [10.1001/jama.281.17.1591](https://doi.org/10.1001/jama.281.17.1591)

## Worked example

### PSA 0.4 to 0.8 ng/mL over 10 months

Given: `interval_months=10, psa1_ng_ml=0.4, psa2_ng_ml=0.8`

1. ratio = 0.8 / 0.4 = 2
2. psadt_months = ln(2) × 10 / ln(2) = 10.0
3. 10.0 is ≤10 (Pound 1999)


### PSA 0.4 to 0.8 ng/mL over 12 months

Given: `interval_months=12, psa1_ng_ml=0.4, psa2_ng_ml=0.8`

1. psadt_months = ln(2) × 12 / ln(2) = 12.0
2. 12.0 is >10 (Pound 1999)


## Also searched as

- PSA doubling time
- PSADT
- prostate-specific antigen doubling time
- Pound PSADT
- PSA doubling
- biochemical recurrence doubling time
- PSA kinetics

## Parameters

- `psa1_ng_ml` (number, required): Earlier serum PSA in ng/mL (0.2-10000). Pound biochemical recurrence used detectable PSA ≥0.2 ng/mL. magent does not measure PSA.
- `psa2_ng_ml` (number, required): Later serum PSA in ng/mL (0.2-10000). Must be greater than psa1_ng_ml (rising). magent does not measure PSA.
- `interval_months` (number, required): Months between the two PSA values (0.25-120, magent clamp). Pound 1999 does not publish an input band for this two-point tool.

## 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/psadt`
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": [
    {
      "interval_months": "10",
      "psa1_ng_ml": "0.4",
      "psa2_ng_ml": "0.8"
    },
    {
      "interval_months": "10",
      "psa1_ng_ml": "0.4",
      "psa2_ng_ml": "0.8"
    }
  ]
}
```

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

Example 200:

```json
{
  "count": 2,
  "path": "/api/calc/psadt",
  "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": "Pound CR, Partin AW, Eisenberger MA, Chan DW, Pearson JD, Walsh PC",
        "doi": "10.1001/jama.281.17.1591",
        "id": "pound-1999",
        "pmid": "10235151",
        "source": "JAMA. 1999;281(17):1591-1597",
        "title": "Natural history of progression after PSA elevation following radical prostatectomy"
      },
      "formula": "psadt",
      "formula_expression": "psadt_months = ln(2) × interval_months / ln(psa2_ng_ml / psa1_ng_ml)",
      "interval_months": 10.0,
      "pound_psadt_band": "<=10",
      "psa1_ng_ml": 0.4,
      "psa2_ng_ml": 0.8,
      "psadt_months": 10.0
    },
    {
      "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": "Pound CR, Partin AW, Eisenberger MA, Chan DW, Pearson JD, Walsh PC",
        "doi": "10.1001/jama.281.17.1591",
        "id": "pound-1999",
        "pmid": "10235151",
        "source": "JAMA. 1999;281(17):1591-1597",
        "title": "Natural history of progression after PSA elevation following radical prostatectomy"
      },
      "formula": "psadt",
      "formula_expression": "psadt_months = ln(2) × interval_months / ln(psa2_ng_ml / psa1_ng_ml)",
      "interval_months": 10.0,
      "pound_psadt_band": "<=10",
      "psa1_ng_ml": 0.4,
      "psa2_ng_ml": 0.8,
      "psadt_months": 10.0
    }
  ]
}
```

## Response fields

- `formula` (string): psadt
- `formula_expression` (string): Exact two-point first-order expression used
- `psa1_ng_ml` (number): Earlier PSA used, ng/mL
- `psa2_ng_ml` (number): Later PSA used, ng/mL
- `interval_months` (number): Months between the two PSA values
- `psadt_months` (number): PSA doubling time in months, 1 decimal
- `pound_psadt_band` (string): Pound 1999 split: <=10 or >10 months. Exactly 10.0 is <=10.
- `citation` (object): Pound 1999 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": "Pound CR, Partin AW, Eisenberger MA, Chan DW, Pearson JD, Walsh PC",
    "doi": "10.1001/jama.281.17.1591",
    "id": "pound-1999",
    "pmid": "10235151",
    "source": "JAMA. 1999;281(17):1591-1597",
    "title": "Natural history of progression after PSA elevation following radical prostatectomy"
  },
  "formula": "psadt",
  "formula_expression": "psadt_months = ln(2) × interval_months / ln(psa2_ng_ml / psa1_ng_ml)",
  "interval_months": 10.0,
  "pound_psadt_band": "<=10",
  "psa1_ng_ml": 0.4,
  "psa2_ng_ml": 0.8,
  "psadt_months": 10.0
}
```

## Errors

- HTTP 400 `invalid_psadt`: PSADT needs two rising PSA values (each 0.2-10000 ng/mL) and interval_months (0.25-120). Returned before settlement; you are not charged.
- HTTP 400 `invalid_psa_interval`: interval_months must be a number from 0.25 to 120. Returned before settlement; you are not charged.
- HTTP 400 `invalid_rising_psa`: psa2_ng_ml must be greater than psa1_ng_ml (rising PSA; Pound 1999). 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

- [PSA density](https://magentlab.com/docs/psad) — Compute Benson 1992 prostate-specific antigen density as serum PSA (ng/ml) divided by prostate volume (ml). Volume is length × width × depth × 0.5, or a caller-supplied volume.
- [Gleason score](https://magentlab.com/docs/gleason) — Sum caller-assigned Gleason 1974 primary and secondary histologic patterns (each 1-5) and return score 2-10. magent does not read slides. Not ISUP/Epstein 2016 Grade Groups.
- [D'Amico](https://magentlab.com/docs/damico) — Apply the D'Amico 1998 JAMA clinically localized three-group rule to caller-assigned clinical T (t1c, t2a, t2b, t2c), Gleason sum 2-10, and PSA ng/mL, and return risk low, intermediate, or high. Does not assay PSA, assign Gleason, or compute CAPRA or NCCN groups.
- [CAPRA](https://magentlab.com/docs/capra) — Apply Cooperberg 2005 Table 1 CAPRA points from caller-assigned preoperative PSA, Gleason primary/secondary, clinical T (t1/t2/t3a), percent positive biopsies, and age, and return the 0-10 score, Table 4 Kaplan-Meier band, and Table 4 5-year recurrence-free survival point estimate. Not a diagnosis.

## 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.