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PSA doubling time (Pound 1999)

PSA doubling time

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.

LIVE $0.005 USDC GET /api/calc/psadt

Markdown: /docs/psadt.md · Canonical: https://magentlab.com/docs/psadt

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

Title

Natural history of progression after PSA elevation following radical prostatectomy

Authors

Pound CR, Partin AW, Eisenberger MA, Chan DW, Pearson JD, Walsh PC

Source

JAMA. 1999;281(17):1591-1597

DOI

10.1001/jama.281.17.1591

Worked example

Also searched as

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

Try

Opens the live endpoint. Unpaid browser requests show the paywall; agents should send Accept: application/json.

/api/calc/psadt?psa1_ng_ml=0.4&psa2_ng_ml=0.8&interval_months=10

Full URL: https://api.magentlab.com/api/calc/psadt?psa1_ng_ml=0.4&psa2_ng_ml=0.8&interval_months=10

Call

Expect HTTP 402 until you retry with PAYMENT-SIGNATURE. Incomplete query params return HTTP 400 before any quote or charge.

curl -i -H "Accept: application/json" "https://api.magentlab.com/api/calc/psadt?psa1_ng_ml=0.4&psa2_ng_ml=0.8&interval_months=10"

Parameters

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.

POST /api/calc/psadt Max 25 unit_amount + extra_item_amount * (n - 1) extra $0.002 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 (fixture)

{
  "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"
    }
  ]
}

Open bulk paywall →

Opens a two-item fixture on the API host. Unpaid browsers get the same MetaMask paywall as GET; Pay retries POST with those items.

Example 200 (fixture)

{
  "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

Example JSON

Machine form of the same example. Frozen fixture. Not a live lookup.

{
  "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
}

Client errors (HTTP 400)

Invalid params return 400 without charge. Shared HTTP 402 and 503 meanings: Payments.

Related tools

• PSA density — 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 — 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 — 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 — 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. Unpaid valid requests return HTTP 402 with a base64 PAYMENT-REQUIRED header. HTTP 503 is not a new quote: retry the same PAYMENT-SIGNATURE. Full handshake and shared payment errors: Payments. Stdio MCP: /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.