MAGENT

PSA doubling time calculator: the two-point formula (Pound 1999)

PSA doubling time is how long a rising PSA takes to double. With two PSA values and the months between them, it's ln 2 times the interval divided by the natural log of the later value over the earlier one. This PSA doubling time calculator does that sum, rounds to one decimal and reports whether the result is 10 months or less, the split Pound 1999 used.

Not a medical device. Not a diagnosis or dosing recommendation.

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What is PSA doubling time?

If PSA rises at a steady exponential rate, it doubles over a fixed number of months. That number is the doubling time. A shorter doubling time means a faster rise. Pound and colleagues studied the natural history of men whose PSA rose after radical prostatectomy and grouped doubling times at 10 months.

This is a two-point calculation. The calculator doesn't fit a line through several readings, and it doesn't measure PSA.

The PSA doubling time formula

PSADT (months) = ln 2 × interval (months) ÷ ln(PSA2 ÷ PSA1)

PSA2 must be higher than PSA1
rounded to 1 decimal

Exact expression the calculator uses:

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

Inputs

InputMeaningRange
psa1_ng_mlEarlier PSA, ng/mL0.2 to 10000
psa2_ng_mlLater PSA, ng/mL; must be higher than the earlier one0.2 to 10000
interval_monthsMonths between the two values0.25 to 120

How the calculation works

  1. Divide the later PSA by the earlier one.
  2. Take the natural log of that ratio.
  3. Multiply ln 2 by the interval and divide by the log from step 2.
  4. Round to one decimal.
  5. Assign the band: 10.0 months or less is <=10; above 10 is >10.

When PSA exactly doubles over the interval, the doubling time equals the interval. A PSA that hasn't risen has no doubling time, which is why the later value has to be higher.

Worked examples

These use Magent's own expected values for the calculator.

Example 1: 0.5 to 1.0 over 8 months

  1. 1.0 ÷ 0.5 = 2, so PSA doubled.
  2. ln 2 × 8 ÷ ln 2 leaves the interval, 8.
  3. PSA doubling time 8.0 months, band <=10.

Example 2: 0.4 to 0.8 over 12 months

  1. 0.8 ÷ 0.4 = 2, so PSA doubled.
  2. The doubling time equals the interval, 12.
  3. PSA doubling time 12.0 months, band >10.

Example 3: 0.4 to 0.8 over 10 months

  1. 0.8 ÷ 0.4 = 2, so PSA doubled.
  2. The doubling time equals the interval, 10.
  3. Exactly 10.0 falls in the 10-months-or-less group.
  4. PSA doubling time 10.0 months, band <=10.

History of the 10-month split

Pound and colleagues published "Natural history of progression after PSA elevation following radical prostatectomy" in JAMA in 1999. The calculator's split at 10 months comes from that paper.

When it's used

When PSA is rising after radical prostatectomy and the rate of rise is to be expressed as a doubling time.

Where it's used

Urology and oncology clinics, and prostate cancer research.

Who uses it

Urologists, oncologists and researchers. The calculator does the logarithms.

Limits of the calculation

  • Two values give a rough figure. Small changes in either PSA can shift the result.
  • It assumes a steady exponential rise between the two readings.
  • The band reports the Pound 1999 split. It isn't a prediction for one person, and the calculator gives no advice about next steps.
  • This page doesn't say what a doubling time means for a particular person.

Clinical decisions belong to a qualified clinician who knows the patient.

  • PSA density divides PSA by prostate volume at one point in time.
  • Gleason score grades tumour tissue; it isn't based on PSA.

Glossary

  • PSA: prostate-specific antigen, measured in ng/mL.
  • Doubling time: the time for a value growing at a steady exponential rate to double.
  • Natural log (ln): the logarithm to base e.
  • Radical prostatectomy: surgical removal of the prostate.

Common mistakes

  • Swapping the two PSA values. The later, higher value goes in psa2_ng_ml.
  • Entering the interval in years. It's in months.
  • Treating 10.0 as above 10. Exactly 10.0 is in the <=10 band.

Source

Pound CR, et al. Natural history of progression after PSA elevation following radical prostatectomy. JAMA. 1999;281(17):1591-1597. DOI: 10.1001/jama.281.17.1591. PMID: 10235151

Frequently asked questions

How do you calculate PSA doubling time?

Multiply ln 2 by the months between two PSA values and divide by the natural log of the later PSA over the earlier one.

What does the 10-month band mean?

It's the split Pound 1999 used: 10 months or less, or more than 10.

Why does the second PSA have to be higher?

A doubling time exists for a rising value and not otherwise. If PSA hasn't risen, there's nothing to double.

Can I use more than two PSA values?

Not in this calculator. It uses two.