This week will be a four part series on PSA Doubling Time (PSADT).

The parts will be as follows:

- Part 1. Introduction & Use
- Part 2. Calculating PSADT
- Part 3. DIY Formulas with Google
- Part 4. Online Calculators

PSA Doubling Time (PSADT) was found to be the most consistent of the top prognostic factors for a variety of endpoints (prostate cancer-specific survival, metastases-free survival, overall or all cause survival) in a 2015 literature review of relevant studies so we focus this 5 part series of posts specifically on it. [PMID: 26180662] [Full Free Text]. (The other consistent key factors were Gleason Score and Time to Biochemical Failure.) This series includes material that was previously part of the Prostate Cancer Calculators post (which is listed as one of the Key Posts on the right hand side) but has been significantly expanded and for this new series.

In Part 1. Introduction & Use, today, we discuss the relationship of PSADT to cell growth kinetics and discuss applications in screening, watchful waiting and survival after recurrence.

In part 2, Calculating PSADT with Graphics we discuss the importance of using graphics in connection with PSADT calculations noting that you can go badly wrong if you do not. Then we present a number of methods (spreadsheet, manual, using Excel or R directly) all of which provide for both calculation and graphics.

In part 3, we focus on the formulas underlying doubling time calculations using the google search bar as our calculator. The calculations are not difficult and its worthwhile spending this short amount of time to get some insight into them.

In part 4, we discuss a number of online calculators. Unfortunately these are

not as useful as the approaches in Part 2 because they either lack graphics

(which can be essential as explained there) or else they use ordinary axes

rather than semilog axes; nevertheless, they can be useful for double checking your results or quickly performing a calculation since all you do is go to a web site and enter your numbers.

*Cell Growth*

According to [PMID: 7523722] (and also mentioned in this PSA Kinetics article) cancer patients showed an early linear (i.e. arithmetic) increase in PSA followed later by an exponential (i.e. geometric) phase of increase in PSA levels. During a linear increase PSA velocity (PSAV) is constant and therefore is a logical measure of increase whereas during the later geometric phase PSA doubling time (PSADT) is constant and so it takes over as the logical measure of increase. Such an exponential rate of growth might be due to exponential growth of the tumour cell population although according to this March 2007 Urology Times article the cell kinetics cannot truly be explained so simply.

Since linear increase mathematically approximates exponential increase at early stages (but not later stages) the linear increases noted may simply be an early manifestation of an increase which is truly exponential.

Also note that during any stretch of time over which PSADT is constant we have the following relationship among PSA, PSAV and PSADT:

PSAV = log(2) PSA / PSADT

where log(2) = 0.6931472. That is the PSAV is proportional to PSA during any stretch of time for which PSADT is constant and if we were to draw the PSA and PSAV curves they would have the same shape during such time stretches -- the only difference being that one is a scaled version of the other. (The reason is that modeling PSA kinetics via a constant doubling time is equivalent to modelling it by an exponential function and the derivative of an exponential function is another exponential function.)

Furthermore it suggests that PSA velocity not only measures aggressiveness but also how long the tumor has been growing. That is, the same high PSA velocity (1) could be due to a less aggressive tumor that has progressed so the PSA in the numerator is higher or (2) it could be due to a more aggressive tumor that has not progressed so the PSADT in the denominator is lower. As a result of these two possibilities Ruth Etzioni [audio interview] [PMID: 17925534] has suggested that PSA velocity is not a pure measure of a single characteristic so PSADT might be a better measure than PSA velocity. On the other hand in an October 2008 study of 199 subjects, PSAV predicted repeat biopsy results better than PSADT [PMID: 18990146].

Note that a smaller PSAV is more favorable since it means that the cancer is growing slower but a larger PSADT is more favorable since it means it taking longer to double.

In a [2010 thesis by E. Mehrara] it is pointed out that statistical analysis of doubling times is complicated by its typically skewed distribution and that its reciprocal (1/PSADT) is more symmetric which is more consistent with many statistical procedures. Equation (10) of that thesis suggests the use of ln(2)/PSADT since that numerically equals the constant in the differential equation of exponential growth. (Also see [PMID:1744013] [Full Text]).

*PSA Rise in Healthy Men*

PSA is said to rise by about 3.3% per year in healthy men but will rise faster than that in cancer patients. [PMID:75436]. The median PSA level for men in their 50's is approximately 1 (see table in upper right of this Dr. Catalona page) so a rate of 3.3% corresponds to a PSAV of 0.033 and inverting the formula from the prior section in turn implies a PSADT of log(2)/.033 = 21 years in healthy men.

*Use of PSADT*

Specific interpretations of doubling time are discussed in this [link] by PCNG, the Cincinnati Prostate Cancer Support Group. We mention three applications here:

*Screening*. In a situation where one is screening healthy men, this PCRI pamphlet suggests that a PSADT of less than 10 years may indicate tumor growth.*Watchful Waiting.*In watchful waiting, a detailed Table by Jon Nowlin on using PSA doubling time (and other criteria) to determine entry and exit from watchful waiting is provided on Terry Herbert's watchful waiting site.*Recurrence after local therapy*. With PSA failure after surgery or radiation a PSADT of less than 3 months can distinguish higher risk from lower risk cases. See Figure 2 in Chodak Review (2006) which shows survival curves for patients with PSADT < 3 months vs. patients with PSADT > 3 months. That figure was derived from [Full Article]. Also see this Table derived from [PMID: 15069112] which shows that median time from PSA recurrence to each of (1) time to metastases and (2) survival time both increase with doubling time. In [PMID: 17418069] Mayo Clinic Researchers found that (a) patients with PSADT < 3 months were at imminent risk of death, (b) patients with PSADT between 3 months and 1 year were at significant risk of systematic disease, (c) patients with PSADT between 1 and 10 years are more likely to have local disease than systematic recurrence and (d) patients with PSADT > 10 years were at low risk of recurrence. This Urology Times, April 2007 article says that according to the investigators these "new findings should prompt physicians whose patients have doubling times of less than 1 year to treat them with systematic therapies."

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