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When is a rising PSA a relief?

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Posted 5/15/2017 4:39 PM (GMT 0)
When the rise indicates good news! Ok, it's up, but it's up in a way that makes sense in a positive forecast model.

While I would be happier if the PSA had never gone up at all, today's test result has a positive implication based on the little known "Gompertz" curve. Now don't run away because I brought up math again! This is pretty straightforward.

PSA kinetics, the pattern of change, is a way to understand what the readings may mean beyond just up or down or simple threshold values. My PSA has been rising since getting off of hormone therapy in March 2016, and it looked a bit concerning with a doubling time of just over 3 months.

However, Snuffy Meyers has said he thinks PSA trends follow Gompertz curves, not simple exponentials. The hallmark of these curves is they may have a steep slope but they have an upper limit, a ceiling value. The steep rise will level off to some value. These curves are very sensitive to the numbers involved, and you need to use some judgement to get a reasonable forecast.

With my latest reading today, it appears that my trend is following exactly such a curve, the rise slowing and approaching a limit of 0.9 or so. If it levels off there as modeled, then all is likely to be well for a long time. I predicted today's reading with this curve based on prior PSA readings, and it's gratifying to have predictions be shown accurate!

Here's an image of the Gompertz curve, with my 4 readings post-testosterone recovery. It's a very good fit!

So, we've pushed the next checkup out now to July 2017. Based on this analysis, I predict the PSA then will be 0.9 (how's that for a stake in the ground?).

Fun with numbers!
Posted 5/15/2017 4:53 PM (GMT 0)
That is a nice fit! So Gompertz is increasing at a decreasing rate. I could use some of that.
Posted 5/15/2017 5:36 PM (GMT 0)
Congratulations on the deceleration!
Posted 5/15/2017 5:36 PM (GMT 0)
Redwing..I share your excitement .
And you have given men with a rising PSA a reason to hope when they are discouraged by a rising PSA.
Now the hard job will be for someone to explain how, from a biological standpoint, this can occur.
If we assume PSA is a valid progression marker, does prostate cancer sometimes stop growing?
Posted 5/15/2017 6:03 PM (GMT 0)
Redwing57,

I really hope that is the case for you. That would be a really, really bright outcome for you and I hope you get it!

If it turns out that way, what does that mean in your specific case? Would it be that after three years of undetectable, you now have some benign tissue producing PSA, but as it stops growing or dies off, you will see stable or declining PSA? Or is it just that sometimes recurrent PCa follows a Gompertzian curve? Whatever, if it never causes you problems rest of life, doesn't matter why, just "good riddance" for that problem, and you can move on with your life, perhaps take up teaching math (ha).

I think maybe you got the Myers curve idea from his online video, "When recurrent PCa isn't cancer". It is so frustrating to try to understand implications of PSA starting to rise at low/stable levels, when the medical community seems split on this. On one hand, we see recommendations to proceed on to RO/MO appointments when recurrent PSA first appears or around the .03 level. And the studies behind this do look compelling. The Myers video, otoh, argues a "go slower" approach. And (at his retirement) I assume he has seen enough in his long career to bring something of value to the discussion, too. Very confusing.

Anyway, hope by this fall, your battle with this is in the rear-view mirror and fading fast.

Robert
Posted 5/15/2017 6:18 PM (GMT 0)

Staying Tuned said...
Redwing..I share your excitement .
And you have given men with a rising PSA a reason to hope when they are discouraged by a rising PSA.
Now the hard job will be for someone to explain how, from a biological standpoint, this can occur.
If we assume PSA is a valid progression marker, does prostate cancer sometimes stop growing?

There are a couple of things that might be behind it. One is likely to be my situation, when one had primary radiation therapy and hormone therapy. If the irradiated prostate tissue slowly wakes up and begins producing PSA again as testosterone recovers, perhaps this type of curve models its behavior. Slow at first, then a steep development, then a leveling as it reaches its maximum output as the androgen receptors eventually get saturated. Maybe it takes quite a while for the testosterone to permeate and get all of the benign prostate cells active. That's all speculative on my part.

The second thing is more widely discussed, and it's due to the resources cells need for metabolism. If a wad of cancer cells begin doubling somewhere, as long as it's small the cells have little trouble getting nutrients from the blood supply nearby, and gets rid of waste easily. Once they develop into a significant mass, the guys on the inside can't get resources anymore. The only ones doing well are on or near the surface of the tumor, and the tumor has to make some wonky blood vessels to get resources into its interior. So, the growth rate slows because of the geometry and shielding of the inner cells.

A large number of small tumors would have a faster growth rate than just a few large ones even at a similar PSA level. Maybe that's part of the variability seen in doubling time models, and why they're hard to apply universally.

And even though this Gompertz curve may model it pretty well, it's really sensitive to the numbers. It can also model nearly infinite upper bounds. So even if the growth would be ultimately limited, it may be so high it's trouble before it reaches that limit.
Posted 5/15/2017 6:39 PM (GMT 0)

Faustmann said...
That is a nice fit! So Gompertz is increasing at a decreasing rate. I could use some of that.


The latter part of the curve does that. The bit I graphed and posted doesn't include the very beginning piece, but generally speaking it is an S-shaped curve, with a pretty sharp rise at the start, and then a slower approach at the top.

Here's a brief description of the Gompertz function.

And yes, Snuffy did mention this in a video I watched. I've seen only a couple mentions of it in the large number of studies I've pored over in the last couple of months.

I wish all PSA trends did this. My exploration of it was largely due to the complete dearth of information for what the PSA trends mean after radiation+ADT recovery begins.
Posted 5/15/2017 8:51 PM (GMT 0)
Man.... I have always been bad at math. This just plain confuses me.

My RO told me that I could get a rise in PSA that would eventually level out to Nadir once I finish with ADT. I assume that is kind of what you are talking about here....right?

I know that I'm a year out from the completion of my HT treatment and then it will be a bit farther out than that in which I should start to think about all this, but I have started to study these things because it does seem to confuse me.

Anyways... Redwinged One...... It looks like good news that you are following that graph pretty darn close, so CONGRATULATIONS...

I always follow along daily here and try to post once in awhile as things have slowed for me treatment wise,which is a very good thing!

Battle On Brothers!!

The Artistic One... Mark
Posted 5/15/2017 10:22 PM (GMT 0)
Nice!! And I always love the math...Glad to see the deceleration in the upward trend ;)
Posted 5/15/2017 11:34 PM (GMT 0)

Artist Mark said...
...My RO told me that I could get a rise in PSA that would eventually level out to Nadir once I finish with ADT. I assume that is kind of what you are talking about here....right?...


It's pretty close, but a step or two more complicated than that. The tricky bit is you'll stay on ADT longer than the radiation. If you didn't have ADT, then after the radiation's done you'd see the PSA eventually decline, maybe "bounce" up a little, and settle to an eventual minimum, or "nadir".

But you'll probably stay on ADT long enough that all of that post-radiation decline, "bounce" discussion and so on will be masked by the ADT suppressing PSA to undetectable the whole time. Once you stop the ADT, your testosterone recovers at some rate, and the PSA does, well, something, or maybe not. Once your testosterone recovers to 150 or so, then the PSA should recover back to whatever the nadir level would have been after radiation anyway. How fast? How closely does the PSA pace the testosterone recovery? No one's looked at it.
That's what's simply been ignored in studies. No one really has mapped that pattern out very well, yet look how many of us it affects. A doctor named Buyyounouski came the closest of anyone in at least one study, but still not real clear.

So yeah, this is looking at the PSA pattern after the ADT "releases", as they call it.
Posted 5/16/2017 12:32 PM (GMT 0)
Redwing - I am not a mathematician, but I can understand what you're describing. . . and I am really excited for you! If the theory holds in your case, things could be very good for quite a long time, and that would be great!

I'll be watching this process with great interest.
Posted 5/16/2017 2:58 PM (GMT 0)
I've never before said this to another man, but that's a good-looking curve you have there...
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