Tall Allen said...
Chaos theory and information/systems theory came together at about the same time to spur a revolution. The idea that "noise" is the real product of complex systems and that "the mean" is just a bi-product has changed everything. If you liked Gleick's book on Chaos, you might also like his book "The Information" about the history of information theory, and "Complexity: The Emerging Science at the Edge of Order and Chaos," by Mitchell Waldrop, about the founding of the Santa Fe Institute, which became the hub for study of Complex Adaptive Systems. All of this has everything to do with cancer (as well as life, consciousness, biology, ecology, evolution, economics, etc.). A paradigm shift occurred in the 1980s that many are still unaware of.
If you want a taste of the mathematics behind "on" and "off" cycles of hormone manipulation for prostate cancer, here are a few to whet your appetite (I have many more). If this is your cup of tea, I hope you will explain the math to me and everyone else here.:
Piecewise affine systems modelling for optimizing hormone therapy of prostate cancer
Nonlinear system identification for prostate cancer and optimality of intermittent androgen suppression therapy
Intermittent Androgen Suppression: Estimating Parameters for Individual Patients Based on Initial PSA Data in Response to Androgen Deprivation Therapy
Thanks, Tall Allen. I'll have to look up those two Gleick books. I haven't followed the field for a long time.
Those links are quite interesting. When reading them, I feel like a Salieri of mathematics, cursed with just enough ability to understand how far short I fall of the brilliance of those guys. It's been quite a while since my calculus and differential equations classes, and I get a bit lost now with embedded state spaces, variational Bayesian (VB) methods, piecewise affine (PWA) systems, and the Gaussian process regression method. I like it, but it's rather beyond my addled brain at this point.
It is generally interesting to see how the repeated cycling maintains peaks lower than the continuous methods do, and gratifying to see the expertise being used in analyzing the underlying dynamics. Perhaps a methodology will settle to guide this IAD process for individuals. Determining the shaping parameters become challenging, since figuring out the right value predictively is way harder than showing what it should have been retrospectively. Understanding the factors that would guide a patient to make the right choice for them is the trick.
Lots of stock market models work beautifully on retrospective data, yet can't predict even short term trends prospectively. Although, the "Quants" have some success in such modelling, www.investopedia.com/articles/financialcareers/08/quants-quantitative-analyst.asp
Bx: 6/12 pos, G9=5+4 (80%, 60%), 4+5 (2@100%, 80%, 10%), PNI+
cT3a (3TMRI: Bilateral EPE, NVB+, SV-, LN-)
Date PSA fPSA
9/12 4.1 15%
3/13 5.2 12% PCA3=31
IGRT by IMRT, 44 done 8/28/13: 50.4 Gy pelvic nodes, 79.2 Gy prostate
ADT2 3 yrs: Lupron/Casodex
Post: (age now 58)
<0.1 PSA (w/ADT2): 8/2013 - 5/2016.
0.2 PSA 8/2016