Model Using PSA Test Can Help Predict Time to Prostate Cancer Relapse

Comparison between the α value with (left, dark) and without (right, light) ADT (A) and the time to relapse with (left, dark) and without (right, light) ADT (B). Bars, percentage of the patients who had a relapse in the corresponding time range.

Model Using PSA Test Can Help Predict Time to Prostate Cancer Relapse | Cancer Network
PHILADELPHIA — A mathematical model that uses four consecutive prostate-specific antigen (PSA) test results from a patient who had prostate cancer surgery can predict the time it might take for the disease to relapse, and this can help clinicians optimize patients' follow-up visits and develop a treatment plan best suited for each individual patient, according to a study published in Cancer Research, a journal of the American Association for Cancer Research.

 “One in four patients who undergo prostate cancer surgery experiences a relapse,” said study lead author Ilaria Stura, of the University of Turin, Italy, in a press release. “Algorithms that use easily obtainable biological data to accurately predict prognosis can help clinicians and patients make more informed choices.”

Based on those patients, the investigators created a parameter known as α, which Stura explained is essentially a ratio between the energy required by a cancer cell to survive and the energy it needs to replicate. Cancer cells have higher rates of replication and thus greater production of PSA, allowing the parameter to represent the aggressiveness of tumor cells.
The α parameter was the only factor found that could significantly predict the time to relapse (P < .001); Gleason score, pathologic stage, post-surgery PSA levels, and other factors could not predict relapse timing.
Specifically, an α of between 0 and 0.01 implies that there is a 62% likelihood relapse will not occur until 48 months after surgery, and a 93.6% chance it will not occur until after 36 months. Between 0.01 and 0.02 was not as strong a predictor; 61.1% of those patients relapse before 36 months, and 22% relapse after 48 months. For larger α values (between 0.02 and 0.04), relapse will occur in less than 48 months 100% of the time, and in under 24 months in 78.9% of cases. For values above 0.04, the time to relapse will be less than 24 months 100% of the time.
Specifically in the patients who received ADT, an α between 0 and 0.01 resulted in relapse more than 48 months out in 72.7% of cases; this number rose to 100% if the adjuvant therapy is given for more than 12 months.
The study is limited by its reliance on retrospective data, but the authors wrote that this could be a valuable and simple tool in helping predict prostate cancer relapse. “We could hence provide a biologically meaningful and practical parameter for promoting personalized medicine in this and possibly in other fields of application,” they wrote.

Math Algorithm Helps Predict Recurrence of Prostate Cancer - MedicalResearch.com
Man has always tried to predict the future, especially to prevent catastrophes, diseases and death. In this case, we want to prevent the ‘personal catastrophe’, i.e. the spread of the disease (recurrence of prostate cancer) in the patient. Our work therefore belongs to the so-called ‘personalized medicine’, a very important and innovative clinical approach.

In particular this study may potentially improve the quality of life of the patients and help the clinicians, since it could give valuable information to the urologist, for example reporting that the growth velocity of the tumor is increasing and that a relapse is expected within few months. With this information, the clinician could chose the best therapy for the patient (e.g. hormone or radio therapy) in order to stop the spread of the disease or, conversely, the use of drugs can be delayed if not necessary.

Obviously clinicians already try to do this, based on their experience, but our method provides further confidence in their ‘investigation’ work, since the algorithm is validated on data coming from a database much larger than his/her personal experience.

A Simple PSA-Based Computational Approach Predicts the Timing of Cancer Relapse in Prostatectomized Patients | Cancer Research

Recurrences of prostate cancer affect approximately one quarter of patients who have undergone radical prostatectomy. Reliable factors to predict time to relapse in specific individuals are lacking. Here, we present a mathematical model that evaluates a biologically sensible parameter (α) that can be estimated by the available follow-up data, in particular by the PSA series. This parameter is robust and highly predictive for the time to relapse, also after administration of adjuvant androgen deprivation therapies. We present a practical computational method based on the collection of only four postsurgical PSA values. This study offers a simple tool to predict prostate cancer relapse. Cancer Res; 76(17); 4941–7. ©2016 AACR.

Major Findings

• In the mainframe of a validated tumor growth model (1), the parameter (α) is a biologically sensible indicator of the growth potentiality of the relapsed prostate cancer.
• Provided only PSA-producing prostate cancer cells may survive after radical prostatectomy (RP), α can be simply estimated on a limited series of PSA values collected after RP, and it proves to be a reliable and robust parameter for predicting the time to relapse.
• In the absence of any adjuvant therapy, the numeric value of α is inversely correlated (P < 0.0001) with the time to relapse.
• When adjuvant androgen deprivation therapy (ADT) is prescribed, α is still well correlated to the timing of recurrence (P = 0.0001), but its value is larger, probably because ADT impacts on the prostate cancer cells' metabolic pathways.
• When the tumor becomes resistant during ADT, α values become even larger, reflecting a direct effect on the cell metabolism.
• This biologically sensible mathematical model may help clinicians in optimizing their follow-up data elaboration to early predict (and possibly counteract) prostate cancer recurrence.

Quick Guide to Equations and Assumptions

As shown by Castorina and colleagues (2), living beings grow according to a common phenomenological universal growth law (PUN), which includes most of the models commonly used (e.g., exponential, Gompertzian,…).

In this article, we focus on a second-order solution of the PUN and apply it to model the PSA dosage p collected at time t, which reflects the biochemical activity of the hormone-sensitive cell population surviving after radical prostatectomy:

  

where p is the PSA value (in ng/mL), P is its limiting value or carrying capacity (in our case P = 100 ng/mL), t is the time of the measurement expressed in months after surgery, and α is the growth parameter for PSA. Note that Eq. A corresponds to the von Bertalanffy law (Eq. B), where K = 1/P, m = 3/4, and n = 1.

Physical data can be renormalized following simple calculations (see ref. 3 for the details), in terms of rescaled fraction r = (p/P)^1/4 and rescaled time τ = α t/4P^1/4 − ln[1-(p₀/P)^1/4], where p₀ is the initial value of the series.

Far from being mathematical tricks, the rescaled units allow us a quick comparison between our experimental data and the parameter-less universal curve r = 1 − e^−τ, obtained by substituting r and τ in the solution of Eq. A. PSA data being very scattered and their time correlation very poor, the α parameter value was evaluated deterministically as:

  

where (p, t) are the PSA values and the times of the measurement, respectively. Note that the physical dimensions of α are ng^0.25mL^−0.25month⁻¹. In principle, α is estimated by all the patient's PSA collection, but in this article, we also investigated the case of fixed values of PSA (i.e., ref. 4) to implement a practically useful algorithm. In the case of adjuvant ADT, which tends to depress the PSA value and the tumor volume, α was calculated from the set of PSA values taken after the end of the therapy.