Mathematical Model May Predict Relapse Times in Prostate Cancer Surgery Patients

Mathematical Model May Predict Relapse Times in Prostate Cancer Surgery Patients

A mathematical model based on four consecutive measures of prostate-specific antigen (PSA) levels can be used to predict the time to relapse in patients who underwent prostate cancer surgery, according to a study published in Cancer Research.

The method detailed in the study, “A Simple PSA-Based Computational Approach Predicts the Timing of Cancer Relapse in Prostatectomized Patients,” was developed in University of Turin, Italy, and may help clinicians improve follow-up care of prostate cancer patients who undergo prostatectomy.

“One in four patients who undergo prostate cancer surgery experiences a relapse. Predicting, and possibly preventing a relapse with adjuvant therapies is a major goal; however, overtreatment is a risk as well, because Androgen Deprivation Therapy (ADT) given after surgery, for instance, may promote the occurrence of new hormone-resistant tumor clones,” Ilaria Stura, a mathematician and a doctoral candidate in the Complex Systems for Life Sciences program at the university, said in a press release. “Algorithms that use easily obtainable biological data to accurately predict prognosis can help clinicians and patients make more informed choices.”

Stura believes the mathematical model can improve a patient’s quality of life, as it provides important clinical information to the urologists. Knowing the tumor’s growth rate or that a relapse is expected with a certain number of months will inform clinicians as to when patients should receive therapy, such as hormone treatment or radiotherapy, to halt the spread of the tumor, or when such therapies should be delayed, avoiding overly excessive treatment.

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

To develop their model, the research team collected retrospective data from 3,538 patients who had undergone prostate cancer surgery. Among them, 707 patients had received ADT after surgery, and 728 experienced a relapse.

Researchers started by estimating the parameter alpha (α) using data from 40 patients who received ADT, and 211 patients who did not. Stura explained that α is determined as the ratio between the amount of energy a cancer cell requires to survive and the energy it takes to replicate, and therefore represents the tumor’s aggressiveness. This is easy to measure because the higher the rate of replication of a tumor cell, the more PSA it produces.

They found that collecting four consecutive PSA values after surgery, α4, was sufficient to predict the time to relapse, with the value of α4 positively correlating with the probability of relapse.

The researchers note that the model does not predict the exact month of relapse, but rather distinguishes between early relapses, which occur within two years after surgery, and late relapses, or those that occur four or more years after surgery.

Nonetheless, their results showed that for patients who had not received ADT after surgery, α4 levels lower than 0.01 were associated with an 82 percent probability that the patients will not relapse within three years, and a 54 percent probability of no relapse within four years. For patients with α4 levels between 0.02 and 0.04, there was a 71 percent probability their tumor would relapse within two years, and a 95 percent probability it would relapse within four years. Finally, for those with an α4 higher than 0.04, the probability of relapse at one year and two years after surgery were 87 percent and 93 percent, respectively.

Researchers also developed a model for patients who received ADT therapy after surgery, accounting for the inability of the remaining cells to replicate and produce PSA due to the hormone treatment. This model also included a parameter accounting for the development of resistance to ADT, when the cells replicate rapidly despite the therapy and patients have a high probability of relapse.

“Our work is another small step towards personalized medicine, and shows how mathematics can be important to better understand tumor evolution,” Stura said. “We are working to improve the reliability of the model by testing it on data from new patients and making the algorithm available for clinicians and patients for free.”

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