Beating the Odds

While organ transplants save lives, they come with their own risks. Transplant recipients develop certain cancers at a rate up to 1,000 times higher than the general population. Why? The very drugs that enable the body to accept a donor organ also suppress the immunities essential to fighting cancer.

Because the types of cancers that develop in transplant recipients vary widely, posttransplant patients would theoretically have to withstand frequent, invasive and hugely expensive screenings from the moment they recover until the end of their lives. But new research shows that doctors should increase cancer checks over time, not soon after transplants, sparing patients extra procedures and medical expenses.

Josh Hiller, Ph.D., assistant professor of math at Adelphi, helped create the mathematical model that predicts the incidences of cancer in transplant patients. Last July, he co-authored an article about risk prediction in carcinogenesis in the Bulletin of Mathematical Biology.

The article examined risk in lung cancer patients as well as transplant recipients. Dr. Hiller and his national research team posited that lung cancer patients who stopped smoking faced the greatest risk of recurrence in the first five years after quitting tobacco. These patients—in direct contrast to transplant patients—need close monitoring at the beginning of their recovery rather than further on.

The article demonstrates the way mathematics can be used to find patterns in data and shows how modeling can help transform cancer treatment and prevention.

“I was always into biology, but my interest increased when I was in graduate school and my father developed cancer,” Dr. Hiller said. “I became interested in mathematics and oncology and started focusing on that.” Working with his adviser—who would become a co-author on his papers—Dr. Hiller used his math and statistical acumen to develop more accurately predictive models.

Dr. Hiller first established a foothold in the field of mathematical carcinogenesis more than two years ago with a co-authored paper that analyzed patterns of cancer incidence. Published in the journal Progress in Biophysics & Molecular Biology, the article refines a classic statistical model of carcinogenesis, known as the “Armitage–Doll model” after the two scientists who first proposed it in 1954. The model suggests that a sequence of multiple distinct genetic events precede the onset of cancer.

“Our research team looked at more than 1,200 global cancer studies published over 60 years to fine-tune the Doll model,” Dr. Hiller said. “We found that the risk of developing cancer is negligible at birth and increases until age 75, then hits a downward slope statistically. What surprised us is that there didn’t seem to be a good model to explain the decrease in cancer risk.”

Cancer incidence is fairly easy to study, Dr. Hiller added, because “you look at the total population and divide it by cancers people develop at any given ages. But the model becomes much harder to create when you’re looking at relative risk of cancers.” Relative risk shows the connection between a risk factor and a particular type of cancer. Scientists compare the number of cancers in a group of people who have a particular trait with the number of cancers in a group of people who lack that trait. For instance, they might compare the relative lung cancer risk for people who smoke with the relative lung cancer risk in a similar group of people who don’t smoke.

Using age as the “relative risk” of cancer onset, Dr. Hiller’s team created a mathematical model showing that incidence of cancer slows after age 75. Because cells in older people begin reproducing more slowly, cancers have less opportunity to form, accounting for the drop in cancer rates in people over 75.

Now, Dr. Hiller is taking the lessons learned from these models and using them in a very different context, working with a newly formed team to find ways for the model to predict deforestation. “I’m currently investigating deforestation policies in Argentina and what effect those policies will have on the local biosphere,” he said.

This research is also applicable in the classroom, where Dr. Hiller teaches courses on statistics and data analysis. He wants students to regard mathematical modeling as a creative endeavor that goes beyond formulas and theories and across disciplines. “It’s totally counterintuitive that a mathematical model that works in cancer epidemiology will work in deforestation prediction,” Dr. Hiller said. “But that’s the beauty of the field.”

» Learn more about Adelphi’s Department of Computer Science and Mathematics

Josh Hiller, Ph.D., is an assistant professor of mathematics and computer science. His research focuses on stochastic processes, mathematical biology (including mathematical epidemiology, models of deforestation and carcinogenesis), algebraic combinatorics and graph theory. He received his Ph.D. in mathematics from the University of Florida.