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Alzheimer's disease cuts the risk of developing cancer, and cancer decreases the risk of developing Alzheimer's disease, a new study suggests.

Researchers found that older people with Alzheimer's disease are less likely to also have cancer, and older people with cancer are less likely to also have Alzheimer's disease, according to the study published in the journal Neurology.

"Since the number of cases of both Alzheimer's disease and cancer increase exponentially as people age, understanding the mechanisms behind this relationship may help us better develop new treatments for both diseases," study author Dr. Massimo Musicco, of the National Research Council of Italy in Milan, said in a news release.

The latest study involved 204,468 people age 60 and older in northern Italy during a six-year period. Researchers said 21,451 people in the study developed cancer, 2,838 people developed Alzheimer's disease and a total of 161 people had both cancer and Alzheimer's disease. Researchers said the number would have been expected to be 281 for cancer and 246 for Alzheimer's disease when looking at how often the diseases occur in the general population.

The findings reveal that the risk of cancer was cut in half for people with Alzheimer's disease and the risk of Alzheimer's disease was reduced by 35 percent for people with cancer.

"While other studies have noted this relationship before, this is the largest study to date and it has several strengths over previous studies, such as looking for the presence of the second disease both before and after the first disease was diagnosed," Musicco said.

"This controls for the possibility that the presence of one disease might obscure the diagnosis of other diseases because any new symptoms might be interpreted as a consequence of the already-diagnosed disease, or in the case of cancer, people might assume that memory problems were a side effect of chemotherapy," he concluded.