For their study, published in Science, the scientists used a mathematical model that analyzed genome sequencing and epidemiological data for 32 types of cancer. Overall, they concluded, 66 percent of mutations that contribute to cancer are due to unavoidable DNA-replication mistakes, while 29 percent are attributable to environmental factors and 5 percent to heredity. That doesn't mean that two-thirds of cancer cases are caused by random copying errors, they said; it can take three, four or more mutations to make a cell turn malignant.

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Moreover, the proportion of mutations due to random copying errors varies depending on the cancer, the researchers said. Random DNA-replication mistakes account for about 77 percent of critical mutations in pancreatic cancer, and virtually all childhood cancer, they said. By contrast, they concluded that more than two-thirds of the mutations in lung cancer were due to environmental factors, mostly smoking.

Humans have trillions of cells, which are constantly regenerating by dividing and making new cells. But each time DNA is copied, the scientists said, an average of three random mistakes will occur. While most are harmless, a small number affect genes that will promote cancer.

The new research builds on a 2015 study that highlighted the role of “bad luck” — random DNA errors — in developing cancer. That study drew vehement protests from some cancer physicians and researchers who worried it would encourage people to take a fatalistic approach to cancer rather than trying to reduce their cancer risk by maintaining a healthy weight, exercising regularly, eating a good diet and avoiding cigarettes.

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The Hopkins researchers have said their earlier work was widely misinterpreted. Nevertheless, in a news briefing earlier this week, they took pains to stress that their study was consistent with estimates that 40 percent of cancers can be prevented, and urged the public to pursue healthy lifestyles.

But they also said it is important for scientists and the public to recognize that a large percentage of cancer mutations occur no matter how pristine the environment or how laudable someone's lifestyle choices.

“Most of the enemies are inside us — they are already here,” Vogelstein said, referring to the random cancer-causing mutations. He said that science needs to find better ways to detect cancer early, when there is a greater chance of curing it.

Vogelstein also argued that the new research about random mutations should offer comfort to people who develop cancer despite having “near-perfect lifestyles,” as well as to parents who are worried that they somehow “gave” their children cancer, either by passing on a harmful gene or inadvertently exposing them to an environmental toxin. “We don't need to add guilt to an already tragic situation,” he said.

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Tomasetti said the work represented a paradigm shift because it marked the first time that researchers had measured the respective contributions of the three dominant causes of cancer mutations.

Some researchers were skeptical, echoing the criticism of the 2015 work. “They say randomness is a major cause of cancer, and they said it last time,” said Anne McTiernan, an internist and epidemiologist at Fred Hutchinson Cancer Research Center. “But the data doesn't convince me.”

She said that environmental causes of cancer have long been underestimated and that estimates on their contribution to cancer will increase as more is learned.

Yusuf Hannun, director of the Stony Brook University Cancer Center, agreed, arguing that the 66 percent contribution of random DNA errors to mutation was “way exaggerated.” In late 2015, a team he led reported that the vast proportion of lifetime cancer risk is due to environmental factors.

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Others welcomed the new Hopkins study. Brian Druker, director of the Oregon Health and Science University's Knight Cancer Institute, said it provided a data framework “to understand much of what we already know about cancer epidemiology.” Often, he said, he sees cancer patients who have had a healthy lifestyle and are looking for an explanation for their disease. “Often there isn’t one,” he said.

Daniel Haber, director of the Massachusetts General Hospital Cancer Center, said it is beside the point to focus on the specific percentage of cancer risk contributed by random errors, environmental factors and heredity. The most important point, he said, is the need for early cancer detection — something that medicine now is “very bad” at.

In their 2015 study, Tomasetti and Vogelstein compared cancer incidence in the United States to the total number of cell divisions to different kinds of tissues in the body. They wanted to determine why, for example, cancer is more likely to develop in the colon than in the brain. They found a strong correlation between cancer incidence and the number of times the stem cells in the tissues divide. They figured that the more cells divide, the higher the potential for random DNA-copying mistakes — and attributed the errors to “bad luck.”

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But critics disliked the “bad luck” explanation and complained that the study was limited to the United States and didn't include the most common cancers — breast and prostate.

In a new analysis also reported Thursday, which included information on breast and prostate cancers, Tomasetti and Vogelstein said they had done additional work that confirmed and broadened their 2015 conclusions. They examined 17 cancer types in 69 countries and found a strong correlation between the number of stem-cell divisions and the incidence of the disease, regardless of the countries' environment or state of economic development.