That is not a good reason to consume antioxidant pills. While the logic may seem sound, there is no convincing evidence that these supplements add to nature’s already formidable means of repairing oxidative damage — and they may even disrupt some delicate biological balance, increasing cancer risk and speeding tumor growth.

But there is no question that oxidation, so crucial to life, rusts our cells and can edge them closer to becoming cancerous.

In examining the possibility that breathing itself significantly increases the risk of lung cancer, the authors of the paper, Kamen P. Simeonov and Daniel S. Himmelstein, began by eliminating confounding variables. Maybe younger, healthier people tend to live at higher altitudes, with older and weaker ones, including smokers, retreating to lower lands. That could create the illusion of a protective altitude effect, but one that has nothing to do with oxygen.

The authors also took into account factors like income, education and race, which affect access to medical care. To reduce distortions caused by noisy data, the researchers excluded counties with large numbers of recent immigrants, who might have acquired cancer-causing mutations elsewhere. Also ruled out were places with a large number of Native Americans, whose cancer rates often go underreported.

Beyond the human variables were geophysical ones. Air at higher altitudes may be less polluted by carcinogens. And since sunlight exposure is more intense, maybe the increase in vitamin D helps stave off lung cancer — an idea previously suggested. Differences in precipitation and temperature might also have some effect.

These data, too, were added to the scales, along with the influence of radon gas and ultraviolet rays, which is greater at higher elevations. The frequency of obesity and diabetes, which are risks for many cancers, was adjusted for, along with alcohol use, meat consumption and other factors.

After an examination of all these numbers for the residents of 260 counties in the Western United States, situated from sea level to nearly 11,400 feet, one pattern stood out: a correlation between the concentration of oxygen in the air and the incidence of lung cancer. For each 1,000-meter rise in elevation, there were 7.23 fewer lung cancer cases per 100,000 people. (The study found no similar correlations for breast, colon and prostate cancer.)