NEW YORK — Even as Herceptin has become a hugely successful breast cancer drug, doctors have been troubled by a question that has billion-dollar implications: How long should patients be treated with it?

Results of two studies, announced Monday, suggest an answer: Neither a shorter nor a longer duration of treatment is better at staving off a recurrence of cancer than the current standard of one year.

The results mean Roche, the manufacturer, has probably dodged a bullet; shorter treatment could mean the loss of $1 billion or more in sales. But Roche is also losing out on a windfall that would have resulted from longer treatment.

Herceptin, with a US wholesale price of $54,000 a year, had global sales in 2011 of $5.6 billion. Most use of the drug is to reduce the chance cancer will come back after a patient with early stage breast cancer has surgery to remove the tumor.

One of the studies, sponsored by Roche, tested whether two years of treatment would be better than one. The study found no difference in the rate at which cancer recurred or in how long the patients lived.

The French National Cancer Institute studied whether six months of treatment would be as good as one year. If so, that would save insurers, government health programs, and patients huge sums of money.

The women who were treated for six months had a 28 percent greater risk of recurrence than those treated for a year. Strictly speaking, it could not be ruled out that six months of treatment might be roughly equivalent to a year. But the results do not seem likely to change the standard of care.