WASHINGTON — After several years of upheaval over the best way to conduct breast cancer screening, researchers are working to find clarity over when women should begin getting mammograms, how often and at what cost.

A pair of new studies clears up some of the uncertainty by finding that women who have a mother or sister diagnosed with breast cancer, or those who have unusually dense breast tissue, should have their first test at age 40 and repeat the exam at least once every other year.

For these women, who face at least twice the average risk of developing breast cancer in their 40s, the benefits of routine screening between the ages of 40 and 49 outweigh the risk of false alarms and unnecessary work-ups that might otherwise put them at greater risk than doing nothing, researchers report in today’s edition of Annals of Internal Medicine.

Of the various recommendations put forth by the U.S. Preventive Services Task Force in 2009, none generated more ire than the suggestion that annual mammograms could do more harm than good for most forty-something women, who are far less likely than older women to get breast cancer. The task force advised women in their 40s to talk with their doctors and make individualized decisions about whether to get a mammogram every other year at most.

The new research was designed to identify women who could benefit the most from having mammograms early and often.

In the process, the doctors and other experts who worked on the studies pushed a relatively new risk factor — breast density — to the forefront in the calculations a woman and her physician make as they decide how assiduously to check for breast cancer.

The two studies arrive at their conclusions through different means. One involved combining and analyzing data from 61 studies that have already been published. The other used computer models to predict the health outcomes of about 44,000 simulated women who had their first mammogram at 50. They then ran the same women through a simulation in which they began screening at 40 and compared the rates of false alarms, breast cancer diagnoses and mortality in both groups.

“The fog is clearing,” said Dr. Diana Petitti, who worked on the 2009 Preventive Services Task Force study. “Personalized breast screening recommendations are better.”

The recommendations from the U.S. Preventive Services Task Force, an independent panel of health experts that advises the federal government, upended the fiercely held beliefs of most practitioners and breast cancer activists by suggesting that women older than 50 should have a mammogram every two years instead of annually, and that most women in their 40s should skip the test altogether. Until then, women over 40 were routinely advised to have a mammogram once a year.