Women going in for mammograms may be told they have dense breasts — which makes it tough to detect breast tumors (which are also dense) and more likely that they will develop breast cancer. But a reassuring new study finds that breast cancer patients with dense breast tissue are not more likely to die of their cancer than women who don’t have dense breasts.

The study, published last Monday in the Journal of the National Cancer Institute, found that while breast cancer is often diagnosed later in women with dense breasts, the cancer is not more aggressive or life-threatening than tumors detected a little earlier in less dense tissue.

“Risk factors for the development of breast cancer may not necessarily be the same as factors influencing the risk of death from breast cancer once it has developed,” wrote the researchers. Women, though, should not ignore a mammogram finding of “dense breasts,” especially when combined with a suspicious finding on a breast exam.

Paying for follow-up testing may be tough if a woman doesn’t have adequate insurance or has a high deductible. The Massachusetts Planned Parenthood affiliate received a $20,000 grant this month to help low-income women gain access to breast biopsies and diagnostic imaging tests, according to Dianne Luby, president of the Planned Parenthood Advocacy Fund of Massachusetts. Unfortunately, the grant won’t be able to cover the expense of cancer treatment.