There is also a theory that all of the radiation contributes to cancer. In fact, I've known three women that each found their lump doing monthly self exams, within 3 months of having a "clear" mammogram, and having had them annually. Knowing your own body, and doing the checks is probably the best thing anyone can do.
Many women have gone to having thermograms, instead of mammograms. The thermograms will detect increased blood flow, which will be present, even before the tumor grows to a size detectable by any means. If there is something suspicious on the thermogram, then a mammogram is usually indicated for further investigation, but until then, one can avoid the radiation. Thermograms have been FDA approved screening tools, for 20+ years, and are effective. (Too bad so many in the healthcare field seem unaware of this.) Unfortunately, one usually has to go to a larger city, such as Dallas, to find a location with the equipment. Also, the thermogram can cover more of the body, so can screen more than just the breasts, should it be deemed appropriate.
