In a pamphlet to help women decide about mammography screening in Britain, the National Health Service now explicitly tells women that their chance of overdiagnosis is about three times higher than their chance of avoiding a breast-cancer death. I can’t tell you if that is the right estimate; since most everyone who receives a diagnosis of “cancer” is treated, overdiagnosis is rarely observed directly, so it is notoriously difficult to quantify. But I can tell you it’s in the ballpark. Our optimistic/pessimistic finding is this: Among a thousand 50-year-old American women screened annually for a decade, 3 to 14 will be overdiagnosed and overtreated.

What about the benefit? Among those thousand women, 3.2 to 0.3 will avoid a breast-cancer death. If you don’t like decimals, call it 3 to 0.

The optimistic estimate reflects the most favorable result of the nine most comprehensive randomized trials of breast cancer screening. But these trials were initiated 20 to 50 years ago. Whether their results are still relevant is a question. Because of substantial improvements in breast cancer treatment, many cancers that would have been deadly 20 years ago now no longer are. The better we are able to treat cancer, the less important it is find it early; in other words, there are fewer deaths for screening to help avoid. This is what is reflected in the pessimistic estimate. One study comparing regions with similar populations and health care systems, but different screening policies (like Sweden versus Norway and Northern Ireland versus the Republic of Ireland), found that breast cancer death rates had declined at similar rates, regardless of when mass screening was adopted.

So put it all together. Among a thousand 50-year-old American women screened annually for a decade, 3.2 to 0.3 will avoid a breast cancer death, 490 to 670 will have at least one false alarm and 3 to 14 will be overdiagnosed and treated needlessly. That may help some women choose whether to be screened or not. But it’s still not very precise, and it doesn’t answer the fundamental question: Now that treatment is so much better, how much benefit does screening actually provide? What we need is a clinical trial in the current treatment era.

Two randomized trials could begin to answer the central question of mammography interpretation: How hard should the radiologist look? Women who view mammography favorably might be willing to be screened under either the current approach or a high-threshold approach — meaning their radiologist would ignore small, likely harmless abnormalities found on a mammogram.Those who view it less favorably might choose that high-threshold approach (knowing that the harms of false alarms and overdiagnosis would be minimized) or forgo mammography completely.

Putting the two trials together, we could finally learn what level of screening minimizes false alarms and overdiagnosis while saving the most lives. Most experts would say that it’s never going to happen. It would cost too much, take too long and need too many subjects.

Maybe they are right. But maybe not. Sure, it would cost millions of dollars. But that’s chicken feed compared with the billions of dollars we spend on breast cancer screening every year. Sure, it would take 10 to 15 years. But it would help our daughters know more. Sure, it would take tens of thousands of women to participate. But maybe they would want to be part of the effort to help sort out the morass surrounding what is one of the most common medical interventions done to American women.

You never know, until you ask.

None of this should dissuade women from seeking a diagnosis when they develop a new breast lump (that’s a form of early diagnosis we all agree on) or from seeking treatment for a diagnosed breast cancer (better treatment, not early detection, is the real success story in breast cancer). The uncertainties are about screening. Women who want to reduce those uncertainties will have to participate in trials.