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With all the Bayesian experts here, it should be a no-brainer to figure out what to make of the recent study (popular description). It says that, despite doubling early detection rates, late stage cancers declined by barely 8%, so most new early detections are effectively false positives, i.e. they would not develop into a life-threatening condition if left untreated. 

Some contradictory quotes:

"We've suggested to women that having a mammogram is one of the most important things you can do for your health, and that's simply not true," Welch says. "I can't tell you the right thing to do, except to tell women the truth, tell them both sides of the story. We shouldn't be scaring women. This is a really close call."

Eric Winer, head of breast medical oncology at Boston's Dana-Farber Cancer Institute, notes that the study found an 8% reduction in the number of women whose tumors were detected at more advanced stages. Even under a scenario in which mammograms led more than 1 million women to receive unnecessary treatment, the screenings would have prevented 410,000 diagnoses of late-stage cancer.

Though women have been instructed that "early detection saves lives," relatively few are told that screenings also have costs, including the risk of undergoing surgery, radiation and drug therapy that doesn't help them, Kramer says. "The risks of overdiagnosis are real, and women ought to know about it," Kramer says.

Given the test's limitations, Winer says, women may choose to have fewer screenings to reduce their risk. "It certainly suggests that a woman who chooses to wait until she's 50 to have mammograms, or who chooses to have mammograms every other year, is making a rational decision," Winer says.

“We’re coming to learn that some cancers — many cancers, depending on the organ — weren’t destined to cause death,” said Dr. Barnett Kramer, a National Cancer Institute screening expert. However, “once a woman is diagnosed, it’s hard to say treatment is not necessary.”

“We are left to conclude, as others have, that the good news in breast cancer — decreasing mortality — must largely be the result of improved treatment, not screening,”

“Instead, we’re diagnosing a lot of something else — not cancer” in that early stage, Bleyer said. “And the worst cancer is still going on, just like it always was.”

 

Another expert, Dr. Linda Vahdat, director of the breast cancer research program at Weill Cornell Medical College in New York, said the study’s leaders made many assumptions to reach a conclusion about overdiagnosis that “may or may not be correct.”

“I don’t think it will change how we view screening mammography,” she said.

 

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I liked this snippet from the respective article of the NYTimes:

(...) proponents [of mammography screenings] have used the most misleading screening statistic there is: survival rates. A recent Komen foundation campaign typifies the approach: “Early detection saves lives. The five-year survival rate for breast cancer when caught early is 98 percent. When it’s not? It decreases to 23 percent.”

Survival rates always go up with early diagnosis: people who get a diagnosis earlier in life will live longer with their diagnosis, even if it doesn’t change their time of death by one iota. And diagnosing cancer in people whose “cancer” was never destined to kill them will inflate survival rates — even if the number of deaths stays exactly the same. In short, tell everyone they have cancer, and survival will skyrocket.

The article (by a co-author of the paper also referenced in the OP's link) also does a better job pointing out various pitfalls in interpreting different metrics.

I am still sitting on my medical test that can diagnose every conceivable condition with a sensitivity of - behold - 100%.

I have always been very skeptical of the idea of "overdiagnosis". Now, overtreatment is a real problem. And I suppose you could have a problem wherein, once you reveal to a patient that they have a tumor, they're going to want it treated regardless of what the statistics say.

But it sounds to me like the real problem is not patients at all, but doctors who insist on treatment because they don't understand statistics.

"[O]nce a woman is diagnosed, it’s hard to say treatment is not necessary." Well, maybe you need to try harder.

Good luck selling the "watch and wait" approach to scared patients who have heard they have (buzzword alarm) "CANCER". Explaining to all their social circle why they ignore the "CANCER" in their body. Psychology is a big factor here.

Even educated patients who know their probability theory will often be plagued of thoughts of "What is my cancer doing right now? Is it growing? Should I really ignore it? It's in my body!" Often times in such cases the (unnecessary) treatment buys you peace of mind, at great cost. It's much more rational to forego the test if you know you'd rather not treat, than expose yourself to (typically) such immense mental duress.

There is a simple solution to this problem: don't call it cancer. I think the name DCIS exists for partly for this reason, although the C standing for carcinoma isn't helping. There are many specific proposals for certain grades of cancer to be called hyperplasia or adenoma, entirely for this reason, but I don't think they've caught on.

So, what we really need is a great placebo treatment with minimal side effects?

Something like Miracle Mineral Supplements? Homeopathy? Or something astrology-based?

Not like MMS, but more like homeopathy. Something along the lines of

"This kind of tumor might be cancerous, or it might not be. There's no way to tell right now. We could treat it aggressively, but that has a n% chance of major side effects without doing much good. We would like to test the effectiveness of natural herbal treatments [or other buzzwords] on early-stage tumors like this one. Drink this type of tea up to four times a day [or take this pill], record when and how often you drink it, and come back for regular screening."

And afterwards "Honestly, there is no way of knowing if that was a benign mass or if the experimental treatment made a difference. We will take your information and use them to determine if there is a statistically significant difference between people based on their use. Based on preliminary information, there is no reason to believe that this treatment is effective, but there is still more data to be gathered." OR "Well, the experimental treatment has failed, but because of the close monitoring we can still begin the conventional treatment in the early stages of development, where they are most effective."

I'm not sure if prescribing placebo when placebo is indicated is a dark art or not...

Homeopathy is probably a more effective placebo than both mineal supplements and astrology. Homeopathy has the feature that you have an authorative human being who really listens to the patient when he describes his various symptoms. Than the authorative human being decides on a particular sugar pill that the patient usually has to take multiple times per day.

If you want a placebo with minimal sideeffects homeopathy is a good pick.

But why minimal side effects? You should look to maximize positive sideeffects. Send the person to a well trained psychologist who encourages good lifestyle changes. Quit smoking. Exercise more. Eat more greens.

Exercise more. Eat more greens.

Blurgh! :-)

Yes, when the doctor knows for sure that a more radical treatment is counter-indicated. Which is the crux of the problem.

There may be pressure on doctors to overtreat if, in terms of possible litigation, the expected outcome for the doctor of overtreatment is better than the expected outcome for undertreatment.

Not only possible litigation. Overtreatment makes money for the hospital.

The paper (Bleyer and Welch, 2012).

Abstract:

Background

To reduce mortality, screening must detect life-threatening disease at an earlier, more curable stage. Effective cancer-screening programs therefore both increase the incidence of cancer detected at an early stage and decrease the incidence of cancer presenting at a late stage.

Methods

We used Surveillance, Epidemiology, and End Results data to examine trends from 1976 through 2008 in the incidence of early-stage breast cancer (ductal carcinoma in situ and localized disease) and late-stage breast cancer (regional and distant disease) among women 40 years of age or older.

Results

The introduction of screening mammography in the United States has been associated with a doubling in the number of cases of early-stage breast cancer that are detected each year, from 112 to 234 cases per 100,000 women — an absolute increase of 122 cases per 100,000 women. Concomitantly, the rate at which women present with late-stage cancer has decreased by 8%, from 102 to 94 cases per 100,000 women — an absolute decrease of 8 cases per 100,000 women. With the assumption of a constant underlying disease burden, only 8 of the 122 additional early-stage cancers diagnosed were expected to progress to advanced disease. After excluding the transient excess incidence associated with hormone-replacement therapy and adjusting for trends in the incidence of breast cancer among women younger than 40 years of age, we estimated that breast cancer was overdiagnosed (i.e., tumors were detected on screening that would never have led to clinical symptoms) in 1.3 million U.S. women in the past 30 years. We estimated that in 2008, breast cancer was overdiagnosed in more than 70,000 women; this accounted for 31% of all breast cancers diagnosed.

Conclusions

Despite substantial increases in the number of cases of early-stage breast cancer detected, screening mammography has only marginally reduced the rate at which women present with advanced cancer. Although it is not certain which women have been affected, the imbalance suggests that there is substantial overdiagnosis, accounting for nearly a third of all newly diagnosed breast cancers, and that screening is having, at best, only a small effect on the rate of death from breast cancer.

There is a related case study on mammography screening in the same issue of the journal.

Do we understand the nature of those false positive cancers? What's happening there? How does the body get rid of those spots on it's own?

From what I know, there are no definite conclusions, but some research suggests that a natural shift in hormonal balance can reverse some breast cancers, as well as cervical and testicular cancers. Here is one popular link, google is full of others.