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Comment by tmoertel | Hacker News Reader

> Here's a fun one. So we decide to run the test twice. And AGAIN it comes up positive. What are the odds that it's a false positive? Again, the exact same logic holds - there are 101 people we are testing. There will be about 1 false positive and about 1 real infection. So the odds of it being a false positive once again are about 50%.

This conclusion assumes that running the test twice is equivalent to running two independent tests for the same condition. For many real tests, getting a false positive once predicts a higher chance of getting another false positive in a repeated test.

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Yes exactly. In fact mammograms are already double-read and agreement is quite high, so this is definitely one of those types of tests. There are benign masses that are radiologically impossible to distinguish until you get a biopsy.

Seems to me the thesis that "mammogram positive" implies "possible cancer" is the faulty one.

In fact, "mammogram indeterminate" is a better diagnosis.

Yes, and this is how the standard of care treats things. You never proceed from positive mammo screen to treatment. You always first do some other steps like ultrasound or biopsy.

In the general case, this is the point where medicine arrive at both a medical and ethical problem. The biopsy and further tests both involve some non-insignificant risk to the patient, as does overtreatment. If 99% or even higher number of patients are false positive, and the biopsy has a risk of causing significant negative sides, at what point is testing doing more harm that good?

This is the general argument against testing for prostate cancer in non-symptomatic patients. If you only test patients that has symptoms then the rate of false positives goes down. The downside is that you only catch late stage patients where treatment might be too late. The alternative (which is used for mammography) is that for every person saved, an order of magnitude more will be permanent harmed by unnecessary surgery.

Yes it's not trivial to balance these things and this is why there have been randomized control trials that look at long term end points where both the costs of false negatives and false positives come into play.

It's also why breast cancer screening is not recommended for everyone, just women over 50.

For women over 50 there has been a decades long sincere effort by the medical community to take this all into account and the consensus is that screening makes sense in that population.

Yes, but every positive mammogram means a percentage of people are going to get treatment, including surgery and radiation/chemotherapy, who never would have developed cancer -- and screening more women, especially those who are likely to generate false positives (younger women) is a very big problem in preventative medicine, especially when introducing a new modality like "3d" mammograms. Orac / David Gorski, MD (Surgical Oncologist (Breast)) has blogged extensive. A good if old starting place is https://sciencebasedmedicine.org/a-holiday-round-in-the-mamm...

> Seems to me the thesis that "mammogram positive" implies "possible cancer" is the faulty one.

It's not, though.

Possible ≠ certain or even likely.

Screening tests are used to determine whether there are indications for more invasive but more conclusive diagnostic tests.

> Possible ≠ certain or even likely.

Yeah but "possible cancer", taken literally like that, is everyone.

> There are benign masses that are radiologically impossible to distinguish

Time to bring out the pigeons.

Having just read the paper again, It’s fascinating.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4651348/

Also depends a lot on the nature of the screening and what is being screened for.

Prostate cancer being somewhat of an outlier as at least to my understanding, essentially all men will end up with some kind of tumor or another if they live long enough, but some large fraction of those won't become something that requires medical intervention before the individual would die from any number of other age-related causes. Outside my area of expertise but the relative size of the tissue that produces various breast cancers as well as the proximity to lymph nodes change the calculus on that a bit.

But I would definitely expect overall screening protocols to evolve as methodologies are developed that can potentially exclude the false positives from another metholodgy. While test A + A may still produce false positives due the nature of the test failing the same way, if we have A + B + C that are all relatively low-impact and not horribly expensive, that may end up being a fairly good program if some combination of A, B, and C generally exclude the parameters that the other produces a false positive for.

> as well as the proximity to lymph nodes change the calculus on that a bit.

That sounds interesting. Why does lymph node proximity matter?

Not 100% sure. But I think the proximity means that its easy for the cancer cell to spread to the lymph nodes, then they’ll get fast tracked around the body, spreading cancer everywhere. Once that happens you’re basically dead, all targeted forms of cancer treatment don’t work anymore, because the target area is basically your entire body.

You're not "basically dead" -- your odds of surviving 5 years drop from around 80% to 30%.

Again outside my area of expertise here, but to my understanding one of the significant risks to breast cancer is that if it spreads into the lymphatic tissue, it can subsequently metastasize across the across multiple other organs while compromising the lymphatic immune response that would normally help limit such a spread.

Prevalence of prostate cancer increases with age >70. Of confirmed cases ~2/3 are low grade, require only "active surveillance". Around 20% are intermediate grade tumors and ~10% are high-grade, aggressive cancer. The basic screening tool is the high-specificity PSA lab test, with biopsy considered the definitive diagnostic procedure.

Except for the highly malignant variety prostate cancer is generally an "indolent" tumor, that is slow-growing. So in the majority of cases chances are good that the patient would die of something else before the tumor becomes the cause of death. However prostate cancer is a leading cause of cancer death in men. In the US ~30k/yr men die of prostate cancer, so it's not a trivial condition.

> For many real tests, getting a false positive once predicts a higher chance of getting another false positive in a repeated test.

Almost all of them, in fact. If improving accuracy was as easy as repeating the test, the doctors would just be told that the correct procedure for this test is to take three readings.

You can expect that this is untrue only if the tests are especially expensive or invasive.

I believe repeating the test is standard procedure for many tests - if the first one is positive. However the repetitions are usually temporally separated (in some cases intentionally, in others because the test takes time.) This is effective in those cases because although there are a lot of temporary causes for a false positive to spike, there are fewer where it's persistent.

https://youtu.be/R13BD8qKeTg

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