Mfcttrf

In medical image processing most of the published works try to reduce false positive rate (FPR) while in reality false negatives are more dangerous than false positives. What is the rationale behind it?

You know the story of the boy who cried wolf, right?

It's the same idea. After some classifier gives false alarms (cries wolf) so many times, the medical staff will turn it off or ignore it.

"Oh, this again! NOPE!"

At least with the bioengineering group I've worked with, the emphasis is on reducing FPR specifically because the goal is to make a tool that will alert physicians to potential pathology, and they've told us that they will ignore a product that cries wolf too much.

For a product that aids physicians, we have to appeal to their psychology, despite the legitimate argument that missing the wolf on the farm is worse than crying wolf.

Edit: Decreasing false positives also has a legitimate argument. If your computer keeps crying wolf while getting the occasional true positive (and catching most of the true positives), it's effectively saying that someone might be sick. They're in the hospital. The physician knows that the patient might be sick.

TL;DR: diseases are rare, so the absolute number of false positives is a lot more than that of false negatives.

Let's assume that our system has the same false positive and false negative rate of 1% (pretty good!), and that we're detecting the presence of new cancers this year: 439.2 / 100,000 people, or 0.5% of the population. [source]

• No cancer, no detection: 99.5% x 99% = 98.5% (98.505%)


• No cancer, detection: 99.5% x 1% = 1.0% (0.995%)


• Cancer, detection: 0.5% x 99% = 0.5% (0.495%)


• Cancer, no detection: 0.5% x 1% = 0.005%

So we can see that we have a problem: for everyone who has cancer, two people who didn't have cancer wind up with invasive surgery, chemotherapy or radiotherapy.

For every person who fails to have a present cancer detected, two hundred people receive actively harmful treatment they didn't need and can't really afford.

Summary: the question probably* isn't whether one false negative is worse than one false positive, it's probably* more like whether 500 false positives are acceptable to get down to one false negative.

* depends on the application

Let me expand a bit on @Dragon's answer:

• Screening means that we're looking for disease among a seemingly healthy population. As @Dragon explained, for these we need extremely low FPR (or high Sensitivity), otherwise we'll end up with many more false positives than true positives. I.e., the Positive Predictive Value (# truly diseased among all diagnosed positive) would be inacceptably low.




• Sensitivity (TPR) and Specificity (TNR) are easy to measure for a diagnostic system: take a number of truly (non)diseased cases and measure the fraction of correctly detected ones.




• OTOH, both from doctors' and patients' point of view, the predicitive values are more to the point. They are the "inverse" to Sensitivity and specificity and tell you among all positive (negative) predictions, what fraction is correct. In other words, after the test said "disease" what is the probability that the patient actually does have the disease.




• As @Dragon showed you, the incidence (or prevalence, depending on what test we're talking about) plays a crucial role here. Incidence is low in all kinds of screening/early cancer diagnosis applications.
  
  To illustrate this, ovarian cancer screening for post-menopausal women has a prevalence of 0.04 % in the general population and 0.5 % in high-risk women with family history and/or known mutations of tumor suppressor genes BRCA1 and 2 [Buchen, L. Cancer: Missing the mark. Nature, 2011, 471, 428-432]




• So the question is typically not whether one false negative is worse than one false positive, but even 99 % specificity (1 % FPR) and 95 % sensitivity (numbers taken from the paper linked above) then means roughly 500 false positives for each false negative.




• As a side note, also keep in mind that early cancer diagnosis in itself is no magic cure for cancer. E.g. for breast cancer screening mammography, only 3 - 13 % of the true positive patients actually benefit from the screening.
  
  So we also need to keep an eye on the number of false positives for each benefitting patient. E.g. for mammography, together with these numbers, a rough guesstimate it that we have somewhere in the range of 400 - 1800 false positives per benefitting true positive (39 - 49 year old group).



• 
  

  With hundreds of false positives per false negative (and also maybe hundreds or even thousands of false positives per patient benefitting from the screening) the situation isn't as clear as "is one missed cancer worse than one false positive cancer diagnosis": false positives do have an impact, ranging from psychological and psycho-somatic (worrying that you have cancer in itself isn't healthy) to physical risks of follow-up diagnoses such as biopsy (which is a small surgery, and as such comes with its own risks).
  
  Even if the impact of one false positive is small, the corresponding risks may add up substantially if hundreds of false positives have to be considered.

  
  
  

  Suggested reading: Gerd Gigerenzer: Risk Savvy: How to Make Good Decisions (2014).

  
  



• Still, what PPV and NPV are needed to make a diagnostic test useful is highly dependend on the application.
  
  As explained, in screening for early cancer detection the focus is usually on PPV, i.e. making sure you do not cause too much harm by false negatives: finding a sizeable fraction (even if not all) of the early cancer patients is already an improvement over the status quo without screening.
  
  OTOH, HIV test in blood donations focuses first on NPV (i.e. making sure the blood is HIV-free). Still, in a 2nd (and 3rd) step, false positives are then reduced by applying further tests before worrying people with (false) positive HIV test results.




• Last but not least, there are also medical testing applications where the incidences or prevalences aren't as extreme as they usually are in screening of not-particularly-high-risk populations, e.g. some differential diagnoses.

False Positive Rate (FPR) also known as false alarm rate (FAR); A large False Positive Rate can produce a poor performance of the Medical Image Detection System. A false positive is where you receive a positive result for a test, when you should have received a negative results. For example A pregnancy test is positive, when in fact the person isn't pregnant.

Clinician's time is precious

From within the field of medicine, clinicians often have a wide variety of illnesses to try to detect and diagnose, and this is a time consuming process. A tool that presents a false positive (even if at a low rate) is less useful because it's not possible to trust that diagnosis, meaning every time it makes that diagnosis, it needs to be checked. Think of it like the WebMD of software - everything is a sign of cancer!

A tool that presents false negatives, but always presents true positives, is far more useful, as a clinician doesn't need to waste time double-checking or second guessing the diagnosis. If it marks someone as being ill with a specific diagnosis, job done. If it doesn't, the people which aren't highlighted as being ill will receive additional tests anyway.

It's better to have a tool that can accurately identify even a single trait of an illness, than a tool that maybe fudges multiple traits.