Etydhv

In medical image processing most of the published works try to reduce false positive rate (FPR) while in reality false negative is more dangerous than false positive? 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.

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.

I think burden of responsibility plays a major role here.

For example, if due to the lack of imaging tools 40 patients with true cancers were not diagnosed early, we believe it is nobody's direct fault.

However, if 10 patients from those 40 are labeled as "have-cancer" using an imaging tool, but 3 patients were truly "no-cancer"s, i.e. true positive = 7 and false positive = 3, financial, physical, and psychological costs (for further tests, medications, and stress) inflicted upon those 3 patients are deemed to be doctor's responsibility which prescribed and acted upon that tool. In other words,

Society does not credit the doctor +7 -3
= +4 points but -3 points!

Therefore, false positives damage the credibility of doctors in the eye of patients, and thus credibility of that tool in the eye of doctors. This is a reason why "they would not use the tool anymore" as pointed out by @Dave.

Credibility, as the major concern here, can be formalized with precision, i.e.
$$textprecision=fractexttrue positivetexttrue positive + textfalse positive$$Precision goes to one (maximum possible) when false positive goes to zero, or true positive goes to infinity. However, the latter is way harder to achieve than lowering the false positive. For example, if up until now the tool has tp = 9 and fp = 1, its precision is
$$p=frac99+1=0.9$$
If it diagnoses the next patient wrongly as "have-cancer", fp goes up to 2, and precision down to 0.82. To restore the precision back to 0.9, the tool must find 9 patients with true cancer, which requires testing hundreds of patients, to reach
$$p=frac1818+2=0.9$$
again. Therefore,

It is very hard to revert the damage of false positive on credibility

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.