Would YOU want to know the odds?

My brother was recently diagnosed with cancer.

Some folks think it is strange that he does not want to know "the odds".

I, however, think it is wise for many different reasons.

This is a "calibration" curve showing how most people process "odds" or "uncertainty".

The straight, green line that cuts across the graph diagonally is "perfect calibration."  That is not how folks intuitively process data, even ones that are highly trained in statistics.

The red, broken line more closely represents how people mentally "map" odds.  Most people are fairly well calibrated for 50:50 odds.  That is, the flip of a coin.

Most people are marginally calibrated for 25% and 75% odds.  When, in fact, the odds are 25% we treat them as if there was a 10% or 15% chance of occurring.  When there is actually a 20% chance of an event occurring we round down to 0%.  In a similar way, odds of 80% round up to 100% after being bent by our mental prism.

For all practical purposes that means that a patient who is told that their chances of survival are less than  20% will bend that information into certain doom.  They will lose the will to live.

Here is the pay-off line:
Based on the heuristics of how people process information: It would be more honest to dial in a little bit of Kentucky Windage and tell people with a 0.5%-to-20% chance of survival that they have a 25% chance of survival (which they will interpret as 10%-to-15% chance) than to than to tell them the mathematically defensible odds of survival (which they will morph to 0%).

But even that is misleading
To quote Gordon Dickson's Dorsai

Estimates had been...five percent (casualties) for the defending forces.  But such figures, without meaning to be, are misleading.  To the man in battle, twenty percent, or even five percent casualties do not mean that he will be five percent or twenty percent wounded... 

For life and death are binary.  There is no such thing as being a little bit dead.

Even if your odds of survival are one-in-a-million, iff you are the one...then you are still 100% alive.  The clarity of hindsight informs us that "your" odds for survival were 100%, just like the odds of that ovum being fertilized with that spermatozoon were 100%...in hindsight.

As a final consideration, consider the odds of a misdiagnosis.  Surely those odds are higher than 1%.

Healthcare practitioners
The game changes quite drastically for healthcare practitioners.  Doctors must use math to determine the course of treatment that offers the greatest benefit and the least harm.  Intuition is just not good enough.

Nurses must be protective of their own mental health.  Good nurses have an empathy bond with their patients.  "Knowing" that a patient might be dead in two months facilitates protective pre-grieving.  It also keeps the world orderly and sufficiently predictable to keep them from going bat-shit crazy.

The folks who are ripped to shreds are the doctors and nurses who are afflicted with cancer.  Perhaps even worse are the doctors and nurses who have close family who are diagnosed with the types of cancer that typically have 5%-to-20% survival rates.   Their professional training drags them one way.  The bonds of family anchor them.  What gives?

That is where we are today.  I have a brother with cancer.  I have a sister who worked as a nurse on the oncology floor for 25 years.  My sister lost her daughter in 2010 so she knows the agony of losing a child...and it tears her up when mom and dad ask her questions.  I have another brother who is a radiologist.  Actually, I have it pretty easy.

Bonus link on calibration and the appropriateness of extreme confidence.