50% survival rate : science

[–] [email protected] 42 points 6 months ago (1 children)

Assuming X~B(20,0.5), that gives us a p-value of...

0.00000095367431640625

Time to reject H0!

[–] [email protected] 19 points 6 months ago (1 children)

You're assuming those 20 were the only ones. Zoom out.

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[–] [email protected] 81 points 6 months ago (2 children)

First 20 patients died until the surgeon learned how to do it, next 20 survived. Technically it's 50% survival rate

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[–] [email protected] 50 points 6 months ago (2 children)

Can somebody explain the difference between the mathematician and the scientist parts of this?

[–] [email protected] 206 points 6 months ago* (last edited 6 months ago) (4 children)

The normal person thinks that because the last 20 people survived, the next patient is very likely to die.

The mathematician considers that the probability of success for each surgery is independent, so in the mathematician’s eyes the next patient has a 50% chance of survival.

The scientist thinks that the statistic is probably gathered across a large number of different hospitals. They see that this particular surgeon has an unusually high success rate, so they conclude that their own surgery has a >50% chance of success.

[–] [email protected] 60 points 6 months ago (3 children)

Thanks. I suspect a mathematician would consider the latter point too though.

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[–] [email protected] 9 points 6 months ago (1 children)

...How much is the total amount?

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[–] [email protected] 37 points 6 months ago (1 children)

Plot twist: 50% of each individual patient survives. Hope you get lucky with which organs make it

[–] [email protected] 6 points 6 months ago (2 children)

The left 50% or the right 50%

[–] [email protected] 4 points 6 months ago

Bottom 50%

[–] [email protected] 2 points 6 months ago

yes

[+] [email protected] 111 points 6 months ago* (last edited 5 months ago) (6 children)

[deleted]

[–] [email protected] 21 points 6 months ago (2 children)

Is the surgery incredibly risky overall but the surgeon only takes patients with the highest chances of survival?

[–] [email protected] 16 points 6 months ago (1 children)

If you were the patient, you'd still be happy about that. If the surgeon is cheating the stats, but has already accepted you as a patient, then you have the highest chance of survival.

[–] [email protected] 3 points 6 months ago

Great point, you’re right!

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[–] [email protected] 3 points 6 months ago (2 children)

How would you scientifically measure a difference between those two definitions?

[–] [email protected] 4 points 6 months ago* (last edited 6 months ago) (1 children)

In a statistical regression model, that would be a variable that encodes a specific individual; although encoding hypothetical (the scientific meaning of that word, not the layperson meaning) attributes of that individual is probably functionally equivalent, more useful, and easier to conduct.

[–] [email protected] 4 points 6 months ago* (last edited 6 months ago)

Attributes of the surgeons is not easier, because you need to pick the correct attributes.

Really you just need an indicator variable showing 1 if its data from the surgeon under analysis and zero otherwise.

Then test for that indicator variable being statistically larger than 0.

[–] [email protected] 53 points 6 months ago (2 children)

I mean, say this doctor has a 100% success rate but another doctor has 0%. Those two doctors collectively have a 50% success rate but it you have far better odds with the first doctor than the second

[–] [email protected] -1 points 6 months ago (2 children)

@Cenotaph Nope, say the first doctor did 100 successful cases, the other did 2 successful and 2 failed, then the collective would be (100+2)*100/104 = 98.07%

So the number of cases would matter.

[–] [email protected] 21 points 6 months ago

Of course. My point was only that there is definitely a difference between an individual doctor's success rate and the overall success rate of a procedure across all doctors, responding to the commment I replied to.

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[–] [email protected] 9 points 6 months ago (1 children)

The two doctors would only have a combined 50% success rate if they perform the same number of surgeries

[–] [email protected] 27 points 6 months ago (1 children)

After a certain point, it's really society's fault for letting the surgeon batting 0 continue performing surgeries.

[–] [email protected] 5 points 6 months ago (1 children)

That surgeon is bound to get one right one of these days!

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[–] [email protected] 75 points 6 months ago

Doctor stabs you. "Oh no! Questioning the surgery claims another..."

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[–] [email protected] 220 points 6 months ago (2 children)

"You should know that 9 out of 10 people who undergo this surgery will die. But don't worry, the last 9 people who took this surgery all died, so you're in the clear!"

[–] [email protected] 15 points 6 months ago (1 children)

Technically 1 out of 1 people who undergo that procedure die, eventually. Same is true for people who elect not to have the procedure done, eventually.

[–] [email protected] 27 points 6 months ago (1 children)

That's not confirmed. Only about 93% of people who ever lived died so far.

[–] [email protected] 26 points 6 months ago* (last edited 6 months ago) (2 children)

Death rate is also strongly correlated with when you were born. We’ve gotten much better at not being dead in the last 100 years. For people born in 1924 the death rate is nearly 100%, but for people born in 2024 it has dropped close to zero!

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[–] [email protected] 26 points 6 months ago

😱😱😱

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