Bayes' Theorem and Cancer Screening
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- Опубліковано 6 вер 2024
- Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! Bayes' Theorem and Cancer Screening.
A very real life example of Bayes' Theorem in action. ** According to some data I found online (not sure how accurate it is), mammograms are actually less reliable than the numbers I used! Pretty amazing to me... *
Hey Patrick! Please, never ever remove any of your videos. I am watching this after 8 years you've posted it. There will be people who will watch it 20 years later.
I agree :)
Watched this in early undergrad 2015 and I started grad school last month and needed a refresher. It even sticks better after all these years !!!!
I’m theperson watching it 9 years after
Probability is giving me cancer.
it is a painfully difficult subject i think. intuition usually is of no help
patrickJMT It made more sense when I was just taking combinatorics, but now I'm in statistics and all the notation is just making it more confusing.
Good one :)
100%
Don't worry, it's only 8% probability
bought a new mic, hopefully it will help!
This tree diagram method is incredible!! Formal notations always made this problem look difficult, but you made it so simple that even a 9 year old kid can understand this!! HATS OFF TO YOU SIR!
the stuff you can do with stats pretty much blows my mind; i think it is great stuff
This is a great video. I would wish all doctors think about this and share this information with their patients when they get a positive result. However, once you hear Cancer, it is hard to hear anything else.
Thanks a lot Sir. Your tree method is awesome. I'm able to solve all the problems now
all the problems???
Relax man Einstein wasn’t capable of that
2ew lm
@@anushasattu8010 yes
I think this has to be the best tutorial for learning Bayes' Theorem, Thank You!
7 years old video and still one of the best out there
Woooooooooow you taught me in less than 5mins what my lecturer didn't teach in hours. Thank you so much for simplifying everything. I'm gonna teach my friends and recommend them here.
I got this, which made more sense to me since the numbers add up to 100% for having cancer or not given a positive or negative test result respectively:
P(Cancer | +) approx. 8.3%
P(Cancer | - ) approx. 0.1%
P(Healthy | + ) approx. 91.7%
P(Healthy | - ) approx. 99.9%
The idea of the tree diagram makes this the best approach to teaching the intuiton underlying Baye's Theorem.
I will always come back to this explanation of Bayes theorem, no matter which phase of life I am in, thank you!
There's a small piece of background information missing here. In the original explanation of the problem on other links, the figure of 10 out of 1000 women is based the rate of women had a mammogram and who had cancer. The 1 percent is not some separate number from the tracking of the mammogram results. The subtle context is important in understanding the problem.
Thanks! Great video..
However, it is important to keep in mind that this is only true for screening tests evaluating people randomly selected from the population.
In clinical reality, prior probability {P(cancer)} is not equal to 0.01. The thing is that 1% prevalence is estimated for the general population, but those who are specifically looking for the test may have, for example, some clinical symptoms and their prior is going to be substantially higher).
Good point. Hopefully people watching this video don't break out Bayes Theorem to loved ones if they get the bad news.
after watching video im feeling dat i hv a cancer lol
not really randomly... like, they were women from 40 to 50 yo.
Well explained. I was a little "upset" by how misleading the last statements were in the video but for anyone who understands the entire process, it is a really great example.
thank you! thank God sb said it
At 1:04, isn't it supposed to be that:
A = The woman has cancer
B = A positive test?
بشر الحافي 1+
cool
The tree diagram greatly simplified figuring out how to solve the problem. It made Bayes Theorem easier to understand.
Hey! Just wanted to drop in a thanks. I watched this video the night before an exam and a VERY SIMILAR question like the one discussed here came up and the tree diagram approach was what I used. It felt effortless. Cheers!
awesome! glad it helped
literally the only explanation i understood on youtube after 30mins of searching. thank you so much
the tree diagram helped out a lot more than I thought
This guy is the OG! The tree diagrams really helped me understand Baye's Theorem.
This is by far the best tutorial for bayes theorem. !!!!! Awesome thanks !
Omg this question came in the midterm yesterday but I didn’t know how to solve it and now I see this. I might cry in any minute.
This is my favourite video for revising Bayer's theorm .. Gr8 work Patrick
Watching 1hour before exams. This is the best video 🔥thank to your tree method
You should have another video about a the probs of having cancer given you were tested positive on a second exam if already tested positive on the first one, like P( A | (A|B))
we already have P(A|B), so just apply the same rule again, just the B from P(A|B) is now the result of P(A|B)
I saw ur all 3 videos on Bayes..... They have explained it in a perfect manner while giving it mathematically and real life examples. Best thing was that u are exactly to the point... Thanks a lot
I couldn't wrap my heard around this thing... spent hours today trying to understand it.. but I just had a vague understanding of the Bayes' theorem... After watching 3 of your videos, I am fully clear about it... Thanks!
Hello, my name is Athelstan. This video was extremely helpful. I'm only 11 and I understood every word you said. This helped me a lot with Bayes' Theorem. I thank you again patrickJMT .
You are clearly the best patrick. Smooth work. Thanks so much
Was sruggeling for hours without being able to answer Bays theoram question correctly for with 100 certainty.. The Tree diagram technique did the trick. Thank you so much. Really appreciate it.
I think you got your formula wrong :) it should be P(B|A) since you mentioned B is "woman who has cancer" and A is "positive" so P(B|A) - probability woman have cancer given the test is positive?
+Christine Teh thank you i was looking for this because isnt P(B|A) already given as 90% his whole thing was inverted made me so confused. The data that was unknown was P(A|B) the probability of testing positive if you are already positive?
What's bugging me is that in the beginning we say:
A = "a positive test"
B = "has cancer"
...so it should be P(A) = 90% and P(B) = 1%, as stated in the text, right? But then later (06:21) we put *P(+)* (= P(A)) *=* *10% x 90% + 99% x 10%*
What exactly am I overlooking here? :/
You seem to have overlooked the fact that P(+) includes the chances of getting a positive (0.01*0.9) and the chances of getting a False positive (0.99*0.10)... we aren't just considering the chance of getting a positive if you HAVE cancer, we need to take into consideration the chance of getting a positive if you DON'T have cancer... I hope I was able to help
Apart from contradicting what A and B were defined as at the start this is a great video thanks!
Thank you so much you saved me with how to sketch a graph in math and now with this in philosophy! Lots of love and respect!
very nice video.
this is why mammogram is a screening test and not a diagnostic test, we don´t want to make a diagnosis of breast cancer with mammograms but rather select the patients that would benefit from going to breast biopsy.
It is better to send a patient to breast biopsy when she doesn´t have breast cancer than not sending a patient to breast biopsy when in fact she has cancer.
this ilustrates the concept that in screening tests we sacrifice specificity to increase sensitivity and miss the diagnosis in very few patients even though we increase the number of a false positive result.
another example would be HIV; we screen patients for HIV with ELISA; Which is a highly sensitive test with very low specificity, therefore it is not diagnostic. patients who had a positive ELISA should undergo western blot which has high specificity.
The tree approach was simple to follow. The notation at the beginning was not consistent and was misleading.
Your talent of explanation is always 100% according to Bayes' Theorem. P(A | B) = 1, where A = "Excellent explanation" and B = "(by) Patrick"
Thank you! Very much
Thank you Sir. You're a great teacher. I have now fully understood the concept of how to calculate probabilities with and without replacement.
I want to give you a very warm thank you, this video was just amazing
What's the math notation for finding P(+)? I would think, P(+) = P(+|Cancer) + P(+|NoCancer) ...right?
Damn you, Patrick. I'm on break and I still can't stop watching your videos!
This is the most helpful explanation of Bayes' Theorem I've encountered. Love it, grokked it!
That was great man..really helpful..the tree method and defining the fact that the 90 and 10 doesn't have to add up to 100 ..cleared all the Confusion away..thanx man..
Been struggling with this just understood now after long hours of scrolling through UA-cam thanks so much
The tree method makes these type of examples so easy. Thanks a lot.
How I can like this video multiple times? This man is a legend, salute!
I agree with Sanoob below. The tree visual is so very effective. It strikes me though, that I've never seen nor heard any lecturer or expert explain, how the probabilities of .01 and .99 were derived. I think this can be a point of confusion. Until today, I always thought these preliminary probabilities were somehow tied to medical test this example/video is featuring. Were these (.01 & .99) probabilities derived from a different medical test? If so, then why don't we just use the other test, as it appears it was able to come up with these finite probabilities. Why mess with a medical test that produces probabilities of these probabilities. Perhaps it is just my lack of brain power, but I would always think the featured medical test itself came up with these in the past and we were using these (.01 & .99) probabilites from the medical test's historic data. I fear no one can even follow what I am saying.
Hey patrick, I apologize if you've already covered some of this stuff. But I'm doing my final year in high school this year, and I'm taking calculus. My teacher has given the class work sheets and whatnot, on exponential functions. I think I've seen some of your videos on the topic already, but they weren't able to clarify what I'm looking for. I'll try and make sense with this; I was given a question where we have to simplify and express with positive indices and there was a question
Thank you very much for your helpful video. I just got a little confused because at first you let
B= the woman has breast cancer
A= a positive test
but later while resolving the question, you flipped A and B.
At 3 mintues 30 seconds, you said that
A= is that you have cancer and
B= test positive.
Maybe I don't undertand it well but could you please clarify it ? Thank you very much
+g3osom1 hmm ok I will have to watch it again. thanks
Well explained! Thank you..
Also, what of the patient has BRAC2 mutation. 26% BRAC2 has the probability to have cancer.. How will we make the tree?
Thanks for the video, you did a great job explaining the concept! However, it's important to know that the chances of getting breast cancer change depending on your age. Your numbers are probably pretty accurate for a younger woman, but for older women the positive predictive value of the test is much better (i.e. a positive result on a mammogram is much more likely to indicate that the woman actually has cancer). This is because breast cancer is more common in older women, so the top branch of your tree diagram would be a good bit higher than 0.01.
thank you patrik , i was struggling with this kind of problem, and the diagram part is so beautiful to understand
I saw another video which suggested that using this test result as a prior if another test is done and its result evaluated, the confidence of the diagnosis increase multiple fold. Essentially the prior of 1% is that of the population. A new prior based on the first test in evaluating a second test can add to the accuracy. Generally many go for confirmation of a serious diagnostics with a second test / opinion. I used to think that may not be so meaningful. But after watching that video, it appeared it was most sensible. I am referring to it here, because such an extension of narrative seemed to be a desirable thing to do. Your video may well be watched by many with cancer. So it could be helpful to talk about that.
You got me through all of calc. Now you're getting me through this. Why couldn't my teacher show me the tree ffs? You saved me again.
Please make a video explaining this question.
Two sources of name and address data have been acquired and merged into a single file. In the combined file, 60% of the records came from Source A and 40% of the records are from Source B. It is also true that the names are correct on 80% of records from Source A, but only 50% of the Source B records have a correct name. If a record is selected from the combined file and is found to have a correct name, what is the probability that the record came from Source A?
Finaly someone has explained it in a sufficiantly thurough and geeky manner that I can grok it. Thankyou!
I am learning how to apply Bayes' to various Genetics problems. The equation listed in my book is different from the equation applied to this problem, we use:
Pr{A|B}=(Pr{B|A}*Pr{A})/((Pr{B|A}*Pr{A})+(Pr{B|A'}*Pr{A'})). What is the difference between the two equations and how do I know which one to use?
Tree diagram really helped. Thanks.
Thankyou you so much sir ..your tree diagram cleared all my doubts...loved your explanation
Bayes rule and the law of total probability problems were my favorite part of my STAT 346 course good example
tree method is really good it helps to simplify the problem
You da real MVP
TheTranMan23 patrickMVP
Rachel,
Both formulas are the same. If u see how he calculated probability of +ve test he comes to the same formula as u described.hope this helps
Romendra
The tree diagram makes me understand Bayes. Thanks!
very well explained..cleared my fundamental confusion of conditional probability
To start with ... your "printing" is superb, which I find easier to read and then comprehend ! Thanks !
SIR THANK YOU
Thank you very much Sir for the video. I was really having trouble figuring out with formula, but the tree diagram looks really more easy and favourable. THank you a bunch.. I have however one question left :it roughly says "What is the probability that a randomly selected woman has a breast cancer?" Our teacher solved this one using the formula which i don't get at all. How can we figure this out by using the tree diagram ?
Thank you again!
+hunter sikari I'd like to answer this but I'm probably completely wrong. At the beginning of the problem it says approximately 1% of women aged 40-50 have cancer. This means there's a 1% chance, right?
How do we identify the questions where we have to apply Bayes theorem formula or conditional probability formula ?
Tree diagram from top to bottom:
1. Power of the statistics
2. False negative or type II error
3. False Positive or type 1 error.
4. good
Please verify the understanding, thanks
Power, False negative (type II), false positive (type I), confidence interval (1-alpha) =)
I'm a high school student right now and I always watch these videos! Just kinda curious, which university did you attend? Im going to UChicago
Hi Patrick: Could you do an example on type I & type II error and hypothesis testing using the same cancer testing example. Also, could you do one court example using Bays theorem, and explain false positive, false negative, type I & type II error and do hypothesis testing. Thanks
the best i ve seen on this topic
Great video, definitely free of some logical jumps and hand-waving that are common elsewhere. Have you done a similar video showing Bayesian inference and the process of considering new data given some initial results like this? The iterative inference method and reference to prior knowledge/assumptions is one of the strengths of practical applications of Bayes' Theorem, right? Or is that already on display here since you assume that you have accurate data on real-world true positive rates?
This tree method is gold.. thanks
Fairly sure there was a bit of a hiccough in the math at the end.
the bottom of the denominator should equal to 0,1881 approx, instead of the 0,108.
0.1*0.90+0.99*0.10 = 0,1881
Otherwise nice explanation of the method! Thanks for the video!
I am also confused with the conclusion at the end. 8.3 % only? Why is it so low? What are the assumptions made?
Ooooh! I really really thank you Sir Patrick!!!
SO there is a 91.7 % chance that someone doesn't have cancer but actually tested positive. Is that what you are saying? How is it different from the 10% false positive rate.
What am I missing?
Great video as always. Thanks
Thank you very much for this video, I have a clear understanding of bayes theorem now
great video! you can make it better by using a microphone cover to cover the microphone for less air sound when you say words with S, C, etc.
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Extremely good. Extremely extremely good. I love these applications where ordinary intuition is challenged and even undone. So this example leads us to ask how much time, money and emotional stress should be devoted to the mammogram as a diagnostic tool? I know your task here is not medical research, but if there are better and less stressful ways of isolating pathology, then...
I think a way to 'see it' might be to imagine a lottery where you also roll a 10-sided die. The chances of a good roll on the die are insignificant next to the odds of a good ticket. However, I'm pretty sure doctors run multiple cancer tests to increase accuracy.
thanks guy. saved me from having to watch that other dude's 10 part youtube series on this topic which kind of creeped me out due to it's esoteric feeling and stuff.
Finally understood this. Thank you and God bless
You are very welcome
Oh my good god, if you watch one video on Bayes' Theorem, make it this. Cheers buddy, this helped so much
Pat: please consider using a limiter on your microphone. It will make for less distraction for your listeners. Otherwise, great job!
best explanation i've found online
Thank you so much, the real life example you used helped a lot
thank you thank you! I watched a few videos before this one and this is the one that finally made sense to me!
@patrickJMT, That's a great video, great explanation. Thanks a lot. Best regards
What an interesting example! I want to be sooo good at statistics. Thank you! ^_^
awesome and awesome..really very helpful to understand Baye's law.
By the way, this is known as the positive predictive value. Just in case someone wants to look it up and find out more.
Brilliant example. Thank you.
Jeeeeeeeeez been watching video after video this is the first one that made it clear!!!!!!!!!!
hey
You have saved my life yet again! Thank you!
It was all fine up to the point when you multiplied `branches` for all positive and added them. Can anyone please elaborate on that part?
you're adding up all the possible probabilities you could get a positive test. It's like finding the probability of rolling an even number on a die. P(Even number) = P(2) + P(4) + P(6) = 1/6 + 1/6 + 1/6 = 1/2. Finding the probability of rolling an odd number would be the other half, that makes P(Even) + P(Not even) = 1.0
@@theralhaljordan7337 I see that makes sense. Thanks for the explanation.
Thank you so much!! 😭 May god bless you!