False Positives & Negatives for COVID-19 tests | Using Bayes' Theorem to Estimate Probabilities

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Suppose you test positive or negative for SARS-Cov-2, the coronavirus that causes COVID-19. What are the chances you actually have the disease? In this video we're going to look at Bayes' Theorem from mathematics to help us compute the conditional probabilities. COVID-19 tests are actually in two categories, genetic tests and antibody tests, and both of these have different levels of sensitivity and specificity - i.e how accurate they are. While Genetic tests have extremely low false positive rates, some antibody tests do have higher false positive rates and, given the low prevalence in the general population, Bayes' theorem demonstrates how problematic this can actually be.
Disclaimer: I'm not a medical doctor or epidemilogist, just a math prof, and so these toy examples are meant to illustrate the ideas of Bayes' theorem, not make actual concrete predictions based on a specific test.
Intro to Bayes' Theorem Video: • Bayes' Theorem - The S...
Some references:
FDA (genetic test have nearly 100% specificity):www.fda.gov/me...
Genetic Test False negatives: www.medscape.c...
Abbott Test study showing 15% false negatives: www.npr.org/se...
Antibody test sensitivity and specificities: www.centerforh...
Antibody tests false positive due to cross-reactivity with other coronavirus antibodies: www.aruplab.co...
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►LINEAR ALGEBRA: • Linear Algebra (Full C...
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This video was created by Dr. Trefor Bazett. I'm an Assistant Teaching Professor at the University of Victoria.
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14 окт 2024

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Комментарии : 227

@nickpekelsma-menlopeck 4 года назад

Good job making a difficult concept more intuitive.

@AstroKidLo 3 года назад

This was a great explanation but it would be nice if you were to mention the benefits of multiple testing. With a prior Hypothesis of 50%, a second test would increase the chances drastically. That would highlight the true nature of Bayes' Theorem, in which a hypothesis gets more accurate the more information is gathered

@deal2live 3 года назад

In the UK we had a big media bust up and social media and fact checkers calling foul on one some one saying that false positive was huge (90%). Basically the described the same you did. the balance between prevalence and false positives is so counter intuitive that even 'smart' journalist failed to see it!

@berserker66lewis78 3 года назад

And Matt Hancock failed to see it too. He had no idea that if the tests have between x% false positives then this is a % of the tests, not as he thought a % of the pcr positives.

@BasPronk 3 года назад

I would have liked to see a graph showing the percentage of false positives in relation to the prevalence of the disease, keeping the test parameters (sensitivity and specificity) the same.

@arnoldbirkenhager1290 3 года назад

Great vid Trefor! I did a Bayesian analysis some time ago to demonstrate to my colleagues that they should still go on their clinical instincts even if I patient tested PCR negative. Some publications report that the sensitivity and specificity of the RT-PCR are actually lower than previously thought. Sensitivity ~70%, specificity ~95%. This is still a good test to confirm COVID-19 when your suspicions are high, but not so good to rule out the disease in the same circumstances. Coughing, sneezing, fever and/or loss of taste or smell, still equals isolation for 7 days, despite a negative PCR. Currently, there are very cheap home tests available that claim a very high sensitivity (~97%) and specificity (~99%). The problem is that the studies of those tests have relatively low numbers of test subjects (around 600, in one case) and that the goal was to verify a positive PCR, not actually to verify COVID-19. How useful are those tests? I would really like you to do a video on this.

@goncalodvd 3 года назад

To randomly test population with no syntoms on a less than 1% prevalence they are good to wipe your ass in them ...

@ubomban 4 года назад

It is all about ct values, every test with ct value more than 35 is too sensitive, when they test you, they use 40 cycles that is why they get so many false positives and they put lockdowns based on those false results...Juliet Morrison, a virologist at the University of California-Riverside, said she believes any test with a cycle threshold over 35 is too sensitive. "I'm shocked that people would think that 40 could represent a positive," she said

@rossd6809 4 года назад

Add in the error associated with declaring a positive result from a cycle threshold value you might have a further inaccuracy.

@trevorpullen3199 3 года назад

9 months later and still no one had no idea what the false positive or false negative rate is for PCR tests. Yet the world continues to test millions of people per day and make drastic government enforced mandates based on the results of those tests.

@goncalodvd 3 года назад

Crazy isnt it? And then they call us, the ones that studied this, negacionists. They need to get hanged ...

@danawilson2771 4 года назад

Couldn't be more timely. I had to pause and rewind a number of times to get your fast, staccato delivery. All went OK until the rationale for the "two bucket problem" and rapid fire presentation of false negatives. Suggestion: Khan Academy modules often say, "Now stop the playback and try to work it out before going on". Worth trying.

@herseem 3 года назад

This concept is best explained using diagrams. In my experience, most people, when they get the concept of Positive Predictive Value, they are shocked. Also in my experience, of dealing with HIV, is that most public health professionals really don't get this.

@goncalodvd 3 года назад

Exactly. And that ignorance created this mess along with politicians trying to save their necks ...

@divyanshipandey4580 5 месяцев назад

thank you so much ... i was so worried that how will i pass this exam... but your videos are seriously helping me to understand the topics clearly ... THANK YOU

@walterpu8357 4 года назад

Didn’t do well in your calculus 3 exams this morning, but click this video anyway when it appears on my RU-vid page

@SimonTaylorUK 3 года назад

Came here via WQU data science course needing some background on Bayes. Using COVID as an example helped a lot to clarify the key points. I really enjoyed this explanation thank you!

@DrTrefor 3 года назад

Glad it was helpful!

@davidduncan8244 3 года назад

Dr. Bazett , would you look into the PCR test, The inventor of the test was obstinate stating the PCR should never be used to diagnose the test. Lets say a 30 times increase

@rngmarmalade8159 3 года назад

You gave 2 definitions for False positives, the first one was at 5:33 P(DF|+)while the second is at 10:40 P(+|DF)

@rehabalsaleh166 3 года назад

Outstanding! Absolutely one of (if not the) best videos I've seen regarding Bayes' theorem! Keep up the hard work! Thank you so much!

@beckyparker6733 4 года назад

Typos: _ (negative sign) was incorrectly labeled as Testing positive (copy/paste typo likely) I saw "Cor" rather than "Cov" near the end of the video. Otherwise well done!

@v8pilot 2 года назад

This is interesting to me. In the early days of the covid pandemic the UK govt was publishing scary numbers for covid infections. They referred to a +ve test as "a case" even though in the past "a case" was a patient who displayed recognisable symptoms *and* who had had a +ve diagnostic test. But I was convinced that, with a largely healthy population many of the +ve's had to be false positives.

@r0m4132 3 года назад

My professor gave this example in one of the lectures and I couldn't wrap my mind around it, but thanks to you I can now. Thanks :)

@DrTrefor 3 года назад

You're very welcome!

@kucken64 2 года назад

Wonderful video. Will be showing this to all of my student's to help them wrap their head around Bayes' Theorem.

@DrTrefor 2 года назад

Cool!

@raduandreinegrila215 4 года назад

Your conclusions are true and thank you for another great video ! However, in reality P(cov) is much higher for a person that actually gets to be tested because, regardless of Prevalence of COVID19 in the general population, the person being tested is not randomly picked from the population, but is part of the biased sample of people who either have COVID19 like symptoms, or else have been contacts of COVID19 confirmed cases (this biased sample approach to testing also has the corollary of missing a lot of cases, as asymptomatics, mild symptomatics or their contacts are not usually tested). Secondly, even if the person was randomly selected form a population with a prevalence of 1% of COVID19, the test is usually repeated more than once and a second consecutive false positive should be far less likely, as after the first test P(Cov) becomes 0.49 and P(DF)=0.51, so P(Cov|+) =0.95 *0.49/(0.95*0.49+0.01*0.51)=0.989. That is, you have about a 1.1% percent chance of a second consecutive false positive. I am also not a doctor, except in physics, so please correct me if I am wrong in my reasoning.

@raduandreinegrila215 4 года назад

@@DrTrefor thank you. Any thoughts on the second observation concerning a second test? Are my calculations correct? :"Secondly, even if the person was randomly selected form a population with a prevalence of 1% of COVID19, the test is usually repeated more than once and a second consecutive false positive should be far less likely, as after the first test P(Cov) becomes 0.49 and P(DF)=0.51, so P(Cov|+) =0.95 *0.49/(0.95*0.49+0.01*0.51)=0.989. That is, you have about a 1.1% percent chance of a second consecutive false positive. I am also not a doctor, except in physics, so please correct me if I am wrong in my reasoning."

@billcrawford4547 3 года назад

Wider use of PCR testing (to gain admittance to various places, to remain in school/college, etc.) is becoming more widespread. (One daughter is tested weekly at college.) And the use of contact tracing dramtically spreads the impact of false positives. An example: our school quarantined 150 people based on the positive test result (misnamed a "case") of one person. Using just Bayes and not the other significant, known problems with PCR testing, there is a 50/50 chance 150 people where sent home for nothing. Unconscionable.

@billcrawford4547 3 года назад

And, no, people are not being tested twice before being quarantined. Furthermore, if the probability of a false positive is 0.49 (using just Bayes - would be higher due to other problems with PCR testing), then getting the right test for a non-COV person with two tests is 0.49x0.49=0.24.

@JohnMartin-jx1wz 2 года назад

Not all people who are tested have symptons.

@chrisimming9454 2 года назад

Except that isn't always (maybe most often not the case) the case. People are being encouraged to get tested whether they have symptoms or not. School children are being tested whether they have symptoms or not. Employers are testing all employees whether they have symptoms or not. In Jan Feb 2021 the US government is providing free tests without regard to symptoms. I have gone to the testing site before and after travelling, for example, to get tested as required in some cases and never had symptoms and there was no requirement to have symptoms for any of those tests. It makes more sense to only test symptomatic people esp those with comorbidities but that isn't what's happening.

@coleabrahams9331 3 года назад

How did you make such a cool set up with the animation (which I assume was created via PowerPoint) as the background and you talking over it??? Please tell me

@DrTrefor 3 года назад

Yup green screen with PowerPoint!

@coleabrahams9331 3 года назад

@@DrTrefor thanks so much

@craigburton4447 4 года назад

Could you do an explainer on pre test probability, it seems a lot of people think that testing people with symptoms with result in 50% or even 90% false positives, really good video tho, I subbed

@DrTrefor 4 года назад

The example of this video used people chosen at random, when you select instead for people who have a symptom you have to change the prevalence. So for instance, if covid-19 had 1% prevalence in the population in total, it might have - just making up a number - 10% prevalence among the subpopulation of people with covid-19 like symptoms, which is going to dramatically drop the percentage of false positives.

@anon9454 2 года назад

One word for this explanation- Beautiful

@wyattstevens8574 9 месяцев назад

Here's an alternate form of the theorem, posed by Grant Sanderson: For the case of +ve test, start with prevalence (prior) in the form of odds. Now just multiply the ratio of positive/negative by the positive Bayes factor, which is the TPR/FPR (number of times as likely that a resulting positive test *should* be positive). For -ve tests, start with 1-prevalence as odds. Multiply this ratio by FNR/TNR to see your expected chance of being a should-be positive now, in this case. By the way, if you remade this video (or another exploring the Sanderson shortcut) the prevalence today (January 14, 2024) is about 0.3% (~ active cases/world population)

@fma-d8j 3 года назад

Thank you. could you please make more example videos for Bayes' theorem?

@DrTrefor 3 года назад

I have several in the "discrete math" playlist:)

@flatorsharp 4 года назад

Isn't there a possibility of what could be called a 'feedback loop' in the value of 'prevalence' if a person uses a percent positive that is increasing - given that the increase may be due to false positives?

@goncalodvd 3 года назад

Absolutely.

@reemabdullah9905 2 года назад

you saved me! Your explanation is the best!! wish if your videos can be shown to us during lectures

@curtisvongunten1509 4 года назад

I find that most discussions of binary classification logically emphasize sensitivity and specificity too much over precision (positive predictive value) and negative predictive value. The .49 being described at the end is precision (positive predictive value). It addresses the following: of all of the tests that come out positive, what proportion of those are true positives. The predictive values aren't any more or less important than sensitivity and selectivity, they just emphasize different aspects of the confusion matrix. F1 score is a metric that includes sensitivity and precision: en.wikipedia.org/wiki/F1_score

@ccuny1 2 года назад

Hello Dr. Bazett. Like Astro Kid Lo' below, I am curious about the effect of multiple testing. There are medical articles describing re-testing a couple of days later, but to keep things simple, I have just been wondering if taking the same test twice in a row makes any difference to the results. I think it does, but I get into a real tangle trying to think it through, for two reasons. First, I don't know whether I can say that the two events (the two tests) are independent. I think I can but I keep thinking of qualitative reasons while this may not be the case. Assuming they are independent, then would it be correct to assume that the prior probability becomes the conditional probability after the first test? If so, then the second test - although it suffers from the same weaknesses as the first - should increase accuracy. And yet, the intuition (which is often wrong but difficult to get rid of) is that it matters not one bit if you take a second text immediately since it suffers from the same weaknesses as the first and because it is taken immediately after the first test, it should yield exactly the same result whether accurate or inaccurate. I really need help thinking through it...

@ScreamKii 3 года назад

I came to quickly learn Bayes’ Theorem, but subbed because of THAT SHIRT! lol (kidding, I subbed because your explanation was amazing and easy to follow, thank you!)

@DrTrefor 3 года назад

haha, thank you!

@dangalpern2979 4 года назад

Professor: You went too quickly for me to follow at the end when you discussed the question of false negatives. Suppose a person had experienced Covid-19 symptoms and duly isolated herself until symptom free. But she never received a viral test while with symptoms, due to the scarcity of viral tests or for whatever reason. Nonetheless, she recovers. Now, several weeks after such (apparent) recovery she wants to learn if she really had the disease. And for several reasons, including personal (or professional interest): had she properly been diagnosed while with symptoms (perhaps via a telemedicine call, or self-diagnosis) before? More importantly, she'd like to be able to discern if she now retains at least some immunity (even if limited in degree or time) against reinfection? This time, however, she is able to obtain a relevant test, that is, a serum or anti-body test. But (disappointingly) it returns negative -- that is, the test has not detected antibodies. I think there are two possibilities: either the test properly discerned that she has no antibodies (and so likely has no immunity, and likely did not have Covid-19) or else that she has antibodies that the test failed to detect (and so she likely had Covid-19 and likely has at lease some measure of immunity for some period of time). How does she figure out the odds? Not sure how to use Bayes' theorum for this. Thank you, in advance.

@drjdidier 4 года назад

If, given the video’s assumption, covid affects 1% (our “priors”) of the healthy-asymptomatic-population, then we can safely assume that your patient does not fit into this subset. We would have to adjust our priors based on the expectation that a person who has or had symptoms characteristic for covid would have a greater than 1% probability of being infected with covid. What is the probability? Well it would depend on whether the symptoms are pathognemonic for the disease or whether they only indicate a possibility of infection. If we assume that the patient has a 30% probability of being infected based on the symptoms, then this becomes our new “priors”. We know that odds = .3 / .7 (P of being infected /P of not being infected ) = 0.42857 We also know that post test odds = pre-test odds x likelihood ratio for a negative test = .42857 x (1-sensitivity)/specificity = .42857x .05/.99 (based on the sensitivity and specificity provided by the video) =0.021645 Probability of a negative result = odds/(1+odds) = .021645/1.0021645 = 2.16% So the probability that she has the infection given a negative test result is about 2% percent in this case. .

@JohnMartin-jx1wz 2 года назад

True negative values.

@jonnicholls8256 4 года назад

Great video. Right up there with Numberphile and Eddie Woo. When I listen to maths professors online they always explain things with crystal clarity. As a 'high school' teacher, I find this a tricky task indeed! I have one question. How can scientists judge the accuracy of their tests without depending on the tests themselves for the figures. So for example with COVID 19, we need the tests to determine the prevalence of the disease within the population. But then we need to know how accurate our testing is - there seems to be an infinite regress here??

@jonnicholls8256 4 года назад

Thanks Trefor, really appreciate you taking the time to answer my question - I guess my question and the answer you have given really applies to any kind of inductively reasoned conclusion and demonstrates the need for caution here. Incidentally, I've stumbled upon your channel quite accidentally whilst looking for useful videos that discuss the mathematics behind the recent outbreak. But it seems that you've created content on a whole range of topics that could be useful to my classes - particularly on calculus and proof. I look forward to watching them - perhaps with my class - and would like to thank you on behalf of myself and my UK students. All the best.

@berserker66lewis78 3 года назад

This is very interesting and backs many of my comments on false +ves. Have you looked into Benfords law on the number of pcr positives in different countries. Can it be applied ? I know in some cases it won't work, but I would be interested to see if you considered it. Thanks

@auntbelinda6555 3 года назад

PCR doesn't have high specificity unless you know that the RNA segment is truly unique ONLY to SARS Covid-19.

@goncalodvd 3 года назад

The latest figures I read for PCR specificity were 90% AT BEST in a controlled lab environment (which is ABSOLUTELY NOT what you see in the hospitals and testing facilities) ...

@surendrabarsode8959 4 года назад

This is really a brilliant stuff! Easily understandable explanation of Bayes Theorem in the context of Covid-19. Thanks!!

@hemofilter 3 года назад

Actual false positive rate by rtPCR (as defined by negative viral culture) was measured early in the pandemic as 0.83. I will cite the article when I find it again.

@mishudhar9920 4 года назад

Always wait for your video. When you discuss something i just stucked that topic in my brain. Thanks a lot from the other part of the world.

@marnixmeersman9587 4 года назад

So sensitivity of a test is related to the outcome of the test given you have Covid-19. And specific is related to the outcome of the test given you do NOT have Covid-19?

@harinisubramanian2234 3 года назад

Sensitivity of a test is the chance that it can detect you have COVID-19, given that you actually have COVID-19; i.e. the chance of the test being sensitive to the presence of COVID-19. Specificity, on the other hand, is the chance of that the test can specifically detect COVID-19 patients specifically, from the general population. A poor sensitivity of a test is the chance of the test failing to detect COVID-19 if you actually are a COVID patient (resulting in false negative results), while a poor specificity of a test is chance of a test failing to distinguish a true COVID-19 patient from a false positive COVID patient (resulting in false COVID+ results). Hope this helps :)

@pipertripp 4 года назад

I've read about Bayes a couple of times and have seen the exposition of the false positive "surprise" (think the example used as mammogram false positives), but this is the first time I've really grocked it. Yet another subject I really want to explore and develop competency in... I need to teach my self basic statistics too. Would that be considered a prereq for Bayse? It's something I should learn anyways, but with limited time I gotta be smart about it.

@ruedigersens9888 4 года назад

one more time Trefor Bazett at his best! A request from me: Could you please prepare the mathematical fundamentals to calculate excess mortality rates for COVID-19? greetings from one of your german fans. there is currently a lively discussion in Germany about the significance of published figures with - thank God - generally low death rates.

@paulagratefulnoend9683 4 года назад

Yes please!!!!!

@bobchapman7662 4 года назад

I am not so sure about excess mortality, as that is just comparing the numbers of fatalities with the average per given time period over the past number of years, normally 5 years. The one thing you can be sure with death statistics is that they are certain, assuming that they are recorded correctly and im confident that in European and American official statistics they are. i dont think you need to be concerned with probablities of dying once you are dead.

@bigyin2794 4 года назад

Dr Bazett, (BTW I understand the 2x2 matrix, spec, sens, PPV and NPV) you say that PCR has high specificity, please tell me against which gold standard test the PCR has been tested to generate your assertion that PCR has high specificity?

@DrTrefor 4 года назад

PCR is the "gold standard". As in, there isn't a different more accurate test, because here we are looking at the actual genetics. This is why the false positive rate is almost zero for this test.

@2o4II112II26o2 4 года назад

@@DrTrefor Dr Mike Yeadon would disagree with you; see him interviewed by James Delingpole; he has worked in the field his whole career.

@craigpetroskey8934 4 года назад

Specivity : PCR tests are used to detect ordinary non-coronaviral influenza and viral pneumonia in addition to coronaviral disease. What are the chances of someone having viral pneumonia or common influenza instead of COVID19? I think there are a lot of infected persons who have one of the former, rather than the latter.

@sade799 4 года назад

PCR tests are MISUSED to detect these viruses. See what the inventor of the test, Kary Mullis had to say on the abuse of his test. He was appalled and depressed about this till his dying day (last August....right before all this kicked off!!)

@hedles 4 года назад

@@sade799 Here it is: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-rXm9kAhNj-4.html (The context is using PCR for HIV testing, but the same principle applies.)

@sade799 4 года назад

@@hedles That's great - thanks. Good find!

@crypticnomad 4 года назад

For some reason the P(A|B) syntax is hard for me to wrap my head around but not if I use true positives, false positives and priors/prevelance. For example: T=true positive, F=false positive, R=prior, P=(T*R)/(T*R)+(F*(1-T)) seems easier for me to understand. How would I determine the probability having it given two positive tests? Would the new denominator simply be (T*R)+(T2*R2) or (T*R)*(T2*R2) or something else entirely?

@kapakyf3601 3 года назад

Conclusion: It very much depends on the prevalence, this is why you should focus tests on people with symptoms and direct contacts only. The assumptions 95%/99%/1% are very important and can totally change the final conclusion, just do the math for 10%/20% of prevalence. Atm the prevalence in my country would be higher than 1% even if we carried completely random tests on the population. This doesn't mean that massive testing is useless, it can actually be very helpful when done correctly. Another thing, I hear a lot of specialists saying that the PCR isn't 100% specific for one reason only: the possibility of contaminating the samples while handling them. Do you know how unlikely that is to happen in 1st world labs? Join another thought, why do hospitalizations and deaths follow the tests trends? If this would be such a major issue as some claim (50% of false-positive!?!?) don't you think it would be easily noticed? there are politicians and footballers being tested every other day...

@goncalodvd 3 года назад

The highest measured prevalence in the real word with random tests done to a statistically relevant number of individuals was 3%. PCR is USELESS and a FRAUD !!

@deanhuiz 2 года назад

Great video, pity about the mistake “ - = Test positive “ at 5.00”->

@hansvetter8653 3 года назад

I heart that "sensitivity" of the pcr-method is in the order of 98,6% (Dr.osten pcr-test), but "specifity" is lower in the range of +90% ... is'nt "sensitivity" controlled by the number of applied cycles (ct) during the pcr-test-procedure? ... and is'nt "specifity" controlled by the molecular length of the applied "primer" during these pcr-tests? ...

@chrisimming9454 2 года назад

Is there any follow up now with estimates of the actual values for these variables?

@ADX77 2 года назад

I know your numbers are made up for the discussion but, do we get our prevalence number of 1% from the 0.49 probability of the test being correct? In other words, how do we know prevalence is accurate?

@thelongwayhomeful 4 года назад

Very nice presentation. Cut back on the coffee. Bayes Theorem although proven algebraically cannot be as valid as real-world hard measurement. The thought of using variables that are inaccurate alone speaks to the danger of computation results that are inaccurate. Perhaps a graph thrown in might be better. Thank you for an excellent effort.

@callum4387 3 года назад

Very useful video, explains a difficult concept well.

@atomiccc11 3 года назад

Is it correct to assume that prevalence of disease is based on the use of tests themselves? And if so, doesn’t that mean that estimate of prevalence is likely biased?

@markportnoy6290 4 года назад

Thank you. This was illuminating.

@joaomatheusarantes6452 3 года назад

Couldn't you balance the prevalence probability based on the anamnesis or medical record of the patient? Of course this would be very subjective, but it could better explain the likelihood for COVID when testing people in risk area/profession or that had contact with other sick people recently. Great video BTW.

@stephenbetley9596 4 года назад

Unfortunately this starts well and goes a bit pear shaped. It was done in May when the degree of viral load and post-infection viral shedding was not known. As of 9/20 we now know differently and that an overly sensitive PCR testing protocol (ct>=35) can produce significant amounts of false positives for patients now non-infectious. So the sensitivity here needs to take in the minor factor of low sensitivity and the major factor of over-sensitivity.

@ubomban 4 года назад

They use 40 cycles, that is why they get so many false positives ...Juliet Morrison, a virologist at the University of California-Riverside, said she believes any test with a cycle threshold over 35 is too sensitive. "I'm shocked that people would think that 40 could represent a positive," she said

@nn-uj1iv 4 года назад

Thank you for explaining this.

@piltonswrangbrahma5140 3 года назад

Using Bayes's theorem to test if I'm gonna pass my semester or not xD

@sharan9993 3 года назад

Lmao😂

@gregoryagogo 4 года назад

In my humble opinion, I'd say for me, it doesn't matter either way whether I "have it" or not.

@rupe-huzz 4 года назад

Wow! just can't get enough of this stuff. Big Thanks Prof. Bazett!

@jojorusinek7492 4 года назад

Can a test ever have a specificity of 100% ie all negative tests are true negatives without any false positives? If so, what happens to the likelihood ratio in such a case for a positive test[ sensitivity / (1-specificity) ] ? thx!

@DrTrefor 4 года назад

In the real world I'd say no, because there are ALWAYS some tiny risk of lab errors, perhaps even just switching samples. But mathematically, we can always use a limit when things are approaching zero.

@drjdidier 4 года назад

@@DrTrefor thanks doc! appreciate it!

@The482075 4 года назад

If 99.9% was a statistic for a large population (more than a million), I get the feeling that Dr Trefor Bazett's draw would drop. That 0.1% is gargantuan.

@CAILZZZ 3 года назад

You're not speaking about cycle threshold (CT) and how it affects sensitivity and specificity ... and how it can raise false negatives (low CT) or raise false positives (high CT) exponentially. Thx for the explanation ... but you forgot an important variable. Also, since these calculations depends on the ''Bayes theorem'' ; achieving almost 100% specificity or somewhere close, specifically for viral RNA, is practically impossible. This is why the concept of prevalence is important and was added. For this to happen we would need an enormous database of all the virus in existence and find specific sequences for what we try to find. There is billion of billion of different virus. This is why prevalence is important in order to maintain the test result precision in an ok ratio for true-N/False-N/True-P/False-P ---) this ref : (FDA (genetic test have nearly 100% specificity):@t). This kind of test is far from perfect ... far from Black and white.

@farhanaaktershifa8269 3 года назад

what should I calculate if the question wants the probability for the patients misdiagnosed

@sbrito-espinal8862 4 года назад

I kmow someone that was postive 3 back to back tests and then negatie results in 2 back to back test. Three weeks later the 6th test results was Indeterminate - Positive. Same tests all 6 times , don't even know what to make of this

@Algo1 4 года назад

So, checking if I understood: provided we have good tests i.e high specificity and sensitivity, we should be getting more positives than real cases, which I'd say is a good thing since all positives are treated as if they have the disease i.e they are quarantined, etc. If the situation was reversed and we had a 50% likelihood of a false negative, we'd be in big trouble. Correct?

@yoavhal6050 4 года назад

actually-the nasal swab tests (for this corona virus) have NPV of less then 75%- it makes them useless as screening tools- and very dangerous ,actually-given the prevalence of the disease.

@billcrawford4547 3 года назад

@@yoavhal6050 I would appreciate links to your assertions. PCR testing is problematic, and your sources would help.

@uzijn 4 года назад

For someone who isn't very good at maths, if I receive a single positive test result for COVID-19 then what is the actual probability that I have COVID-19? If I receive a second positive test result, what's the actual probability then? Thank you.

@DrTrefor 4 года назад

Part of the challenge is we can’t answer this unless we know what the prevalence is where you live AND the type of test

@uzijn 4 года назад

@@DrTrefor Is there an average that you can give or is the answer really... we don't know yet?

@lukmankarlia8058 3 года назад

Imagine recording everyone that's died WITH or after testing positive from the common cold/flu.

@tannereustace 10 месяцев назад

What I don't understand is, assuming you are showing covid symptoms, then wouldn't your probability of just having covid consequently increase?

@DNBMP764 3 месяца назад

Showing symptoms would increase the infection rate from 1% to some much larger %. That changes everything and the probability will drop drastically from 50%. Try an infection rate of 80% instead of 1% and do the same problem . Pretty cool how the math works.

@phunkyd1 4 года назад

So, there is a surpringly high chance that for a given (positive) test, the person is DF. However, wouldn't we be able to get high accuracy in determining overall cov % in the population (even with low actual cov %) by taking into account the expected results given 0 cov?

@V.G.-yp3fr 5 месяцев назад

is there any way to confirm the results of these calculations?

@kissthesun30 3 года назад

Hi, what should I do if the example is: Prevalence: 2% of USA Sensitivity: 0.999 False positive: 0.01 USA population: 330million New York: 8.3 million LA: 4million The question is, suppose there is a person who tests positive, then there is a 10% chance that they are either from NY or LA. What is the probability that if a person is from LA or NY, that he/she will test for positive? I'm so dead-end and been trying to figure it out for days. Please help!

@LMOrnstein 4 года назад

Wow! Thanks so much.Very clear and I'm terrible with math. Good job! Signed, a teacher.

@LHA100 4 года назад

Hi, How do we know the prevalence of the disease?

@DrTrefor 4 года назад

In this case it is something we are assuming, i.e. something external to this equation. So you have to have some estimate of that ahead of time.

@goncalodvd 3 года назад

@@DrTrefor We actually have abundant evidence by now that it varies from 0,2% and 3% depending on the time of the year ...

@xicufwm 2 года назад

10:11 ok, só P(+|Cov) is 0.95 but what about P(+|Cor)? This new variable was introduced and I got confused hahahaha I know it was just a typo and, jokes aside, great video on probability! Cheers!

@munsters2 3 года назад

Well explained. Thank you.

@bookswithlilly 29 дней назад

this was so helpful! thank you!

@kingbornguerrier7427 3 года назад

Thank you for the breakdown

@Allthepills 4 года назад

When I use the Bayes plug in i only ever get the answer (1) - dont know what I'm doing wrong

@DrTrefor 4 года назад

me neither lol:D

@Allthepills 3 года назад

@@DrTrefor do you do online tutoring?

@juliasaa9746 4 года назад

what if i want to find out about the probability of all the test being positive given that you have the disease?

@PatrickPitso 4 года назад

So, basically. The probability of having it increases, given that the person tested regardless of the test result

@crypticnomad 4 года назад

I have a question that I'm not really sure how to setup in a way I could use bayes. So we know that in the past presidental election that roughly 60% of VEP(voting eligble population) actually voted and that roughly 94% of the VEP had a preferences for either canidate(meaning roughly 6% didn't like either canidate). What is the probability that the then ~64% of the VEP which voted and have a preference for either canidate properly represents the preferences of the 94% of VEP who have a preference for either canidate? Assuming it was a truly random sample the answer would be really close to 100% but if we assume that there is a bias of some sort in that 64% who actually voted how would I determine the probability that they do or do not properly represent the preference of the 94% of VEP who have a preference for either canidate. For the sake of argument lets say "properly represents" means a margin of error of +/- 2-3%

@TheHodgePodgeLifestyle 3 года назад

I got a negative from my rapid test. Somebody told me that it might be a false negative and is convincing me to take a swab or saliva test. What should I do?

@scotthamilton007 3 года назад

A few errors in this presentation. One occurs at 4:31, where I believe you end the sentence saying the opposite of what you mean. I suggest you re-do it.

@goelisa9977 4 года назад

This just illuminated my path to my Math AA SL IB exploration. Thank you!

@Babdan 3 года назад

HAHAH IM DOING THIS TOO FOR MY MATH AI SL exploration

@goelisa9977 3 года назад

@@Babdan contact me!!!

@katiejones8476 3 года назад

SAME he is a LIFESAVER!

@sjdbsn1174 Год назад

Hi, I hope you’ll be able to see this considering that the comment was two years ago, but I would like to ask you some questions about your IA because Im doing the same for mine… I’m having difficulties with the prevalence rate, because I don’t know how to calculate it as there is no information for it in my country, and i tried calculating it but also i don’t know if the info on the internet is correct. So, how do you find the prevalence rate and do you even have to calculate it? And is it a problem if some info on the Math IA aren’t correct(not including the math) because there are numbers of limitations to the research… Also, did you do well and would you consider it a good topic to do your Math IA on?

@vadimmanevich3751 3 года назад

I did not understand much. I always struggled with stats.

@HannesSchnaitter 4 года назад

What if you do a second, different test. E.g. first an antibody test and then a genetic test. Let's say the blood/genetic material was taken at the same time. How would you combine the test results.

@raduandreinegrila215 4 года назад

Please (double)check my calculation in the comment above, for the case of a second test. "Secondly, even if the person was randomly selected form a population with a prevalence of 1% of COVID19, the test is usually repeated more than once and a second consecutive false positive should be far less likely, as after the first test P(Cov) becomes 0.49 and P(DF)=0.51, so P(Cov|+) =0.95 *0.49/(0.95*0.49+0.01*0.51)=0.989. That is, you have about a 1.1% percent chance of a second consecutive false positive"

@phunkyd1 4 года назад

It would be great if this was the case - just give everyone that gets a positive result another test. The problem is that a repeat test on the same person is not indipendent of the first one. If a DF person got a positive result in test, they have a higher chance than 5% to get another (false) positive, because perhaps there was a persistent cause that this specific person got a positive result, such as remains of antibodies of another virus

@muhammedkaif28 Год назад

Sir why we use this theorem to detect the COVID test

@dachyomi7808 3 года назад

Just pointing out the infection is not the Disease, just because you have the infection it does not mean that you have the disease

@deezenuts6432 4 года назад

Say in your area 10% population is affected by COVID. And the nearby test center has a machine which is 90% accurate. If a random Person from your area is tested positive by this test center , what is the probability that he is actually positive?

@curtisvongunten1509 4 года назад

'accurate' is a technical concept in binary classification. It's the true positive and true negatives divided by the total population tested: en.wikipedia.org/wiki/Sensitivity_and_specificity Since 10% of the population is truly positive, a test that classified EVERYONE as negative would be correct 90% of the time (i.e., it would have 90% accuracy). This is why 'accuracy' isn't usually a metric used for assessing how good something is at classifying something as 'yes' or 'no'. You'd have to provide a sensitivity and specificity % to answer your question, and although practically as one goes up the other goes down, they are different and you can't derive one from the other.

@curtisvongunten1509 4 года назад

Also, your question is about Precision: of all of the positive tests, which proportion of people tested are truly positive. It's very important and often when people build statistical prediction models (machine learning) they balance the trade-off between sensitivity (also called 'recall') and precision. en.wikipedia.org/wiki/Precision_and_recall

@peddy1one 4 года назад

Shouldn't the prevalence probability be based on the prevalence in the testing population only, not geographic population? Otherwise you'd need to add more layers to account for people not getting tested.

@peddy1one 4 года назад

And if it is testing population, the 1% seems extremely low, granted like you I'm no epidemiology expert.

@peddy1one 4 года назад

Stated differently, you're missing the condition "given you took a test."

@goelisa9977 3 года назад

@@peddy1one Normally prevalance for antibody testing is 5% for COVID testing, for instance Abcott or Siemens

@billcrawford4547 3 года назад

I appreciate your efforts to educate us non-PHD types. Your choices for the specificity and sensitivity closely mirror those in use in the for Covid-19 PCR testing. As surprising as the 49% false positive number may be, it still underestimates the true horror of the PCR test. Your Baseian-focused video does not factor in the distortion caused by the high cycle thresholds being used in Covid PCR tests. It also does not contemplate that the PCR test is designed to find an RNA fragment of a coronavirus, that may or may not be alive (and therefore not a threat), and may or may not be THE cornavirus that we are looking for, but instead the common cold. But let's lock down the country and use extra-judicial, extra-legislative decrees to strip people of their rights on tests that are likely showing false positives in the 50-80% range.

@syamkriz 4 года назад

"95% sensitive means . 95% percentage of time given that you have corona virus, will test positive" and at the end we found that if there is 1% people with corona, Another 1% false positive shall be there. But in that case 95% sensitivity of the test is wrong number right . They have to give some measure like 95% sensitive when tested on these many people. And the manufacturers of the test or government should publish the testname, sensitivity, and number of people found as positive . Or else they should give another sensitivity number called " running sensitivity " :) . Am I correct ?

@syamkriz 4 года назад

@@DrTrefor Thanks for quick response. Your lectures and pleasant appearance is huge motivation for learning mathematics. It makes it look maths more easier and interesting

@putriangelina9165 4 года назад

Thank youu so much, this is very useful for me.

@DrTrefor 4 года назад

Glad it was helpful!

@JohnMartin-jx1wz 2 года назад

Your understanding of specificty and pcr seems off or not quite there.

@josevarghese4668 4 года назад

Great Job Doc! Thanks

@wolfgangflywheel4307 4 года назад

Since the RT-PCR test is qualitative, how can you come up with a quantitative answer?

@CAILZZZ 3 года назад

RT-PCR for qualitative and qPCR for quantitative. But it is sometime measured or done at the same time ... we just say RT-qPCR. The main techniques used for quantitative is fluorometry or spectrophotometry. Just check it ... too long to explain.

@wolfgangflywheel4307 3 года назад

@@CAILZZZ It makes zero sense to have two tests that provide completely different levels of answers (qualitative and quantitative) with a common descriptive moniker. This entire approach is a misapplication of a manufacturing process. These methods do not even detect the RNA, it is detecting enzymes that are found to be associated with this corona virus that are not necessarily exclusive to this virus. Both quantitative and qualitative results are misleading. We need to detect the infectious level of the RNA; currently this is not being conducted with the testing taking place in the USA.

@CAILZZZ 3 года назад

@@wolfgangflywheel4307 Infectious level or contagiosity is not done anywhere in facts (nor in Canada) ... we don't even know if the transmission can be aerosol (making mass non-scealed masks wearing almost completely useless) ... so they are just assuming it. This mean they just make up an aprox. R0. The reason we can quantify it and detect specific part of the RNA at the same time is because of the technique used. But again ... it is far from perfect. All of this clusterF is caused because the RT-PCR technique is not used in a correct manner ... in fact it's just false science they are showing us. In France they use a cycle threshold of 45-50 ? In Quebec Canada we use a CT up to 45. This give an average of 90% false positive rate. No wonder the virus is supposedly less deadly when it's just in fact ... mainly false positives. So we got a pandemic of false positives/asymptomatic carriers ... we only have a pandemic of cases. The death ratio doesn't follow the data. When you don't have an answer, always blame the mutation or the placebo effect and say it is a consensus.

@CAILZZZ 3 года назад

@@wolfgangflywheel4307 CT or cycle threshold is the number of time the genetic material is amplified, since it is so small and can't be detected through normal mean. The problem is that these amplification cycles don't just amplify the covid viral RNA, it amplify everything. Cheating on testing like this also raise the prevalence rating ... thus ... cheating the results even more.

@CAILZZZ 3 года назад

@@wolfgangflywheel4307 And the problem with serological tests is that it's not good early. PCR is also not good early in the sickness but a bit better, if used correctly with a decent CT of course (Should be between 25-35 Max).

@samishsalgaonkar7474 4 года назад

Yes!! This was interesting💥

@ADAPTATION7 3 года назад

Moral of the story: Test when you have specific symptoms in order to get better statistics. Asymptomatic people are of little concern since they are highly unlikely major vectors for transmission.

@AdelaideBen1 4 года назад

There is a serious public health problem with this video - as it suggests that simply prevalence is the defining factor in the correctness of positive tests. The maths is not the problem - but there is an inbuilt inference here that the health system doesn’t account for this. The issue of low prevalence is a concern - but there is a layer of medical assessment that should either pre-select a non random population, or to undertake additional clinical assessments. However this subtlety is missing - and in this day and age when people just cherry pick videos - the take home message here is that if you test positive, then the positive predictive value is so low that it means you most likely don’t need to consider that you are positive (and I am seeing a lot of chatter about this very thing - so people are actively ignoring test results and continuing to go out). As I said the maths is not the problem - but rather it assumes zero additional controls. The conspiracy theory that the test rate is unreliable is increasing the likelihood of people spreading the disease. You have taken a real (though simplified) challenge and made it too easy to misinterpret. Once again - it is not that your conceptual understanding is wrong, just that it is overly-simplified. Educating people is important - but it’s education only if it is bounded- otherwise it’s just fodder for abuse

@AdelaideBen1 4 года назад

@@DrTrefor No probs... it's just that there's so many people out there now that take snapshots of info off the internet and use it to confirm conspiracies. The whole issue of prevalence and ppv is an important thing, and your post was well done. Just nowadays we have to be careful because people are taking things out of context. We had a recent finding that up to 25% of people over here in Australia who had tested positive were not isolating - partly because there is a belief that there's a lot of false positives - not to mention that you can't spread it if you don't have symptoms. I also am astounded that there's still very little legitimate information readily available to people (who aren't comfortable reading medical journals), so they'll take info wherever they can. But definitely a good job at explaining maths concepts in a very accessible way.

@goncalodvd 3 года назад

The health system and the politician ABSOLUTELY DID NOT account for this. I asked this very question to a number of doctors and nurses and they have NO IDEA what Bayes Theorem is for starters. Testing randomly is FRAUD !! Its not even a theory, it IS FRAUD and the ones making the quick buck need to be KILLED !!