Can we Contain Covid-19 without Locking-down the Economy?
machine learning epidemiology worst case statistics hypothesis test covid corona coronavirus
My thoughts on the let-the-young-get-infected argument.

https://medium.com/amnon-shashua/can-we-contain-covid-19-without-locking-down-the-economy-2a134a71873f

Abstract:
In this article, we present an analysis of a risk-based selective quarantine model where the population is divided into low and high-risk groups. The high-risk group is quarantined until the low-risk group achieves herd-immunity. We tackle the question of whether this model is safe, in the sense that the health system can contain the number of low-risk people that require severe ICU care (such as life support systems).

Authors: Shai Shalev-Shwartz, Amnon Shashua

Links:
YouTube: https://www.youtube.com/c/yannickilcher
Twitter: https://twitter.com/ykilcher
BitChute: https://www.bitchute.com/channel/yannic-kilcher
Minds: https://www.minds.com/ykilcher
 Can we contain COVID-19 without locking down the economy? This is a question and I do care about this article because Shai Shalef-Schwarz is one of the bigger names in machine learning theory. So it was interesting for me to see what he and his collaborator here had to say about the kind of outbreak and the strategy to contain it. So contain maybe isn't the right word that they ask. I think the way they ask the question is how are we going to survive this the best? And so this in no means is an endorsement by me. I'm not a medical professional. Please just view this as a commentary and an explanation of what they are saying. I'll give my opinions along the way, of course. So they identify three different models for handling the spread of COVID-19. And we'll start with the third one because they argue for the first one and this builds more suspense. So they say there is countrywide lockdown, right, until the spread of the virus is under control. They say it could take anywhere from weeks to months. It is the safest route, but it does not prevent a second wave from occurring. Now, of course, if you have people, let's say these are people, right, then the thing is everyone just stays in there, stay in your house, right, everybody, right, until it's kind of gone. Now they say correctly there is a risk of a second wave because only a single infected person, because there's no immunity, still has the potential of creating another epicenter. So they don't consider this option. The next option is called containment-based selective quarantine, which means find all the positive cases and put them in quarantine. So let's say we go here and we let you roam around freely, but we know we can test people and we know that some of them are positive. So we simply tell them to stay at home, right. Now this depends a lot on how well you can test people, and it also depends on what they claim the contagious time interval. We know that there are people that are contagious without showing symptoms. So unless you can test every single person all the time, this is likely to not really help a lot. There's various data from various countries that actually shows it can reduce the load, but they basically argue against that because there are these contagious people and you can never test fast enough or accurate or thoroughly enough. And then they say there is risk-based selective quarantine, which means what? It means that some of these people are going to be at risk. And in this case, we obviously mean old people. So old people, I'm going to draw them with a cane, not because old people aren't fit, just because they have better tastes in canes. And then there are young people and they run a smartphone with TikTok. And what we're going to say is that you youngsters, you're not really at risk from this. So you go out, you sneeze on each other, you go about your life normally, and you old people basically stay at home until all the young people have immunity. So we ramp up the cases and then it flattens out eventually in the low-risk population. And at that point, there is enough herd immunity, right? All these people are now immune so that the old person here, even if they now go out again, they won't catch it because everyone's already had it. So they argue for this particular strategy, or at least they analyze this particular strategy. Now, I have to say at the beginning that the core assumption here is that this quarantine of the high-risk people, you can do basically in a perfect way. So the assumption here is that you are able to perfectly quarantine all the high-risk people and that the level of infection in the low-risk population has no influence on the level of infection in the high-risk population. And in my opinion, I simply don't believe that. I simply don't believe you can build this quarantine. I think even these old people, they need food sometimes, the nursing home needs staff. So even if they can reduce their contact to the outside world, they cannot fully be sheltered. And that means the more infections you have in the low-risk population, the more infections you will have in the high-risk population. So I think the fundamental core assumption of this model is quite flawed. That being said, let's analyze it. So we assume that all the high-risk people, none of them is going to get sick because they all stay at home. So the math in this paper is actually pretty basic. So we'll go through it a bit more detailed. So we'll understand the core argument. So they introduce the following quantities, M here. M is the low-risk population, right? This is the population size. V or new, let's call it new. New here is the probability. So that's the probability that if you are sick, you need to go to the ICU. Right? So sick means simply you have the virus. And ICU means that the symptoms are so bad that you need help from the medical system in order to overcome the disease. So if we multiply the population size by the probability that if you get sick, you need to go to the ICU, what do we get? We get a worst-case scenario. So basically the authors here, and I find this is the good part of this analysis. They really don't rely on kind of pandemic dynamics, epidemiology, exponential growth and so on. They simply consider the worst case. So MD here, if you multiply these two numbers, what does that mean? That is the number of severe cases. Severe meaning you need ICU cases. If everybody gets sick, if all get sick. If everybody gets sick at the same time, right? Same time. So this is the work. So let's say we all go out, the lowest population, and we all sneeze in each other's faces as much as we can. And we just all get sick at the same time. Then this here is the number of people going to the ICU. Right? And if this, so they introduce this quantity B here, B is the number of beds in the ICU. If the number of beds in the ICU is larger than the worst case, severe cases, right? Then we are safe. So that's the argument. Basically it's not that we are safe. It is no one will die from lack of an ICU bed. Which is kind of the lever we have as a population. If you assume everyone's going to get sick anyway and so on. If the number of beds is larger than the worst case number of ICU patients, we are safe. That's at least how they define safe. Alright, so that's their premise. Now what are they going to do? They're going to find a quantity where they can bound this thing. So they are going to find a bound, an upper bound on the number of severe cases. And if this upper bound is lower than the number of beds, then they can say we're safe with this method. See this is a worst case analysis under their assumptions. Alright, so I said they don't resort to any kind of epidemiological dynamics. They simply estimate this thing from current numbers. I'm going to introduce two more quantities here. P star and K. Now K is the current number of severe cases. So this is kind of an analog to this thing here. So these two are connected. This is the current number of severe cases and this up here is the total possible, like the worst case number of severe cases in the future. Likewise, P star here is the percentage of people, the percent of people that are sick. And they claim correctly this is unknown. So if we could test everybody who is sick, not severe, just sick. And up here this has no connection because of course you can imagine here another factor times, let's call this P plus or something. Which is the number of people who are sick in the worst case, which of course in our worst case scenario is one. So that's why they don't include it here. So this is the current percentage of sick people. So this here is a percentage and this here is an actual number. Keep that in mind. All right, now if we do some basic reformulation here, if we take this P star and multiply that by, you see it in this corner here, multiply it by the total size of the population, right? We get the number of people who are currently sick. This is a percentage of current sick ones, this is the total size of the population. Get the number of people who are currently sick. If we take that in the denominator and put K here, which is the number of people who are currently severe, then we get an estimate of this quantity new. So remember what new is? New is the probability if you are sick, you go to the ICU. So the ICU means you're severe, right? So these are the current number of sick people and these are the current number of severe people. This gives you an estimate of if you are sick, what's the probability that you're severe? Now they argue that this number, it doesn't change, independent of, so this quantity here is a constant. So the probability that if you are sick from this virus, you go to the ICU, doesn't change over time. So we can estimate it with current numbers, right? Which is a pretty reasonable thing to assume that this stays constant unless the virus mutates or something. So we know the total size of the population. We know the current number of severe cases. You can make an argument about that. So do we really know the current number of severe cases? Because there is an exponential growth involved, this might be difficult to estimate. And they say the same thing. So they say this is the only time where they reference the dynamics of the situation. It grows at an exponential rate. So what we can do is we can take a worst case upper bound, they say, to be on the safe side, perform a worst case analysis. So instead of taking K, they add this confidence interval on it that is based on concentration inequalities. So they don't use K, they use this K tilde here, which has two additional summons here. That is supposed to be an upper bound with confidence, at least one over delta here. And this you can set, for example, to be 0.05. That gives you a 95 percent confidence that this is an upper bound on that. Now, this comes from some concentration bound. And there are certain assumptions behind this upper bound here, which I don't know enough about to critique them here. I'm going to assume they are reasonable. If they are not, then of course, that is an additional point of criticism of this work. All right. So instead of using K here, we are saying we're on the safe side and we use this K tilde. So we know this as well. Now, the unknown quantity, of course, is this thing here, P star. What is the percentage of people that are currently sick? So the goal is now to find that. So they say, OK, if we plug in this upper bound of K tilde, then with this probability, we can upper bound this quantity, nu, which is exactly what we wanted, because we need to upper bound MD. That's what they say here. So since at the top we saw that M times nu equals MD and we want to upper bound MD, we can rearrange this thing. If we plug in these two together, we see that the M cancels out. We can upper bound MD by this quantity here. The upper bound on the current severe cases divided by the percentage of the currently sick people. So again, they reformulate and they plug in. This, of course, needs to be smaller than the number of beds. So they plug this in here and they say, now what we have to do to see is if this quantity is larger than this quantity of two quantities we know, then we are safe. Now, again, our goal is going to be to find a quantity that lower bounds P star, but up, but is larger than this quantity here. And they do this via hypothesis testing. They call this quantity here, they call it P tilde. And they do a hypothesis test for classic statistics where they ask, is P star significantly larger than P tilde? If that's the case, then we're safe. If not, we're not. And how do they do that? They say, OK, we have the population. I did draw this at one point. Let's go back there. We have the population here, right? And what we can do is we can just go out and uniformly, uniformly test people, like just randomly select people. Now, this is an old person, old people stay at home. So we randomly select people to test and their test results come back. And this one, this one's healthy, this one's healthy, this one's healthy, this one's not healthy. And so we have four tests and out of the four, one was positive. Can we work out a hypothesis test from that? So can we decide whether P star is probably much larger than P tilde or not? And the answer is yes, because this is a uniform sample. You can work out using classic statistical tools whether or not you can reject an old hypothesis or not. And they actually work this out and they do give a number here. And that's this. So they say if we test N, which is four, let's say four and a half times this quantity B divided by K. So the number of beds divided by the upper bound on the current severe cases. So we test four point five times this many people. Then if we find at least 10 positive cases or more, then with a probability of 95 percent, we know that the risk based model is safe. So the more, of course, the more infected people you find in this case, the better, because that means because the number of severe cases stays constant at any given time. It means that a lot more people are infected. That means the probability that you are going to become severe is lower. That's why it says at least. So again, you go out, you test N people and according to this formula, plug in the numbers here for your current situation. If you find at least 10 people, then with a probability of at least 95 percent, you know that this model is safe. Cool. And this is done using, you know, classic statistical testing hypothesis testing literature. So I think that is a pretty cool result. But I do severely criticize the underlying assumption, which is that you can perfectly enforce this quarantine. Of course, if you can't, it means that there is a direct correlation between the number of sick people in your low risk population, the number of sick people in your high risk population, which means that more of the high risk population are going to get infected as well, which again means that your number B of ICU beds is going to drop severely because they have a higher hospitalization rate, which makes your entire model that we developed down there less valid, because now this used to be a constant in the model. It's now no longer a constant. It's sinking. And the worse it gets, the more it's sinking. And yes, so that that may make what you initially thought was a safe model into a very non safe model very quickly. And that doesn't include all the high risk people that are going to be in danger additionally because you can't enforce the quarantine. All right. So this was my take on that. Take it for what it's worth. And I wish you a healthy pandemic. Bye bye.
 Can we contain COVID-19 without locking down the economy?
 This is a question and I do care about this article because
 Shai Shalef-Schwarz is one of the bigger names in machine learning theory.
 So it was interesting for me to see what he and his collaborator here
 had to say about the kind of outbreak and the strategy to contain it.
 So contain maybe isn't the right word that they ask.
 I think the way they ask the question is how are we going to survive this the best?
 And so this in no means is an endorsement by me.
 I'm not a medical professional.
 Please just view this as a commentary and an explanation of what they are saying.
 I'll give my opinions along the way, of course.
 So they identify three different models for handling the spread of COVID-19.
 And we'll start with the third one because they argue for the first one and this builds more suspense.
 So they say there is countrywide lockdown, right, until the spread of the virus is under control.
 They say it could take anywhere from weeks to months.
 It is the safest route, but it does not prevent a second wave from occurring.
 Now, of course, if you have people, let's say these are people, right,
 then the thing is everyone just stays in there, stay in your house, right, everybody, right, until it's kind of gone.
 Now they say correctly there is a risk of a second wave because only a single infected person,
 because there's no immunity, still has the potential of creating another epicenter.
 So they don't consider this option.
 The next option is called containment-based selective quarantine,
 which means find all the positive cases and put them in quarantine.
 So let's say we go here and we let you roam around freely,
 but we know we can test people and we know that some of them are positive.
 So we simply tell them to stay at home, right.
 Now this depends a lot on how well you can test people,
 and it also depends on what they claim the contagious time interval.
 We know that there are people that are contagious without showing symptoms.
 So unless you can test every single person all the time, this is likely to not really help a lot.
 There's various data from various countries that actually shows it can reduce the load,
 but they basically argue against that because there are these contagious people
 and you can never test fast enough or accurate or thoroughly enough.
 And then they say there is risk-based selective quarantine, which means what?
 It means that some of these people are going to be at risk.
 And in this case, we obviously mean old people.
 So old people, I'm going to draw them with a cane, not because old people aren't fit,
 just because they have better tastes in canes.
 And then there are young people and they run a smartphone with TikTok.
 And what we're going to say is that you youngsters, you're not really at risk from this.
 So you go out, you sneeze on each other, you go about your life normally,
 and you old people basically stay at home until all the young people have immunity.
 So we ramp up the cases and then it flattens out eventually in the low-risk population.
 And at that point, there is enough herd immunity, right?
 All these people are now immune so that the old person here,
 even if they now go out again, they won't catch it because everyone's already had it.
 So they argue for this particular strategy, or at least they analyze this particular strategy.
 Now, I have to say at the beginning that the core assumption here is that this quarantine of the high-risk people,
 you can do basically in a perfect way.
 So the assumption here is that you are able to perfectly quarantine all the high-risk people
 and that the level of infection in the low-risk population has no influence on the level of infection in the high-risk population.
 And in my opinion, I simply don't believe that.
 I simply don't believe you can build this quarantine.
 I think even these old people, they need food sometimes, the nursing home needs staff.
 So even if they can reduce their contact to the outside world, they cannot fully be sheltered.
 And that means the more infections you have in the low-risk population,
 the more infections you will have in the high-risk population.
 So I think the fundamental core assumption of this model is quite flawed.
 That being said, let's analyze it.
 So we assume that all the high-risk people, none of them is going to get sick because they all stay at home.
 So the math in this paper is actually pretty basic.
 So we'll go through it a bit more detailed.
 So we'll understand the core argument.
 So they introduce the following quantities, M here.
 M is the low-risk population, right?
 This is the population size.
 V or new, let's call it new.
 New here is the probability.
 So that's the probability that if you are sick, you need to go to the ICU.
 Right? So sick means simply you have the virus.
 And ICU means that the symptoms are so bad that you need help from the medical system in order to overcome the disease.
 So if we multiply the population size by the probability that if you get sick, you need to go to the ICU, what do we get?
 We get a worst-case scenario.
 So basically the authors here, and I find this is the good part of this analysis.
 They really don't rely on kind of pandemic dynamics, epidemiology, exponential growth and so on.
 They simply consider the worst case.
 So MD here, if you multiply these two numbers, what does that mean?
 That is the number of severe cases.
 Severe meaning you need ICU cases.
 If everybody gets sick, if all get sick.
 If everybody gets sick at the same time, right?
 Same time.
 So this is the work. So let's say we all go out, the lowest population, and we all sneeze in each other's faces as much as we can.
 And we just all get sick at the same time.
 Then this here is the number of people going to the ICU.
 Right? And if this, so they introduce this quantity B here, B is the number of beds in the ICU.
 If the number of beds in the ICU is larger than the worst case, severe cases, right?
 Then we are safe.
 So that's the argument.
 Basically it's not that we are safe.
 It is no one will die from lack of an ICU bed.
 Which is kind of the lever we have as a population.
 If you assume everyone's going to get sick anyway and so on.
 If the number of beds is larger than the worst case number of ICU patients, we are safe.
 That's at least how they define safe.
 Alright, so that's their premise.
 Now what are they going to do?
 They're going to find a quantity where they can bound this thing.
 So they are going to find a bound, an upper bound on the number of severe cases.
 And if this upper bound is lower than the number of beds, then they can say we're safe with this method.
 See this is a worst case analysis under their assumptions.
 Alright, so I said they don't resort to any kind of epidemiological dynamics.
 They simply estimate this thing from current numbers.
 I'm going to introduce two more quantities here. P star and K.
 Now K is the current number of severe cases.
 So this is kind of an analog to this thing here.
 So these two are connected.
 This is the current number of severe cases and this up here is the total possible, like the worst case number of severe cases in the future.
 Likewise, P star here is the percentage of people, the percent of people that are sick.
 And they claim correctly this is unknown.
 So if we could test everybody who is sick, not severe, just sick.
 And up here this has no connection because of course you can imagine here another factor times, let's call this P plus or something.
 Which is the number of people who are sick in the worst case, which of course in our worst case scenario is one.
 So that's why they don't include it here.
 So this is the current percentage of sick people.
 So this here is a percentage and this here is an actual number.
 Keep that in mind.
 All right, now if we do some basic reformulation here, if we take this P star and multiply that by, you see it in this corner here,
 multiply it by the total size of the population, right?
 We get the number of people who are currently sick.
 This is a percentage of current sick ones, this is the total size of the population.
 Get the number of people who are currently sick.
 If we take that in the denominator and put K here, which is the number of people who are currently severe,
 then we get an estimate of this quantity new.
 So remember what new is?
 New is the probability if you are sick, you go to the ICU.
 So the ICU means you're severe, right?
 So these are the current number of sick people and these are the current number of severe people.
 This gives you an estimate of if you are sick, what's the probability that you're severe?
 Now they argue that this number, it doesn't change, independent of, so this quantity here is a constant.
 So the probability that if you are sick from this virus, you go to the ICU, doesn't change over time.
 So we can estimate it with current numbers, right?
 Which is a pretty reasonable thing to assume that this stays constant unless the virus mutates or something.
 So we know the total size of the population.
 We know the current number of severe cases.
 You can make an argument about that.
 So do we really know the current number of severe cases?
 Because there is an exponential growth involved, this might be difficult to estimate.
 And they say the same thing.
 So they say this is the only time where they reference the dynamics of the situation.
 It grows at an exponential rate.
 So what we can do is we can take a worst case upper bound, they say, to be on the safe side, perform a worst case analysis.
 So instead of taking K, they add this confidence interval on it that is based on concentration inequalities.
 So they don't use K, they use this K tilde here, which has two additional summons here.
 That is supposed to be an upper bound with confidence, at least one over delta here.
 And this you can set, for example, to be 0.05.
 That gives you a 95 percent confidence that this is an upper bound on that.
 Now, this comes from some concentration bound.
 And there are certain assumptions behind this upper bound here, which I don't know enough about to critique them here.
 I'm going to assume they are reasonable.
 If they are not, then of course, that is an additional point of criticism of this work.
 All right. So instead of using K here, we are saying we're on the safe side and we use this K tilde.
 So we know this as well.
 Now, the unknown quantity, of course, is this thing here, P star.
 What is the percentage of people that are currently sick?
 So the goal is now to find that.
 So they say, OK, if we plug in this upper bound of K tilde, then with this probability,
 we can upper bound this quantity, nu, which is exactly what we wanted, because we need to upper bound MD.
 That's what they say here.
 So since at the top we saw that M times nu equals MD and we want to upper bound MD,
 we can rearrange this thing. If we plug in these two together, we see that the M cancels out.
 We can upper bound MD by this quantity here.
 The upper bound on the current severe cases divided by the percentage of the currently sick people.
 So again, they reformulate and they plug in.
 This, of course, needs to be smaller than the number of beds.
 So they plug this in here and they say, now what we have to do to see is if this quantity is larger than this quantity of two quantities we know, then we are safe.
 Now, again, our goal is going to be to find a quantity that lower bounds P star, but up, but is larger than this quantity here.
 And they do this via hypothesis testing. They call this quantity here, they call it P tilde.
 And they do a hypothesis test for classic statistics where they ask, is P star significantly larger than P tilde?
 If that's the case, then we're safe. If not, we're not.
 And how do they do that? They say, OK, we have the population.
 I did draw this at one point.
 Let's go back there. We have the population here, right?
 And what we can do is we can just go out and uniformly, uniformly test people, like just randomly select people.
 Now, this is an old person, old people stay at home.
 So we randomly select people to test and their test results come back.
 And this one, this one's healthy, this one's healthy, this one's healthy, this one's not healthy.
 And so we have four tests and out of the four, one was positive.
 Can we work out a hypothesis test from that?
 So can we decide whether P star is probably much larger than P tilde or not?
 And the answer is yes, because this is a uniform sample.
 You can work out using classic statistical tools whether or not you can reject an old hypothesis or not.
 And they actually work this out and they do give a number here.
 And that's this.
 So they say if we test N, which is four, let's say four and a half times this quantity B divided by K.
 So the number of beds divided by the upper bound on the current severe cases.
 So we test four point five times this many people.
 Then if we find at least 10 positive cases or more, then with a probability of 95 percent,
 we know that the risk based model is safe.
 So the more, of course, the more infected people you find in this case, the better,
 because that means because the number of severe cases stays constant at any given time.
 It means that a lot more people are infected.
 That means the probability that you are going to become severe is lower.
 That's why it says at least.
 So again, you go out, you test N people and according to this formula,
 plug in the numbers here for your current situation.
 If you find at least 10 people, then with a probability of at least 95 percent, you know that this model is safe.
 Cool.
 And this is done using, you know, classic statistical testing hypothesis testing literature.
 So I think that is a pretty cool result.
 But I do severely criticize the underlying assumption, which is that you can perfectly enforce this quarantine.
 Of course, if you can't, it means that there is a direct correlation between the number of sick people
 in your low risk population, the number of sick people in your high risk population,
 which means that more of the high risk population are going to get infected as well,
 which again means that your number B of ICU beds is going to drop severely because they have a higher hospitalization rate,
 which makes your entire model that we developed down there less valid,
 because now this used to be a constant in the model.
 It's now no longer a constant.
 It's sinking.
 And the worse it gets, the more it's sinking.
 And yes, so that that may make what you initially thought was a safe model into a very non safe model very quickly.
 And that doesn't include all the high risk people that are going to be in danger additionally
 because you can't enforce the quarantine.
 All right.
 So this was my take on that.
 Take it for what it's worth.
 And I wish you a healthy pandemic.
 Bye bye.