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- Oct 6, 2010
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- Oct 6, 2010
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Velodude said:
AC says in the article that he already lost 4 of the 7.5 kilos he gained, so he's only up 3.5kg (7.7 pounds) at the moment
We already have other evidence, the meat tests, that indicate that CB contamination occurs infrequently. What these new data would do would allow a calculation of the odds of someone in a group testing positive. E.g., if the odds, based on meat tests, are one in ten thousand that a single individual tests positive for CB, they drop to about one in a hundred if one hundred individuals are tested. That is, the odds are about 1% that one of those one hundred individuals will test positive. That is already a high enough probability that one would have to consider it carefully in comparison to the transfusion scenario. If a thousand individuals were tested, or one hundred individuals were tested ten times each during the year, the odds would drop to about one in ten. That number alone would probably be sufficient to get a rider off, regardless of the evidence for transfusion.
One problem here is that this scenario assumes that every test of every individual occurs after eating meat. One would have to take into account how frequently meat-eating actually occurs. But this rough calculation does show that if a large number of individuals test negative, it potentially supports the case of one individual testing positive. The key is having a very accurate and independent estimate of the odds of a single individual testing positive. This is where the meat tests come in. While they might in fact not be accurate, WADA is basing its case on the fact that they are, so is not in a position to argue otherwise without damaging its case. And in any case, pretty much everyone agrees that if they aren’t accurate, then they underestimate the probability, not overestimate it.
You are assuming the only admissible evidence is data supporting transfusion. I don’t think it’s that simple. Given how unlikely contamination is, I think all WADA has to do is point out the plausibility of transfusion. Absence of evidence, as the old saying goes, is not evidence of absence. If your argument is taken to its logical conclusion, then the possibility of all the atoms that constitute the chair I’m sitting in randomly moving together to another place ten feet across the room “wins” over transfusion, because the former possibility is non-zero, whereas the latter is supported by no admissible evidence. As this absurd example shows, we have to draw a line somewhere and say that sometimes events for which there is no evidence are indeed more likely than events of a very low probability.
When Floyd got popped for testosterone, WADA did not have to provide evidence showing that he applied a patch on a certain day. It was enough that a) Floyd had the substance in his body; and b) he couldn’t provide a satisfactory explanation for how it got there. Bert had CB in his body and the only explanation he has provided for it is of vanishingly low probability—really, the odds of contamination may be no greater than the odds that Floyd’s IRMS values were the result of some special diet he ate.
FWIW, Bert’s behavior throughout—I’m thinking of all these “test me anytime, anywhere” protests--is of someone who was not subjected to those tests at that time, who is not worried that they will pull up more evidence against him.
Merckx index said:
Thanks for another interesting post Merckx Index, again I wonder if you can clarify a couple of things something for me, as I've always struggled with probability theory.
First, and simply as I've lost track, is the 1 in 10,000 you're using above an example probability for the sake of argument, or has it been derived from the EU meat statistics?
The second query is the more conceptual one. You seem to be saying that if you test one person with odds of 1 in 10,000 and he tests postive then that's vanishingly low probability. But if you then test another 99 people and they are all clear then you'd expect the positive result once every 100 times you test a group of 100 people - so again 1 in 10,000 tests would be positive, but you're expressing the probability as one in a hundred that someone in that group of 100 tests is positive.
As far as I can understand the two things are just different mathematical ways of expressing the same base probability, and yet in one expression you conclude its vanishingly low probability, but in the other you consider it high enough to consider carefully against transfusion. So I'm not sure why that would be. Am I missing something here?
- Sep 25, 2009
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i have noted several times that too much abstract reliance on the clen testing statistics, however telling and relevant to the case, has the potential of misleading.
i might agree that taken fwiw, the eu-wide stats are credible and point to an unfavourable probability for steak vs transfusion.
but that's not how the arbitrating panel looks (or should look) at it ! in considering the steak contamination probability, they would inevitably apply the specific circumstances an athlete was in.
for ex, in contador's case, as i argued so many times, they must consider if the entire story of the steak purchase is true and what is the probability of it (as a cover story) coinciding with the transfusion or the probability of it coinciding with the positive on the 21st. another applicable consideration is how the testing statistic apply to the local scene etc.
none of the above considerations are conclusive, but added together, they might suffice to put enough holes in the wada (and m.index) over-reliance on general stats, though i agree, the stats are very serious.
the key question for the arbs was - are contador's claims of the potential contamination in the eu country sufficiently probable or credible for his circumstances ? if the answer is yes, he then is required to show the 3 conditions for 'no fault or negligence' criteria - the route of administration, the lack of awareness, no intent or real perf. enhancement.
i don't know what is that probability that the panel will be satisfied with. i think they will use common sense. of course, as each arb understand it.
again, probabilities should be not just credible in a general sense but case-specific and when they are too abstract (or in their view far-fetched) a rational panel will dismiss them as they have allegedly done with ashenden. here's another reason i don't engage in these types of arguments...they are open-ended and can lead to chasing wild geese.
i might agree that taken fwiw, the eu-wide stats are credible and point to an unfavourable probability for steak vs transfusion.
but that's not how the arbitrating panel looks (or should look) at it ! in considering the steak contamination probability, they would inevitably apply the specific circumstances an athlete was in.
for ex, in contador's case, as i argued so many times, they must consider if the entire story of the steak purchase is true and what is the probability of it (as a cover story) coinciding with the transfusion or the probability of it coinciding with the positive on the 21st. another applicable consideration is how the testing statistic apply to the local scene etc.
none of the above considerations are conclusive, but added together, they might suffice to put enough holes in the wada (and m.index) over-reliance on general stats, though i agree, the stats are very serious.
the key question for the arbs was - are contador's claims of the potential contamination in the eu country sufficiently probable or credible for his circumstances ? if the answer is yes, he then is required to show the 3 conditions for 'no fault or negligence' criteria - the route of administration, the lack of awareness, no intent or real perf. enhancement.
i don't know what is that probability that the panel will be satisfied with. i think they will use common sense. of course, as each arb understand it.
again, probabilities should be not just credible in a general sense but case-specific and when they are too abstract (or in their view far-fetched) a rational panel will dismiss them as they have allegedly done with ashenden. here's another reason i don't engage in these types of arguments...they are open-ended and can lead to chasing wild geese.
- Mar 17, 2009
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Speedzero said:
Funny when he received his weight in honey (a couple of days prior to the Saxo Bank camp) he only weighed ~64 kg just two kilos over his listed race weight. I think AC is sandbagging, yet again. Or it's true and we've exposed another AC-related conspiracy
- Jun 7, 2011
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Publicus said:Funny when he received his weight in honey (a couple of days prior to the Saxo Bank camp) he only weighed ~64 kg just two kilos over his listed race weight. I think AC is sandbagging, yet again. Or it's true and we've exposed another AC-related conspiracy
That or he just doesn't like honey and told a white lie to keep the amount of honey as low as possible.
Dr. Maserati
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- Jun 19, 2009
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GJB123 said:That or he just doesn't like honey and told a white lie to keep the amount of honey as low as possible.
Exactly - when it comes to the honeys they always lie about their weight.
It shouldn't get a rider off, since the odds that a particular rider would test positive are unchanged at 1/10000. We still need to compare 1/10000 to the likelihood of a transfusion for that particular rider.Merckx index said:
BTW, my phrasing of "odds" and "likelihood" highlights one of the issues here. We can relatively straightforwardly estimate the odds eating CB-contaminated food by looking at frequencies of failed animal tests. It isn't obvious how one would estimate the strength of the evidence for or against transfusion.
- May 18, 2009
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KingsMountain said:
And why is that?
This is like a kid coming to school with the "dog at my homework" excuse, and the teacher unable to give him a zero until the school proved he didn't have a dog or if he did, they analyzed its feces to prove there was no paper residue within it.
The fact that WADA has to prove anything to disprove an astronmically low statistical likelihood makes this whole deal a farce. I know we like to be long winded in this thread but it boils down to this.
MI upthread said the only way they could find for AC is if they bought the food contamination theory. That is correct, and that is what they will do then clam up. It is a nice out to get the result that was wanted all along.
If the 1/10,000 shot claim of the athlete is to be accepted as fact over the (say) 1/3 chance of transfusion (1/3 being unmentioned reasons), we might as well skip all legal proceedings and just ask the rider how it happened, and connect disciplinary actions to that claim directly.
Oh wait, this is actually the way it works in soccer and tennis.
Oh wait, this is actually the way it works in soccer and tennis.
Don’t know about Bert, but I could eat my weight in honeys, for sure. More than my weight.
Both to some extent. The WADA estimate was apparently about one in 17,000, but ten thousand is what the poster July threw out, and is a round number easy to work with and close enough for purposes of a rough calculation. The purpose of my calculation was not to provide more evidence for or against Bert, but just to show that having more test data could improve Bert’s odds.
Yes and no. The odds that Bert tests positive are one in ten thousand, correct. But the odds that someone tests positive are one in a hundred, so Bert can now argue that his positive is not that unlikely. It’s very unlikely to happen to him, yes, but not nearly so unlikely to occur, and that’s all that really matters here. IOW, what Bert has to prove is that the event, the incident, is of reasonable probability. From a scientific point of view, and a legal one, it’s the occurrence that has to be accounted for, not the fact that it occurred to this person rather than that person.
Think of a murder trial, where a key witness just happened to be in the right place at the right time to observe the murder. One might argue that it is extremely unlikely that this particular person happened to be at this particular place at this particular time. What are the odds that you walked past this alley, say, at this time, when you were in fact walking all over the big city that day? But there were hundreds of thousands of people walking about in the city that day, so the odds were not at all remarkable that someone could have been in that place at that time. That is all that matters, not who that particular person was.
Contrast this with the situation if the city were deserted that day. There was a holiday, very bad weather, or some other constellation of events such that very few people were out and about. Now it becomes very pertinent to question the witness’s story. It does seem very unlikely that, even if he were out that day, he would be in that particular place at that particular time. It seems to be too much of a coincidence.
Or think of a lottery. The odds against any particular person winning the lottery are astronomical. But given the large number of people who play it, the odds are not at all high against someone winning it. So when someone does win it, we don’t say that it’s impossible, that there was fraud or cheating. We just say that that person was extraordinarily lucky.
In fact, every day things happen to people that, applied to that specific individual, are wildly improbable, but which we accept because we know they have to happen to someone. Very low probability events happen all the time, they have to happen given the large number of people and activities that are constantly in play. We can predict that they will happen, we just can’t predict who they will happen to.
I tend to agree with you, Chris, but this is a remarkable turnaround for someone who a while back said Bert should get off because “stuff happens”. What stuff happened to you to change your mind?
You probably won’t believe this, Python, but even I find this discussion too abstract. Yes, we are getting off the realities of the case here. I can only emphasize that I raised this point not because I think it has a lot of relevance to Bert’s case, but because in the future, if enough riders are tested with high sensitivity technology, we might expect to see a positive, even if the meat tests are accurate.
This is a good point. I have always given Bert credit for having in fact eaten steak the day of or day before the positive. Of course, he had plenty of time before the positive became public to fabricate a story, but as you and others have discussed earlier, a lot of people would have had to be in on the lie. A big question for me, though, is how often do riders eat steaks during a GT? I know they can consume as much as 8000-9000 calories a day, some of that presumably is always meat (and remember, not just beef but chicken and pork can be CB-contaminated). If it turns out he ate meat frequently during the Tour, this point might not help much.
Both to some extent. The WADA estimate was apparently about one in 17,000, but ten thousand is what the poster July threw out, and is a round number easy to work with and close enough for purposes of a rough calculation. The purpose of my calculation was not to provide more evidence for or against Bert, but just to show that having more test data could improve Bert’s odds.
Yes and no. The odds that Bert tests positive are one in ten thousand, correct. But the odds that someone tests positive are one in a hundred, so Bert can now argue that his positive is not that unlikely. It’s very unlikely to happen to him, yes, but not nearly so unlikely to occur, and that’s all that really matters here. IOW, what Bert has to prove is that the event, the incident, is of reasonable probability. From a scientific point of view, and a legal one, it’s the occurrence that has to be accounted for, not the fact that it occurred to this person rather than that person.
Think of a murder trial, where a key witness just happened to be in the right place at the right time to observe the murder. One might argue that it is extremely unlikely that this particular person happened to be at this particular place at this particular time. What are the odds that you walked past this alley, say, at this time, when you were in fact walking all over the big city that day? But there were hundreds of thousands of people walking about in the city that day, so the odds were not at all remarkable that someone could have been in that place at that time. That is all that matters, not who that particular person was.
Contrast this with the situation if the city were deserted that day. There was a holiday, very bad weather, or some other constellation of events such that very few people were out and about. Now it becomes very pertinent to question the witness’s story. It does seem very unlikely that, even if he were out that day, he would be in that particular place at that particular time. It seems to be too much of a coincidence.
Or think of a lottery. The odds against any particular person winning the lottery are astronomical. But given the large number of people who play it, the odds are not at all high against someone winning it. So when someone does win it, we don’t say that it’s impossible, that there was fraud or cheating. We just say that that person was extraordinarily lucky.
In fact, every day things happen to people that, applied to that specific individual, are wildly improbable, but which we accept because we know they have to happen to someone. Very low probability events happen all the time, they have to happen given the large number of people and activities that are constantly in play. We can predict that they will happen, we just can’t predict who they will happen to.
I tend to agree with you, Chris, but this is a remarkable turnaround for someone who a while back said Bert should get off because “stuff happens”. What stuff happened to you to change your mind?
You probably won’t believe this, Python, but even I find this discussion too abstract. Yes, we are getting off the realities of the case here. I can only emphasize that I raised this point not because I think it has a lot of relevance to Bert’s case, but because in the future, if enough riders are tested with high sensitivity technology, we might expect to see a positive, even if the meat tests are accurate.
This is a good point. I have always given Bert credit for having in fact eaten steak the day of or day before the positive. Of course, he had plenty of time before the positive became public to fabricate a story, but as you and others have discussed earlier, a lot of people would have had to be in on the lie. A big question for me, though, is how often do riders eat steaks during a GT? I know they can consume as much as 8000-9000 calories a day, some of that presumably is always meat (and remember, not just beef but chicken and pork can be CB-contaminated). If it turns out he ate meat frequently during the Tour, this point might not help much.
What we're trying to determine is: which is more likely, transfusion or contaminated meat? While it is true more tests increase the probability that some tested person will have eaten contaminated meat, the probability that some tested person transfused also increases. We shouldn't compare the joint probability of a positive due to meat from a sample of 100 tests to the probability that a single person transfused.Merckx index said:
If, for example, the probability that a tested person transfused is 1/1000 (10X more probable than he ate contaminated meat), the likelihood that a positive test arose from transfusion is 10%, while it is 1% that it was caused by contaminated meat.
IOW, we can compare the joint probabilities of the two scenarios over all tested individuals, or we can compare the probabilities for a particular person. It is incorrect and highly misleading to compare a joint probability of scenario A with the singular probability of scenario B.
The difficulty here, as I mentioned before, is how to assign a "probability" to the transfusion scenario. It is not a random event; it takes intent, planning, and execution. It seems to me that the "probability" that AC would transfuse is different from that for a domestique who rides for an out of contention team. That's why I think it is probably better to work with individual probabilities.
I have no problem with this. Group statistics are to a large extent (but not completely, see below) irrelevant in assessing whether Bert would have transfused. But this doesn’t make them irrelevant to the question of CB contamination. You apply whatever is relevant and appropriate to each question. When it comes to eating contaminated meat, the probability is the same for Bert as for anyone else, and this should be taken into account in assessing the likelihood of contamination.
If I understand you correctly, you believe that a) considering Bert as a member of a group would increase the odds of transfusion, just as it does for CB contamination; but b) we shouldn’t consider him as a member of a group, because he is more likely to transfuse than the typical or average rider. Therefore, c) we must consider him as an individual, foregoing the greater odds of transfusion if a member of a group—because the increased odds, unlike that with CB, are counteracted by the fact that other riders are less likely to transfuse.
Yikes. Let me try to deconstruct all this. I don’t agree with a). As you point out, transfusion is a matter of intent, not random chance, so considering him a member of a group doesn’t increase the chances of transfusion at all. It might increase the chances of his testing positive for transfusion. I will address that later.
I mostly agree with b), just because transfusion is not a random process. Membership in a group, in this situation, is not too relevant. Of course he wouldn’t transfuse if he wasn’t a rider, and we need to know something about how likely it is that riders in general transfuse, but given that background, our further approach considers him individually (c). But as I said before, I don’t agree that considering him a member of a group would increase the odds of transfusion—even if each member were equally likely to transfuse. Again, the group approach assumes randomness.
IOW, this is apples and oranges. The group approach simply isn’t very relevant to cases of intent, rather than cases where something happens to someone randomly. We take Bert’s case individually because we can get a better estimate of the odds than we could by considering him as a member of a group. Not a higher estimate, a more or less favorable estimate, but a better, more accurate estimate.
We consider CB contamination as a group effect for the same reason. The fact that the odds are higher is not the point; this approach is taken because it is better, more insightful. It incorporates additional information (the fact that other individuals tested negative), and thus tells us more about what is actually going on. You seem to think it’s some kind of trick that maximizes the probability, and therefore shouldn’t be allowed unless all analyses employ it. It’s not a trick, it’s the best use of the available information.
So to the extent that transfusion is not based on tests, a group approach is not relevant. However, some of the evidence for transfusion is, or could be, based on tests. Should group stats be applied here? For example, what about passport anomalies, if they in fact exist in Bert’s case? The point here is that the passport system is already based on group stats. Since every rider in the peloton is subjected to it, the likelihood of a false positive resulting from mass testing is already taken into account in defining what is suspicious. In fact, all doping tests take false positives into account, or are supposed to. One major reason it’s so easy to beat doping tests is that the bar for a positive is set very high. It’s set high precisely so that riders who test positive can’t claim that they are a false positive. Even taking into account that someone in a large number could test positive, the numbers are still stacked against them.
What about DEHP? This is not a validated test; while a lot of studies have been made of it, I’m not aware that anyone has published a rigorously estimated false positive rate—mostly because the whole notion of a false positive is only relevant to transfusion and doping, which have not been studied very thoroughly. So yes, you could argue that if many riders were tested for DEHP, the possibility that one of them who didn’t transfuse tests positive goes up.
But this is less significant than CB just because DEHP is not a validated test. WADA is only claiming that the positive supports transfusion, not that it nails the case. If the test ever were validated—and it now appears it won’t be—the group effect would have to be taken into in setting the criterion for a positive. As it stands now, how strong the evidence of DEHP is—even discounting the two step problem—is fuzzy, and subject to a lot of interpretation. A more rigorous analysis based on group effects would not be appropriate at this level of certainty.
Well, no, you don't understand me correctly, and it appears that either you're being a little casual in word choice, or you don't understand joint probability.
So, again, performing multiple tests doesn't change the chances of AC having ingested contaminated beef, nor do multiple tests change the likelihood that he transfused. What multiple tests will do is increase the probability that someone (not necessarily AC) will test positive with the cause being contaminated meat. It will also increase the likelihood that someone (not necessarily AC) will test positive due to a CB-contaminated transfusion (unless you think that transfusion never occurs). Multiple tests will not increase the probability that a particular person (e.g. AC) will have eaten contaminated meat, nor will it increase the likelihood that a particular person (e.g. AC) chose to transfuse.
Suppose that 10000 tests are performed with the odds of meat contamination at 1/10000, and one test is positive. Does that mean meat contamination is shown to be the cause of the positive? No! The probability distribution of positives due to meat is in this case Poisson, and the probability of zero positives due to meat is 0.37. The probability of one meat-caused positive is also 0.37. Suppose that the testing resulted in two positives. The probability that both were caused by meat is 0.18. If we believe that transfusion were the only other possible cause, then it and meat are roughly equally likely to be the cause.
Doing lots of tests for CB in cyclists provides very little additional information, unless we have a way to ascribe the cause of each positive. Of course at present we don't; if we did, CAS probably wouldn't need to rule on AC. If we did a 100,000 tests, and had no additional positives, then we might believe that CB from contaminated meat is more rare than 1/10000. But we'd also have to believe that CB from transfusion is just as rare. It doesn't help us to decide which was the cause of AC's positive.
Finally, I think assessing the likelihood that AC transfused is better done on an individual basis simply because it needs less estimation than trying to estimate the likelihood for the entire group of tested riders. Estimating the joint probability is entirely doable, but since the individual probabilities differ, each one has to be estimated individually. Way too much work.
So, again, performing multiple tests doesn't change the chances of AC having ingested contaminated beef, nor do multiple tests change the likelihood that he transfused. What multiple tests will do is increase the probability that someone (not necessarily AC) will test positive with the cause being contaminated meat. It will also increase the likelihood that someone (not necessarily AC) will test positive due to a CB-contaminated transfusion (unless you think that transfusion never occurs). Multiple tests will not increase the probability that a particular person (e.g. AC) will have eaten contaminated meat, nor will it increase the likelihood that a particular person (e.g. AC) chose to transfuse.
Suppose that 10000 tests are performed with the odds of meat contamination at 1/10000, and one test is positive. Does that mean meat contamination is shown to be the cause of the positive? No! The probability distribution of positives due to meat is in this case Poisson, and the probability of zero positives due to meat is 0.37. The probability of one meat-caused positive is also 0.37. Suppose that the testing resulted in two positives. The probability that both were caused by meat is 0.18. If we believe that transfusion were the only other possible cause, then it and meat are roughly equally likely to be the cause.
Doing lots of tests for CB in cyclists provides very little additional information, unless we have a way to ascribe the cause of each positive. Of course at present we don't; if we did, CAS probably wouldn't need to rule on AC. If we did a 100,000 tests, and had no additional positives, then we might believe that CB from contaminated meat is more rare than 1/10000. But we'd also have to believe that CB from transfusion is just as rare. It doesn't help us to decide which was the cause of AC's positive.
Finally, I think assessing the likelihood that AC transfused is better done on an individual basis simply because it needs less estimation than trying to estimate the likelihood for the entire group of tested riders. Estimating the joint probability is entirely doable, but since the individual probabilities differ, each one has to be estimated individually. Way too much work.
- Sep 25, 2009
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a discussion about joint probability turned in to a disjoint discussion...the path i predicted only few posts up as highly probable and likely to get disjoint. again, we can have fun and compare apples to oranges but that’s not what was taking place in the courtroom.
at this point in time having followed most of the developments closely for the last 18 months, i believe that the leaks from 2 weeks ago are indeed as close to what actually happened in the court room as we were let on up to now. the evidence points to a different decision-making path, albeit also based on statistics, than the 2 learned gentlemen above are arguing….
it’s quite true that eventually the panel will have to chose btw the steak and the plasma bag. but it will almost certainly not be based on impractical and misleading analysis of joint probability of the 2 events.
in stead, the panel has considered each event credibility on its own merits as based on the evidence presented by both sides -transfusion scenario against transfusion scenarios, contamination against contamination…
for ex, the article clearly states that the 2-step transfusion theory was swept aside b/c bert’s lawyers proved it ‘impossible‘. well, that’s an inaccurate terminology perhaps due to the mistake by the journo or the legal rhetoric of bert’s lawyers…regardless, the cas merely had to consider the 2 step transfusion not credible rather than impossible.
i ran my own investigation as to the cas thinking and tried to promote the appropriate discussion as to the reasoning by starting a separate thread but, as often happens in the clinic it went nowhere…good we have only few days left to wait
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