Pending release of details, here’s my best guess of how Froome’s defense went.
It begins with the Heuberger model. As I’ve pointed out earlier, WADA’s mention of samples given shortly after inhalation is pretty much a dead giveaway. No other authors I’m aware of have emphasized so much the importance of measuring samples within an hour of taking salbutamol. WADA further mentions the variability among samples, which is the whole point of Heuberger’s model: that there can be enormous variation in urine levels within the same subject following inhalation of the same amount.
Heuberger’s conclusions, as I’ve discussed several times before, simply aren’t supported by the available studies. They claim they are, but they point to only one study, and that was not using the one hour window that is critical to Froome’s case. There are in fact multiple studies that measured levels one hour after inhalation, and none of a total of several dozen samples reached the 1000 ng/ml level that, according to Heuberger et al, should occur about 15% of the time. I've discussed this in detail upthread.
That ought to be a serious criticism of the model, and a warning flag about using it to support Froome’s case. But even if the model were better supported by empirical data, Froome would want to show that his own physiology conforms to the model. To do this, he would use his Vuelta samples, of which there should have been nineteen, or eighteen other than that from stage 18. It was reported that none of these samples exceeded 600 ng/ml, but that doesn’t mean much unless we know how much salbutamol he inhaled during those other stages.
To simplify, initially, let’s assume he took only 200-300 ug in each of these stages. He claimed he took more on stage 18 because of severe symptoms, and I’m pretty sure his argument is that the levels were much lower on the other stages because he didn’t suffer from those symptoms and so didn’t take as much. To simplify further, we will assume he inhaled those 2-3 puffs near the end of each stage, and didn’t urinate between then and when he gave the sample.
He would thus have a pool of eighteen samples, all of them conforming to the Heuberger model. What he would want to show is that there was great variability in the urine levels. If the maximum was 600 ng/ml., and the minimum was, say, 100 ng/ml., he would argue that there was at least a four-fold variation (600 from three puffs vs. 100 from 2 puffs). Moreover, if he could reach 600 ng/ml with just three puffs, then clearly he might reach 1600 ng/ml with the allowed eight puffs, if we assume rough linearity. This is not far from the actual value of 2000, and actually more than the corrected value of about 1430.
I think this may be the gist of Froome’s argument. Where it gets really complicated is when one no longer simplifies. Did he really take only 2-3 puffs on all the other stages? Or maybe more on some, less on others? Does he have records of this, and can they be accepted as evidence? Can he prove he always inhaled near the end of the stage? Did he never urinate between inhalation and giving the sample (a key assumption of the Heuberger model)?
Remember, he was tested after every stage beginning with stage 3, many of which were flat or hilly runs that didn’t require a solo effort. He might not have inhaled at all on those stages, so he couldn’t use those samples at all in his argument. Even when he did inhale, he might have done so earlier in the stage or even before the stage began. And since he’s arguing he inhaled more on stage 18, because of severe symptoms, he probably inhaled more on stages right before or after that, too.
So Froome is trying to fit his data to Heuberger’s model, but the data themselves—as one would expect on the road—don’t occur under standard, controlled conditions. They’re very noisy. This is even assuming Froome has detailed records of how much he inhaled and when, and that his word should not be challenged. While the Heuberger model can certainly deal with this—there’s no requirement that each sample be taken at the same time after inhalation--it complicates the analysis if the samples aren’t uniform in this respect. Each sample has to be treated individually, and this introduces an additional error or degree of uncertainty when it’s compared to the others. This is beyond the substantial uncertainty already existing, e.g., in the time between inhalations and providing the sample.
The pool size might be greatly expanded—and the noise perhaps somewhat reduced--if Froome also introduced as evidence samples from other GTs, such as the TDF that preceded the Vuelta. But that assumes he has records for those stages, too, and all the other assumptions I’ve mentioned.
So this is a very difficult argument to make. Would it be enough to convince Haas, UCI, and WADA? The Heuberger model predicts about 15% of samples taken one hour after inhalation of 800 ug would exceed the 1000 ng/ml threshold,with about 10% exceeding the decision limit of 1200 ng/ml. I would guess roughly that the model predicts 7-8% would reach Froome’s level. If he took 800 ug regularly, within the last hour or two of a stage, he no doubt would have reached that level several times in the past. His argument has to be, first, that he has rarely taken 800 ug under those conditions, so rarely that he has never before reached even 1000 or at least 1200 ng/ml. And second, that he has reached an equivalent level at times. E.g., if he has a large pool of samples from when he took 2 puffs, several reach 400-500 ng/ml, while the others describe a descending range of lower values.
Perhaps Froome really was able to provide these data, credibly. But until I see the details, I remain deeply skeptical that a) he has records that are detailed enough to use in such an analysis; 2) that enough of the samples were taken within an hour or two of the inhalations, so as to reduce the uncertainties associated with dealing with multiple time points; and 3) his range of values really deviates so much from what has been reported in the literature.
There is one final point I made very early in this thread. If Froome has rarely taken 800 ug in the past, so rarely that he has never exceeded 1200 ng/ml, then it's quite unlikely that the one time he would exceed it, he would do so dramatically, to 2000 ng/ml. That is statistically improbable in a random distribution. While it's true his corrected value was about 1400 ng/ml, until this year, the correction was not allowed. So the 2000 ng/ml level is directly comparable to whatever he recorded in the past. When we say that Froome never exceeded 1200 ng/ml in the past, we mean uncorrected. If he had exceeded that limit, a high USG would not have helped him, by the rules that were then in force.
Speaking of which, don't forget that the correction for SG was only instituted this year (and after Froome's AAF). Had such a correction not been allowed, as was the case in previous years, I doubt that even the Heuberger model could have saved Froome.
Lucky? That he was busted in 2017 and not an earlier year. That his AAF was leaked, stimulating Heuberger et al to do their study. That he has the resources to make this case, obviously.
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