Dopeology

Analysis

The Froome Decision: What, How and Why?

From the 2017 Vuelta until right before the 2018 Tour de France, Chris Froome’s long-running salbutamol case is well known to followers of European professional road cycling. Contributor Andy Smith provides a detailed analysis of the outcome.

Salbutamol is a specified substance, which means that athletes are allowed to use it, to relieve asthma symptoms, within allowed dosing. The maximum allowed dosing is 800 ug - eight puffs on a standard inhaler - every twelve hours. Since the sport's governors have no method of confirming how much an athlete has taken (and here it seems that the Union Cycliste Internationale (UCI) simply accepted Froome’s testimony), a threshold value has been set of 1000 ng/ml in the urine, raised to a decision limit of 1200 ng/ml to allow for measurement uncertainty. The rationale of this limit, supported by a considerable body of research, is that an athlete inhaling 800 ug or less will almost never exceed it. An athlete who exceeds this limit is given notice of an AAF (adverse analytical finding) and must convince the sport's governors that he/she could reasonably have done so without taking more than the allowed amount of the drug.

The circumstances of the case are well known: on Stage 18 of the 2017 Vuelta a España, Froome exceeded the limit by a very large amount; his urinary salbutamol level following the stage was 2000 ng/ml. His case was helped somewhat by a new rule, albeit one not actually announced until two months after Froome’s AAF and which did not go into effect until more than five months after the AAF, that urinary salbutamol levels could be corrected for urine specific gravity (USG). Normal USG is about 1.020, but riders frequently experience some dehydration, resulting in more concentrated urine and hence a higher USG. Since it’s assumed that this would also result in concentrating an excreted drug like salbutamol, the rider is allowed to reduce the recorded concentration by the formula (1 – 1.020)/(1 – USG). Froome’s USG was 1.028, resulting in a corrected value of about 1430 ng/ml.

That value is still well over the limit of 1200 ng/ml. So why did the rulemaker World Anti-Doping Agency (WADA) eventually recommend that Froome's case be dropped?

While the complete details of WADA’s rationale have not been released, enough information has been supplied to the media to understand the probable general outlines. The key point seems to be that Froome’s legal team convinced WADA to ignore - to a large degree - the considerable body of laboratory research on the relationship between salbutamol dosage and urinary level, and focus only on Froome’s own urine samples, of which there were about twenty during the Vuelta. Froome's rationale was that laboratory conditions are different from those in a Grand Tour, where an athlete makes large efforts every day. WADA also alluded to an illness from which Froome had claimed to be suffering and the other medications he was taking for that.

What is the basis for WADA’s current salbutamol threshold?

Before examining Froome’s defence in more detail, I want to present and discuss some of the laboratory evidence underlying the 1000 ng/ml threshold. While I can’t point to a specific study that WADA used as the basis of the threshold, there are many studies that support the reasonableness of the value. During these studies, subjects were asked to inhale a certain amount of salbutamol and then, at a certain time later, provide a urine sample. In this way, it’s quite straightforward to obtain an idea of how likely it is that a dose of a certain size exceeds a certain urinary concentration.

In a recent statement at its website, WADA listed eleven relevant studies, all but one of which has been published.¹ Of the ten published reports, seven examined subjects who inhaled the permitted amount of 800 ug (Sporer et al. 2008a,b; Elers et al. 2010, 2012; Mareck et al. 2011; Dickinson et al. 2014a, b). A total of 187 samples were analysed, of which only three (about 1.6%) exceeded the 1000 ng/ml threshold. Some of these values were corrected for USG and some were not (so there were actually more than 187 values from the 187 samples) but the main point is that, corrected or uncorrected, only three values exceeded the threshold. Furthermore, only one sample exceeded the decision limit of 1200 ng. This was a corrected value, which was increased from the uncorrected value because of dilute urine, that is, the USG was < 1.020. Since the new rules specify that an athlete’s sample does not have use the corrected value if it raises the effective salbutamol concentration, this value would not have resulted in an AAF. In fact, none of the nearly two hundred samples would have.

To give the reader an idea of the typical urine concentration of salbutamol following inhalation of 800 ug, here are some mean values (ng/ml), in some cases also including the standard deviation:

• Elers et al. (2012): 335 (elite athletes) and 401 (non-athletes)
• Dickinson et al. (2014a): 188 +/- 146 (2% dehydration); 364 +/- 285 (5% dehydration)
• Sporer et al. (2008a): 210 +/- 177

The highest mean value was thus about 400 ng/ml, less than half of the threshold. Moreover, the reported standard deviations provide a way of estimating the probability of exceeding the threshold. The greatest probability, estimated from the values of 364 +/- 285 reported by Dickinson et al, indicate that the threshold would be exceeded by about 1% of samples, while the decision limit would be exceeded by less than 0.2% of samples. However, as I will discuss shortly, this study involved dehydration, which would be expected to increase urinary levels; no correction was applied to this. All the other reported means and standard deviations indicate a far lower probability.

Such is the research that underlies WADA’s salbutamol threshold. Athletes do occasionally exceed the threshold and limit. Indeed following the Froome decision, WADA revealed that about forty other athletes had received AAFs for salbutamol in the past five years (not including some cases resolved with therapeutic use exemptions (TUEs) and other factors), of which eight were ultimately cleared¹. However, there is no controlled laboratory study of which I’m aware where a subject inhaling no more than 800 ug exceeded the limit.²

I also want to emphasise several other points about this research:

In all of these studies, urine samples were provided within four hours of inhaling salbutamol, and about half the samples (93) were provided within two hours, while more than 25% (53) were provided within one hour. This is important, because studies indicate that urinary levels of salbutamol levels peak within about one hour after inhaling, so that samples taken at this time would be most likely to exceed the threshold. This was perhaps the most credible conclusion of the study by Heuberger, et al (2018), which created a stir when it was published last April and featured the use of a computer simulation model to conclude that inhalation of 800 ug would result in exceeding the threshold about 15% of the time. This conclusion has been criticised on several grounds, including that it doesn’t agree with actual empirical studies, as the values I have cited above indicate. But the model does predict that values would be at their highest about one hour after inhalation, and this is generally supported by lab studies. This is germane to Froome’s case because, to maximise the possible urinary level from a given dose, he would want to argue that dose was inhaled very soon before providing a sample.

All of these studies examined inter-subject variation, that is, the differences in urinary levels between different subjects given the same dose one time. A separate question is intra-subject variation, that is, how much urinary levels vary in the same subject given the same dose at different times. This point is relevant because, as we will see shortly, this question was apparently addressed by Froome’s team. I am not aware of any lab studies that have examined this question, at least not in any detail. I will point out however that pharmacological studies have generally reported that inter-subject variation is considerably greater than intra-subject variation (Jones and Jonsson 1994; Hanna et al 2005). This is to be expected, because the differences in physiology between individuals should be greater than the fluctuations in physiology in a single individual. So whatever the range of urinary values we find from examining different subjects, we would not expect this range to be greater in a single subject over time.

The question remains of the conditions under which the studies were carried out. As I mentioned earlier, WADA indicated that one reason for dropping the case against Froome was that the existing salbutamol threshold was based on studies that did not take into account the effects of riding in a Grand Tour. Among these conditions it listed intense efforts made every day, a lung infection Froome claimed to be dealing with at the time and any medicines other than salbutamol that he used to treat that infection.³ However UCI, in its own statement, rejected the illness and medication factors as irrelevant, leaving only the effect of intense exercise on salbutamol levels.⁴

Effects of exercise and dehydration on excretion

While there have been claims that these factors do affect salbutamol excretion, there is no published work of which I am aware that indicates the effects are significant enough to warrant changing the threshold.

For example, of the seven studies I summarised earlier, two by Dickinson and his colleagues featured exercise as part of the protocol. In one of the studies, 32 subjects exercised until they lost either two or five percent of their body mass. In the other study, seven subjects performed a five-kilometre run. None of the more than 70 total samples exceeded 1000 ng/ml, though the mean value of urinary concentrations was higher in the five-percent group (see above).

Some studies in which higher doses of salbutamol were inhaled have found that many subjects may exceed the threshold or limit under conditions of exercise and/or dehydration. Haase et al. (2016) reported that about 20% (corrected) to 30% (uncorrected) of samples were over the limit following inhalation of 1600 ug. The Dickinson study to which I previously referred also tested the effects of 1600 ug, and reported that 20 out of 64 samples exceeded the threshold, and 16 out of 64 were over the limit; but as I noted earlier, in that study, urinary values were not corrected for USG. On the other hand, another study by this group reported that only one of ten samples obtained following a 1600 ug dose exceeded the limit, at 1290 ng/ml (Dickinson et al. 2014b). Elers et al. (2011) reported no corrected samples exceeding the threshold following inhalation of 1600 ug by twenty subjects, with one uncorrected sample at 1082.

While these laboratory conditions obviously do not mimic exactly those of a Grand Tour, they provide no evidence that intense exercise or dehydration, by themselves, affect salbutamol excretion enough to account for Froome’s value under conditions when the amount inhaled is within that allowed by WADA. The only way to prove that Grand Tour riders are affected differently would be to test them every day throughout the race but, except for Froome, this has probably never been done.

With occasional random exceptions, riders are only tested following a stage win or placing or while holding one of the leader’s jerseys. For example, Alessandro Petacchi, who tested over the salbutamol limit in the 2008 Giro, provided only five samples during that three-week Tour (Fitch 2017) and, as one of the leading sprinters of his era, he was tested unusually often.

So the data simply do not yet exist for making a study of this order. While statements released to the media may allude to unpublished studies, until these unpublished data are made available, there is no reason to believe they support the notion that a value as high as Froome’s has a significant probability of resulting from a dose of 800 ug. Nothing actually published confirms this. Moreover, WADA has stated, following the Froome decision, that it does not believe the salbutamol threshold should be changed.³ So it is unlikely that any unpublished studies affect this conclusion either.

This conclusion not only prompts serious scepticism over WADA’s decision to drop the case, as I will discuss later, but also calls into question WADA’s claim that Froome could not be expected to perform a controlled pharmacokinetic study (CPKS), that is, a lab test in which he would try to mimic the conditions of exceeding the limit, and show that it could happen again. Even if one really believes, apparently with very little evidence, that these conditions make a difference, a CPKS would still be very useful in providing a general view of Froome’s physiology. For example, are Froome’s urinary levels in the lab consistent with those reported in the studies I have just discussed? If they are, then the decision to drop the case implies that simply riding a Grand Tour, as several riders previously sanctioned for salbutamol were doing, has an enormous (one is tempted to say, scientifically unprecedented) impact on salbutamol pharmacology.

Froome’s defence

Now let us turn to Froome’s defence. As a prelude to this discussion, there are two important facts to restate:

• The 2000 ng/ml salbutamol level, corrected to 1430;
• Froome reportedly never previously exceeded the limit of 1200 ng/ml, at least as far as we know.

Assuming this latter fact is really true, Froome's AAF represents a level at least 67% higher than any other test (that it was reduced to 1430 following the correction for USG is irrelevant because, in previous years, riders would not have been allowed to make this correction so their raw values were what counted).

Given that Froome has probably been tested in excess of one hundred times - the mandatory Grand Tour tests that follow a stage win and/or the wearing the leader’s jersey alone would add up to about eighty (per July 2018) - this is fairly remarkable. More to the point, it requires of him to argue that never or very rarely has he taken the maximum allowed amount of 800 ug prior to a test because, if Froome had done so commonly, one would expect him to have exceeded the limit previously. So while his 2000 ng/ml level could have been a fluke, a literally one-in-a-hundred event, one would not expect a fluke that would be that much higher than the next highest value, after all those tests.

Furthermore it was reported that Froome's urine values during the Vuelta, excepting Stage 18, never exceeded 600 ng/ml.⁵ This requires again the claim that he did not take anywhere near 800 ug on most of the other days. For if Froome had, it would be very difficult to explain how one urine value was so much higher than all the others.

Taking into account all of these facts, Froome’s defence must consist of two general claims:

• He inhaled a much larger amount of salbutamol on Stage 18 than on most other stages, resulting in a large increase in his urine value compared to those other stages; and
• Since even the full allowed amount of 800 ug would normally not result in exceeding the limit (based on the lab studies I discussed earlier), he must provide some other kind of evidence that such a very high value could have occurred.

The first claim cannot probably be proven, but Froome has provided a rationale for it. His argument was that, under normal circumstances, he took only a few puffs per day, but because he was sick late in the 2017 Vuelta, he had to take more. Later, I will assess the problem associated with accepting Froome’s word on what doses he took, and when. For now, I want to turn to the second claim.

How could Froome’s defence establish that a dose of salbutamol within the allowed amount resulted in such a very high urine concentration? The approach they used was described briefly by a recent story in the Times:

In research provided to Froome, Dr Daren Austin, senior fellow and senior director of clinical pharmacology at Glaxosmithkline, said that he had run extensive virtual trials to establish the possibility of breaching WADA regulations while staying within the rules.

“We analysed Chris Froome’s detailed dosing history to calculate the likelihood of him generating at least one presumed [AAF] using various statistical methods,” he said. “Our calculations revealed a surprisingly high likelihood of a false positive.”⁶

To what exactly is Austin referring? As I noted earlier, Froome provided a urine sample every day - possibly excepting the first two days when he didn’t wear the leader’s jersey - during the 2017 Vuelta.

In principle, this could be the basis of a study of salbutamol excretion during a Grand Tour. Every day, he inhaled some of the drug, and every day or nearly every day he provided a urine sample. One could thus examine the dose-response variation over time. Instead of having multiple subjects, all taking the same dose of salbutamol, and examining between-subject variation in urine levels, we have one subject, taking salbutamol doses over time, and are examining within-subject variation. The goal in this case would be to show that there is so much variation in the relationship of the dose inhaled to the urinary level as to allow a significant probability that 800 ug could in fact result in his corrected value of 1430 ng/ml.

This approach is somewhat like that of the biological passport, a method used by UCI to test riders for blood doping in the form of EPO use and/or blood transfusions. In the passport, a rider’s key blood values—hematocrit, hemoglobin, reticulocytes, et. al.—are measured over a period of time and used to create a baseline, or more precisely, a base range. The upper and lower limits of this range are taken as the maximum or minimum values these parameters can have and be consistent with natural variation. If one or more values fall outside this range, the rider is flagged for further investigation.

The approach to which Austin alludes is similar to the passport in that it uses only Froome’s own values to determine probabilities, not the values available from lab studies I discussed above. These are used to estimate how likely it was he could have had a urine level of 1430 ng/ml following inhalation of 800 ug of salbutamol.

To illustrate how this works, let us begin with a simple set of hypothetical data. As I just pointed out, Froome has to claim that most of the time during the Vuelta, he did not inhale that much salbutamol, because his urinary values after all the stages except 18 were so much lower than on that day. So let us suppose he took only 2 puffs, or 200 ug, per day the first ten days, and that the following urine concentrations (ng/ml) were obtained:

• 150
• 80
• 110
• 75
• 220
• 140
• 120
• 250
• 280
• 190

Looking at these values, we can see that a 200 ug dose may result in considerable variation in urine concentration. The mean value is about 160 with a standard deviation of 70. If we assume these values are randomly distributed, we could calculate the probability that a 200 ug dose resulted in a urinary level exceeding any particular threshold. For example, a value of 300 ng/ml would be two standard deviations above the mean, corresponding to a probability of about 2.2%. That is, 2.2% of samples provided following inhalation of 200 ug would be expected to have a urine concentration this high by chance.

However, the actual data Froome’s team would be working with are considerably more complicated.

Firstly, he did not inhale 200 ug every day. Indeed we know that he inhaled much more - presumably the full allowed amount of 800 ug - on Stage 18. Froome probably inhaled a large amount on the day or days immediately preceding and following that stage, since he claimed to be sick at that time and in need of more salbutamol than usual. There might be other days when he inhaled an intermediate amount.

A second complicating factor is the timing of the doses. In the lab, subjects take a measured dose, then at a fixed time later, provide a urine sample. On the road, the time between dose and sample is likely to vary considerably. Sometimes the dose may be taken near the end of the stage, and thus within an hour or so of providing a sample. Other times, the interval may have been longer. Moreover, when larger doses are taken, they are unlikely to all have been inhaled at the same time. If he inhaled 800 ug on Stage 18, he probably took two to three puffs at several different times, spread over a large period during the stage. Still further, Froome may have sometimes urinated during the stage, after inhaling some salbutamol but before providing the sample for testing.

The timing matters because, as I discussed earlier, salbutamol concentrations in the urine peak within the first hour or so after inhalation. If one sample is taken one hour after inhaling a dose such as 200 ug, and another sample taken four hours later, other things being equal, the first sample is expected to have a higher concentration. If two samples are provided the same time after inhalation, but one sample was produced after an intervening urination, this sample would be expected to have a lower concentration.

The upshot is that each sample must be treated as more or less unique. One cannot simply apply a relatively simple statistical analysis, such as determining mean and standard deviation. The values that I listed earlier would need to be adjusted to take into account the differing conditions in which they were obtained; for example, one would need to make an assumption about how much urinary dose falls off with time. Still further adjustments would be required so that these values could be compared with values resulting from inhalation of higher amounts. This requires another assumption, concerning how linear the relationship is between doses of different sizes.

The way Froome’s team reportedly dealt with these issues was to run a series of simulations on a computer—trials in which the urinary concentration following an 800 ug dose is determined based on the all the dose-concentration information from his samples. We are ignorant of the details, but presumably the data were adjusted for the factors that I have just discussed, and possibly others (such as the effect of a dose taken one day on excretion of a dose taken the following day). According to Austin, a very high proportion of false positives - that is, values greater than the threshold or limit - were obtained, perhaps as high as 10%.

On this basis, Froome’s team argued that it was reasonably possible that his very high urinary value on stage 18 resulted from chance. Every time he took a dose of salbutamol, there was large variation in the urinary level, and when he took 800 ug on a rare day, this variation made it possible for his urinary level to exceed the limit.

The trust factor

Without seeing the actual details, my criticism of Froome’s defence must be somewhat limited, but there appear to be several problems with it. One concerns the validity of the information that went into the model. The second involves the model itself. And the third concerns the conclusion from the model.

With regard to the first problem, one obviously has to know the dose of salbutamol inhaled every day. Since Froome was the subject of a doping investigation, one that was specifically aimed at determining whether he was telling the truth when he insisted he did not exceed the allowed maximum dose of 800 ug, there should be an independent means of verifying these doses.

As the preceding discussion should have made clear, it could be in an athlete's interest to lie about the doses taken earlier in the stage, just as it would obviously be in his/her interest to lie about the dose he/she took the day before the limit was exceeded. If one does not accept the latter without corroboration, it is also illogical to accept the former. But I find it very hard to believe that such corroboration could exist. Perhaps the amounts in Froome's case were somehow recorded every day but no such information has been forthcoming. If one does accept the testimoney of an athlete who claims to have recorded or remembered his/her dosage, there is a question of accuracy.

Media reports of Froome's case are contradictory. Froome apparently stated that he took two puffs in the morning (which would have minimal effect on his urinary level), and two at night (which would have no effect if they were taken after the stage). Another report indicated four puffs per day and ten - exceeding the twelve-hour limit - on the day of the high value.⁷ Reporting of Froome's usage has been contradictory at other times too, which could suggest a lack or unawareness of detailed records, but there was no obvious requirement to keep them, at least until it became a critical matter.

Next, there is the question of the timing of the doses. As I discussed earlier, the time between inhalation and providing the sample is a critical piece of information. Even if Froome could state how much salbutamol he took every day and reported this accurately, he would be unlikely to know exactly when he took each puff on every stage.

There are numerous uncertainties in the data. How certain are the doses that Froome claims to have inhaled? How certain are the times he claimed to have inhaled them? How certain are the calculations about how urinary levels change over time following a given dose? With all these uncertainties, one can be justifiably sceptical about the accuracy of estimates of the probability of exceeding the threshold. Simulations are only as accurate as their starting assumptions.

Recalling that I pointed out earlier the WADA conclusion that a CPKS would not be meaningful for Froome, there would still be value in his submitting to such a lab study. One of the most important questions such a study could help answer is whether Froome’s information on dosing during the Vuelta was accurate. A lab study would show very clearly the relationship between dose and urinary level and address the question of how much variability in this relationship could occur from test to test. Even if Froome's legal team insisted that the conditions of the Vuelta were different, lab tests, at the absolute minimum, would provide an estimate of how much those conditions were affecting his urine values. Given how vital such an estimate is to deciding how much Froome’s case would apply to other riders, it is not easy to appreciate why WADA would not take the opportunity to find out.

Validating the model

This brings us to a second criticism. How valid is the simulation model that Austin used?

Simulation programs have been used frequently in pharmacology to predict drug concentrations in the body over time, though generally they are a little different from what I believe Austin used. But regardless of the model used, normally there is a two-step procedure:

First, one builds the model using available data—Froome’s Vuelta samples, in this case. Then one tests or attempts to validate the model by using it to predict values in a separate study. Since Froome’s model was based on his own samples, and all along his team has been arguing that his conditions were unusual, it could only be used to predict other values from his own samples, which I very much doubt has been done. For example, it could be used to predict his urinary values in Grand Tours of the past. But this again would require assuming he knew and truthfully told how much salbutamol he took each day and when—all information, of course, that is long in the past.

In fact, it is worse than that. The word 'predict' as applied to values is not quite apposite here. What the model would do is predict a range of values, and would be validated to the extent that all the actual values fell within this range. But since Froome has never (as far as we know) exceeded the limit previously, there are no values outside of those expected from laboratory studies. So there is probably nothing for the model to predict that would show it to be a more reliable indicator than those studies. Presumably it would reveal considerable variation in urine levels following the same low dose, say 200 ug, but it is unclear how this result would be compared with those from lab studies.

Validation is critical, because by manipulating parameters of a model, one can significantly change the predictions that it makes. Consider again those ten hypothetical urinary values I listed earlier. From the mean and standard deviation, we determined that a level of 300 ug would be exceeded about 2.2% of the time. But the same data indicate that the standard error of the mean, defined as the standard deviation (70) divided by the square root of the sample size (3.16) is about 22. This means the mean might be as low as 138. Using this value, the 300 ug level would be exceeded only about half as often, 1.1%.

The standard error is reduced by increasing the sample size, but Froome’s sample size is limited to about twenty, and we know that not all those samples resulted from inhaling the same amount. When we add in all the uncertainties that I discussed in the previous section, I think it is reasonable to be sceptical of the reliability of any estimate of the proportion of false positives.

What is the false positive rate? And what does that mean?

Now let us consider this false positive rate, the main conclusion from Austin’s model. According to a media report, he claims that it may be as high as 10%. This begs an obvious question: if this is so, why do we not see far more AAFs?

Over the five-year period 2013-17, WADA reported 57 salbutamol AAFs, of which 38 did not involve therapeutic use exemptions (TUEs) or other extenuating factors. Of these, 30 cases led to sanctions, while only eight were cleared.¹ Thus an average of about eight salbutamol AAFs occur each year, with 1-2 being cleared. There are about 200,000 total tests per year (WADA’s report for 2016)⁸, and based on estimates that 5-8% of all athletes have, or claim to have, asthma (Fitch 2006), roughly 10-15,000 such tests may have been performed on them. So even assuming all of the AAFs are false positives, there is only one false positive per 1000-2000 tests. If one assumes only the AAFs that were cleared were false positives, the number is about one false positive per 10,000 tests.

How can this possibly be reconciled with Austin’s claim of a 10% false positive rate?

Part of the answer would be that most of the time athletes do not take the full allowed dose of 800 ug. Austin’s estimate assumes this, whereas athletes probably typically take far lower doses, perhaps 200-400 ug. However, even granting this, one would expect a higher number of AAFs. If the false positive rate is really 10%, then we would have to assume that athletes with asthma take the full allowed amount only 1%, or even 0.1%, of the time.

It would be very useful for WADA to perform a study of salbutamol usage, asking athletes about their patterns of inhalation, but as far as I know, no such information is available.

The other factor implied by both Austin and WADA is, as I pointed out earlier, that the conditions under which Froome was riding were unusual, and affected his salbutamol metabolism and/or excretion. But as I also discussed, there is no actual evidence of which I am aware that supports this. Indeed UCI’s own scientific experts rejected the claim that illness or other medications would affect urinary levels and studies of exercise and dehydration do not indicate a major effect on these levels either.

So the claim of a 10% false positive rate should raise eyebrows. But let us assume that it is well-founded. False positives are defined as samples that exceed the decision limit of 1200 ng/ml. But Froome’s actual Stage 18 sample had a corrected salbutamol concentration of 1430 ng/ml. What percentage of samples in Austin’s simulation would have exceeded that?

Assuming a random distribution of values, there is an easy way to estimate this figure. Recall that I listed earlier some mean values of urinary salbutamol concentrations from lab experiments where subjects inhaled 800 ug. Some of these studies also determined standard deviations, the highest of which was 285 ng/ml. Also recall that I pointed out that the variability, of which standard deviation provides a measure in inter-subject values, is generally much higher than the variability in intra-subject measurements. So being very conservative, we could estimate that the standard deviation of Austin’s hypothetical values should be no more than 285 ng/ml. This is a maximum estimate.

In a normal distribution, 10% corresponds to about 1.3 standard deviations; that is, the highest 10% of values have a standard deviation of 1.3 or greater from the mean value. Using the 285 ng/ml value, we can estimate that these 10% thus exceed the mean by 285 x 1.3 = 370 ng/nl. Since 10% were reported to exceed 1200 ng/ml, the mean value of the hypothetical samples would be 1200 – 370 = 830 ng/ml. Note that this is very high, more than twice as high as the highest mean value reported in any of the lab studies I discussed.

Of course, Froome’s legal team has been claiming all along that the conditions he raced under were different from lab tests, and resulted in the very high value on Stage 18. To have any chance at all of explaining this value, either the mean and/or the standard deviation of his samples must be considerably higher than the corresponding values reported in lab studies, and for the reasons I discussed earlier, it almost certainly is not the standard deviation.

Given this mean value of 830 ng/ml, what proportion of samples would be expected to exceed Froome’s value of 1430 ng/ml? The latter is 600 ng/ml greater than the mean, corresponding to 600/285 = 2.10 standard deviations. About 1.8% of all samples would be expected to exceed the mean by this much or greater.

So even if 10% of the hypothetical values in Austin’s simulations exceeded the salbutamol decision limit of 1200 ng/ml, less than 2% would be expected to exceed Froome’s actual value. This is assuming the variability of these samples was no greater than the highest reported variability in studies of inter-subject values; in fact, it would most likely be lower, in which case the percentage exceeding Froome’s value would also be lower.

Is a probability of less than 2% enough to conclude, as WADA did, that Froome’s sample was consistent with not exceeding the allowed amount? One might argue that a false positive rate of even 2% would be unacceptable for a test intended to detect doping. Though there is no fixed standard that WADA uses of which I am aware: generally speaking, the expected false positive rate in the tests that it uses is around one in a thousand or less.

There is an important piece of context missing. The acceptable rate of false positives when testing a population is very different from that when testing an individual. As I noted earlier, roughly 10-15,000 samples from athletes with asthma are probably tested every year. A two per cent false positive rate (and remember, that is only for Froome’s AAF; Austin is claiming that the rate is 10% for exceeding the limit of 1200 ng/ml) would correspond to 200-300 total false positives, which obviously would not be tolerated. Even if we assume that only a small proportion of these samples come from athletes who inhaled the full allowed amount of 800 ug, the number of false positives would probably be unacceptably large.

However, when evaluating Froome’s defence, we cannot appeal to standards intended to apply to a large population of athletes. The Austin model, based as it is on Froome’s samples, only applies to him. The argument that the conditions under which Froome was riding were unusual and impacted his urinary levels in effect forces Austin and WADA to this position. WADA has even stated that they don’t believe the Froome case means that their salbutamol threshold has to be changed.³ And for him alone, a two percent probability of a false positive must be viewed somewhat differently. It means there is a 98% chance that the positive is genuine. According to the WADA Code §3.1:

The standard of proof shall be whether the Anti-Doping Organization has established an anti-doping rule violation to the comfortable satisfaction of the hearing panel, bearing in mind the seriousness of the allegation which is made. This standard of proof in all cases is greater than a mere balance of probability but less than proof beyond a reasonable doubt. Where the Code places the burden of proof upon the Athlete or other Person alleged to have committed an anti-doping rule violation to rebut a presumption or establish specified facts or circumstances, the standard of proof shall be by a balance of probability.⁹

Mere balance of probability is greater than 50%, while beyond reasonable doubt might be considered > 95%, or perhaps 99%. So a 98% probability that Froome did exceed the allowed amount ought to be enough to warrant a sanction, if one assumes that WADA/UCI must decide to establish an ADRV (anti-doping rule violation). On the other hand, if one interprets the situation such that Froome must rebut the case that UCI has already made against him, he would have to show a greater than 50% probability of a false positive. That is even less supported by the alleged results of the simulation.

How, then, has WADA rationalised its decision? While many have suggested that political factors were at work – for example that there was pressure to drop the case when it became clear that ASO, the organiser of the Tour de France, was planning to bar him from entering the 2018 race - I will consider only the possible scientific explanations.

In one of their public statements, UCI mentioned, as one of the factors underlying their decision: “Mr. Froome could expect to be (and was) tested on almost every day of the Vuelta a España.”⁴ The implication of this statement, I believe, is that UCI considered it very unlikely that Froome would intentionally dope with salbutamol during the Vuelta, knowing he would be tested every day.

Why does this matter? When anti-doping organizations come to their decisions, they consider the various possibility explanations for the AAF, and attempt to estimate their probabilities. We may speculate that even if WADA/UCI believed that the probability of Froome’s AAF was relatively low, they may have felt that an alternative explanation - intentionally doping with salbutamol, through oral dosing - would have been even lower. In this sense, the balance of probability would favor a false positive, even if statistically it was fairly improbable.

Of course, it is impossible to estimate what the probability of intentional doping would have been, and even if it somehow could be ascertained to be lower than the probability of exceeding the limit while inhaling within the allowed amounts, there is still the possibility of inhaling too much, either accidentally, or on purpose because Froome felt he required it. For what it is worth, this seemed to be the view of many salbutamol researchers soon after the AAF became public.¹⁰ While again it may be difficult to make an accurate estimate, it doesn’t seem too much of a stretch to assume, on a day when he needed to take more than his usual dose, he took more than the allowed dose.

Conclusions

WADA’s current threshold for salbutamol is based on more than half a dozen studies and nearly two hundred samples. It has already stated that it doesn’t believe the decision to drop the case against Froome means that the threshold needs to be changed. But WADA is walking a very fine line, because it has to reconcile this stand with the conclusion that Froome’s urinary level, far in excess of the limit, is consistent with inhalation within the allowed amounts. It is argued that the conditions Froome was dealing with would have affected his salbutamol metabolism and/or excretion, but there are no published studies that support this.

Froome’s defence appears to depend on the claim that there was sufficient variation in the urinary levels of his 2017 Vuelta samples to account for a level greatly exceeding the limit. But this variation can probably be estimated only by accepting Froome’s word on the amounts of salbutamol he inhaled throughout the Vuelta, and even then, there would be considerable uncertainties underlying any attempt to use these data to estimate the probability that a single large dose would exceed the limit. The theoretical false positive rate suggested by Froome’s defence of 10% following inhaling 800 ug is clearly rejected by WADA as applicable to anyone other than Froome, yet it has provided no data supporting its contention that the conditions Froome experienced during the Vuelta are unaccounted for by lab studies, let alone that they are not also present for most other riders.

Full closure on the Froome case could include the release of the complete report in which WADA allegedly sets out its reasons for dropping the case. Froome could also release all of his urinary values obtained during the race. In any case, so long as the public is not given access to this information, very serious questions about the fairness of the decision will remain.

Contributor: Andy Smith

Endnotes

1. WADA clarifies facts regarding UCI decision on Christopher Froome, WADA, 11/07/2018
2. Schweizer et al. (2004) reported a runner who had extraordinarily high urinary level of salbutamol following a competition. This athlete submitted to a controlled study in the laboratory, in which 900 ug were inhaled, and still exceeded the limit by a large margin. Apparently this athlete was not studied further, though.
3. WADA will not appeal UCI decision in Christopher Froome case, WADA, 02/07/2018
4. UCI statement on anti-doping proceedings involving Mr Christopher Froome. UCI, 02/07/2018
5. La Gazzetta dello Sport, 15 December 2017
6. ‘10% of tests could be false positives’, Times, 07/07/2018
7. Tweet by @Swift__Girl, Twitter, 09/07/2018
8. 2016 Anti-doping testing figures, WADA, undated
9. World Anti-Doping Code, WADA, 01/04/2018
10. Commentary: The simplest explanation for Froome’s salbutamol test, F. Dreier, VeloNews, 17/01/2018

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