I had a chance to look at those five studies a little more closely, considering only the samples that were analyzed four hours (or earlier) after inhaling 800 ug. Only 3/168 subjects were > 1000, and only one, corrected for USG, was > 1200 ng/ml. Also, two of the studies reported samples at earlier times, including 30 minutes (8 samples, none > 1000); 1 hour (40 samples, none > 1000); and two hours (40 samples, one USG-corrected sample was > 1200). So 1/88 samples > 1000 and > 1200.
Heuberger et al. say their model predicts 15% of samples > 1000 at one hour, and 3% > 1000 at four hours. The only empirical evidence they cite is one study in which 1/28 samples was > 1000, close to their 3% prediction. But in the much larger sample size* of five studies I looked at—which includes the one Heuberger et al referred to plus four others—less than 2% of the samples were > 1000, and about half of the samples in this pool were taken at two hours or sooner, which should have increased the proportion > 1000. Particularly damning are the 48 samples taken at one hour or earlier. If the predicted proportion > 1000 is 15%, it’s highly improbable that 0/48 by chance would be > 1000.
*The effective sample size is even larger than I've indicated, because for many samples, two values are reported--uncorrected and corrected for USG. I count these two values as corresponding to one sample.
Elers1:
http://sci-hub.tw/10.1249/MSS.0b013e3181b2e87dElers2:
http://sci-hub.tw/10.1097/JSM.0b013e31823513e1Mareck:
http://sci-hub.tw/10.1002/dta.367Dickinson:
http://sci-hub.tw/10.1097/jsm.0000000000000072Sporer:
http://sci-hub.tw/10.1097/JSM.0b013e3181705c8cEveryone has pointed out that this is just a theoretical model, but there’s another very important point that’s generally missed. Their case is based on the conclusion that the concentration of salbutamol in the urine reaches a peak very fast—within thirty minutes to an hour. They don’t say this, or at least emphasize it, but most of the empirical salbutamol studies are based on longer times before the urine sample is taken—four hours or more.
This is critical, because it allows them to make this claim of 15% over the threshold without an apparent contradiction with the empirical data. They’re implying the reason most studies don’t show many samples > 1000 is because they don’t take the samples early enough. But as I’ve just shown, there are enough data at these earlier times to call into serious question this premise.
These other studies do support Heuberger’s conclusion that urine level of salbutamol peaks at about one hour after inhalation, but it doesn’t appear to drop dramatically between then and four hours. The Sporer paper reports that the mean urine concentration at 2 hours is 70-80% that at one hour, a difference that is not significant.
A generally similar decrease of mean values was found from 1.5 to 4 hr in the Haase study, which was the one supplying some of the data Heuberger et al used to construct their model. Haase et al tested inhalation of 1600 ug only. In that study, more samples > 1000 were generally found at 1.5 hr than 4 hr, but the difference was not that great. Across all three conditions, and including corrected and uncorrected values, there was a total of 28 samples > 1000 at 1.5 hr vs. 23 at 4 hr. Using the 1200 ng/ml DL, it was 21 vs. 18. This is not consistent with Heuberger et al's prediction that the proportion of samples > 1000 after 1 hr is five times that at four hr. (N.B.: The Haase values are take from Table 2 of their paper; the same values are nominally included in Fig. 2, but several of them are wrong, as easily can be seen by counting the number of points above the threshold line; I don't know how this got past the reviewers).
Haase:
http://sci-hub.tw/10.1002/dta.1828