Tuesday, November 13, 2007

Probabilities

by Ali and TBV

After thinking about the many metabolites of methyl' and dexa', we asked ourselves how likely was it that they might elute in regions that could cause problems.

The familiar USADA 349, Landis B sample F3

We poked at this two ways, a Monte Carlo simulation, and analytically. We assumed 19 metabolites that are free to co-elute with each other, in the 882 seconds between 800 and 1682 seconds, with a uniform distribution. This encompasses the IS to the bumps past the ostensible Pdiols.

The Monte Carlo method made a sheet of 19 columns and 1000 rows, and placed a random value in the range in each cell. The result was around a 0.5 probability of one co-eluting between the start of the 5bA and the end of the 5aA, being the 34 seconds between 1326 and 1360.

The analytic approach yielded:

Probability of peak NOT occurring in range of interest is

(882-34)/882.

Probability of all 19 peaks NOT occurring in range of interest

((882-34)/882)^19.

So the probability of one or more occuring in range of interest is

1-((882-34)/882)^19 = 0.526

In English, there seems to be a 52% chance there is co-elution of at least one of the metabolites of the TUE'd medication showing up in a region likely to conflict with the measured peaks.

These are first guesses, but more or less agree. We appreciate correction and feedback.

6 comments:

Mike Solberg said...

Hmmm. Questions:

Why 19? Why not 22? Two main substances that can come out intact, and 20 metabolites (four from dexa' and 16 from methyl').

How sure are we that 800 to 1682 is the full range over which these compounds could elute. I guess 800 is legit, because nothing elutes before that, right? But do we know that nothing would elute after 1682 if they kept the machine going?

Why pick those 34 seconds? Wouldn't you have to narrow it down to just a small number of seconds specifically around the peaks of interest?

Statistics is not my thing!

syi

Ali said...

You could certainly change the values if you wished. If the range was from 800 s to 2000 s and you had 22 peaks, that would give a 46.8% chance (using method described above, with 34 s). Personally, I'd leave it at 34 s. As things stand, the 5B and 5a peaks appear to interfere with each other. I believe that anything appearing within or between these peaks could influence the results for both.

Always open to correction of course.

m said...

TBV,

Computer scientists shouldn't do biology. GIGO, garbage in garbage out.

OMJ admits the possibility of a substance hidden under the 5A or 5B peak. What does your simulation add. Nothing, because your assumptions are arbitrary.

1. There is 34 seconds between the 5A and 5B, or 3.85% of the total 880 seconds.

2. How can you assume that all 19 of the cortisone metabolites will elute in the F3 fraction between 800 seconds and 1600 seconds. Why not some in the F2 or F1, why not none in any. We don't know.

3. More importantly, so what if some unidentified substance elutes between the 5A and 5B. If noise and evenly distributed then no problem it doesn't affect the carbon rations per both Meier (slide 16 bottom left and middle) and Brenna. If a peak, we already have exactly such a peak in Landis' F3 GCMS (which disappears in the F3 GC-IRMS) and the Shackleton chromatograph. Shackleton found no problem in his. Meier tried to claim it would bias the 5A to a higher delta, but Brenna showed it would be exactly the reverse, a lower delta.

4. Finally your modeling is incorrect, assuming you are claiming the unidentified substance elutes as a peak rather than eluting evenly as noise. The unidentified substance peak has to have some width, i.e. in the F3 the 5A and 5B peaks were said to be 20 seconds wide. You are assuming the unidentified peak is 1 second wide, so has 34 out of 882 chances of landing within the target zone. But if you assume the unidentified substance peak is 20 seconds wide, you have at most 14 out of 880 chances of landing completely within the 34 second gap and perhaps less depending on what assumptions you want to make. This is all moot anyway, because if the peak eluted between the 5A and 5B you should be able to see it. And in fact we do see it as I noted in 3 above. It's just that Meier, Brenna, and Shackleton say it doesn't affect the carbon values.

tbv@trustbut.com said...

What this adds is some quantitative modeling to the probability of known 'stuff'. We can debate the accuracy of the model.

1. Not a point of dispute?

2. Good point. Probably conservative to divide by 3 until something more is known about the selectivity of the fractionation. That's a good argument.

Similarly, one could arguably stretch it out to 1800s, but that is not much different at this scale, affecting the result by around 20%. At this level of accuracy, probably not critical.

3 Is there any reason to believe a substance elutes as noise? I don't believe so; I think if it elutes at all with any structure it will form a peak. I don't think the noise argument goes anywhere.

Similarly, I've already addressed Brenna's testimony, which I do not believe addresses third-peak substances as well as you do. We'll agree to disagree on this, I think.

4 First, a peak has a center; we're modeling whether the center of one of these new peaks might lands in the region of interest. If it co-eluted in the gap region, it is an open question whether you would see it; the only way to really know would be to have the full-scan mass-spectra and look for anomalies.

TBV

tbv@trustbut.com said...

Mike,

19 instead of 22 because we can't count and miscommunicated. Since it's an error on the conservative side, we didn't think it worth fixing.

TBV

Ali said...

m,

Regarding you 9:24 comment, I don't believe anything I've been involved with could be described as anything more than mathematical modelling. It's not biology. What we did was described in detail, along with the assumptions made. Constructive criticism is always welcomed. I see nothing constructive in describing it as garbage. If you have knowledge of how these other 20 or so other metabolites behave, then we'd be more than happy to modify any modelling done to reflect that ... ?

Your 3) refers to diagrams which show two peaks so close that their tails touch (as with the 5b/5a peaks). I'd appreciate you describing how you could squeeze a third peak between them without it also being within them ?. I wasn't under the impression that everyone agreed that co-eluting peaks do not influence each other.

Your 4) has already been addressed, but perhaps assuming that something is incorrect simply because it is not understood is not the first step that the enquiring mind should take. I'm always asking questions when I don't understand things. A reluctance to question, for whatever reason, is an impediment to learning.

Ali