You3 does some 'splaining

In this post by You3 at DPF, we get the start of an understanding of the impact of background subtraction, along with a summary of the important parts of the defense as presented:

I think that the Landis defense was pretty clear that they assert that there was an error in the analysis.

The defense lawyers presented evidence that

1) the analysis failed to conform to various International Labratory Standards,
2) the analysis failed to conform to the IRMS equipment manufacturer's specifications,
3) the documentation on what algorithms are implemented for background estimation and subtraction by the IRMS machine no longer exist
4) the operators and their supervisor were not trained by the IRMS manufacturer or someone qualified by the manufacturer
5) the executed process was not documented sufficiently to be reviewable or repeatable,
6) there were no controls in place to establish or validate the accuracy of background/baseline subtraction for complicated urine matrixes
7) there were no IRMS calibration samples for 3 of the 6 metabolites
8) there were no SOPs in place to specify the process for the placement of integration limits.

[more]


From here on out, we're starting to get into the deep end.

I don’t think this forum [DPF] has done much exploring the process of background subtraction and the nature of the potential errors that might occur. As far as I could tell, the Isoprime1 software allows the specification of some number of points that are believed to lie on the the background baseline curve. The software then interpolates a curve between the points and considers this the background baseline 12C height. Further, it must interpolate the d13C values along the line between the points. This, in effect, establishes a 13C height curve, but the height is 2 orders of magnitude smaller than the 12C curve. To the extent that the reference points are further apart or the actual background baseline is more complicated, the more prone to error will be the estimate of the curves.

The testimony from Davis was that no one knows anymore what algorithms are used by the IsoPrime1 OS2 software to do the interpolation of the 12C background baseline height or the d13C values along that line. Anyone who has drawn smooth curves with reference points in PowerPoint or any other drawing program knows that unexpected twists in the curve can occur as points are specified. The IsoPrime1 operator could view baseline curve and the effect of the baseline curve on the m/z 45/44 ratio plot. But, there was not indicatation that the user interface provided explicit information as to the quality of the fit of the curve, although it did provide the d13C measurements of the peaks after background subtraction.

Let’s look at how sensitive the d13C measurement is to accurate background baseline subtraction. It turns out that the smaller the elute peak and the larger the background contribution, the more sensitive the measurement is to errors in the background measurement. By my estimate, the sample B 5a-diol (USADA0350) measurement is 4 times more sensitive to background measurement error than the 5b-diol measurement in “Mix Cal Acetate 001A-100ng ing” (USADA362). Error is also more likely because the background curve is complex and there appears to be co-elution in the neighborhood of the 5a-diol peak. This differing sensitivity to error between MixCal and urine samples tends to undercut the assertion that the MixCal analysis establishes linearity of measurement since the measurement of background ratios would tend to stress the linearity of absolute measurements of m/z 45 and 44 quantities. In particular, the background has the lowest currents (abundance), but the measurement must still be accurate.

The background area underneath an elute is not documented in the LDP. In order to estimate the area, I assume the elute peak is a Gaussian curve. From the area and the height, the standard deviation can be calculated. I then estimate the width of the peak as 6 standard deviations. I estimate the height of the background contribution from looking at the plots on USADA0349 and USADA0363. Then, I calculate the area of the background as the product of that height and the width of the elute peak.

The table below captures the characterization of the two peaks:
(edit: Note, I take the reported area to reflect just the elute, not inclusive of the background. I can't be certain this is correct. By examination of the plots, the height includes background.)

                    5a-diol        5b-diol
                    Landis B/F3    MixCal
Values from the LDP:
Elute d13C:           -31.88         -33.63
Raw peak height:        2.33e-09       3.28e-09
Elute 12C area:         2.1502e-08     2.7273e-08
Background d13C:      -56.94         -77.27

Estimates:
Background height:      5.0098e-10    2.0077e-10

Calculated values:
Elute std dev           4.69          3.53
Percent raw 12C
area elute:            60.4%         86.5%
Percentage raw 12C
area background:       39.6%         13.5%
13C/12C ratio:          1.087896e-02  1.085929e-02
Elute 13C area:         2.3392e-10    2.9617e-10
Elute width:            28.1         21.2
Elute height:            1.83e-09     3.0792e-09
Raw peak d13C:         -41.80       -39.52
Raw peak 13C/12C:        1.076744e-02 1.079309e-02
Raw peak 12C area:       1.4097e-08   4.2565e-09
Raw peak 13C area:       1.4939e-10   4.4135e-11

I can now calculate the amount of background 13C that needs to be attributed to the elute peak, instead of the background, in order raise the d13C measure of the peak by 3 delta units. The Landis 5a-diol needs to change attribution of 0.48% of the background 13C, while the MixCal 5b-diol needs to change by more than 4 times more at 2.01%. Note that the background d13C measure for the Landis 5a-diol is still in line with that of the blank sample analysis at -64.54.

If the background subtraction for the Landis sample was in error, attributing 0.48% too much 13C to the background, then a d13C measure that was 3.00 delta units too negative would result. Did this happen?

                    5a-diol            5b-diol
                    Landis B/F3        MixCal
Percentage of
background 13C
re-attbributed to
elute:                 0.48%             2.01%  
Percentage of
elute & bkg 13C:       0.190%            0.271%
New elute 13C area:    2.3465e-10        2.9709e-10
New elute 13C/12C:     1.091283e-02      1.089311e-02
New elute d13C:      -28.87            -30.62
Delta change:          3.01              3.01
New bkg ratio:         1.054569e-02      1.015224e-02
New bkg d13C:        -64.54            -96.55

Lastly, I calculate the percentage of background 13C that needs to be attributed to the elute in MixCal analysis in order to generate a 0.5 delta error, such that the error would be at the edge of the margin of uncertainty. When this percentage of re-attribution is applied to the Landis sample a delta change of 2.01 occurs, an error more than 4 times larger.

                      5a-diol               5b-diol
                      Landis B/F3           MixCal
Percentage of
background 13C
re-attbributed to
elute:                  0.3341%               0.3341%
Percentage of
elute & bkg 13C:        0.1323%               0.0451%
New elute 13C area:     2.3443e-10            2.9632e-10
New elute 13C/12C:      1.090254e-02          1.086492e-02
New elute d13C:       -29.78                -33.13
Delta change:           2.10                  0.50
New bkg ratio:          1.056138e-02          1.033284e-02
New bkg d13C:         -60.14                -80.48

This analysis does not consider the contribution of oxygen isotopes to the errors. The background curve interpolation actually needs to interpolate a baseline value for all three detected ions. Around 7% of the m/z 45 ions are actually oxygen isotopes, not 13C. The contribution of the oxygen isotopes is calucated from the abundance of m/z 46 ions.

Any error that creates a more negative measurement is amplified by a reduced derivitization ion correction. An error of -3.0 delta units will generate a larger error in the corrected value.