Supplemental Data Table 1

Mass transitions and expected retention time for each parameter.

Q1
(m/z) / Q3
(m/z) / Retention Time(min)
uAllo-Ile/uIle/uLeu/uNle / 132.1 / 86.1 / 5.51
EtN_IS / 202.2 / 113.1 / 4.07
EtN / 210.2 / 121.1 / 4.07
Gly_IS / 216.1 / 113.1 / 3.84
Gly / 224.1 / 121.1 / 3.84
Sar/bAla/Ala_IS / 230.2 / 113.1 / 4.58
Sar/bAla/Ala / 238.2 / 121.1 / 4.58
GABA/bAib/Abu_IS / 244.2 / 113.1 / 5.54
GABA/bAib/Abu / 252.2 / 121.1 / 5.54
Ser_IS / 246.2 / 113.1 / 3.61
Ser / 254.2 / 121.1 / 3.61
Pro_IS / 256.2 / 113.1 / 5.73
Pro / 264.2 / 121.1 / 5.73
Val/Nva_IS / 258.2 / 113.1 / 6.88
Val/Nva / 266.2 / 121.1 / 6.88
Thr_IS / 260.2 / 113.1 / 4.47
Thr / 268.2 / 121.1 / 4.47
Tau_IS / 266.1 / 113.1 / 2.83
Tau / 274.1 / 121.1 / 2.83
Hyp_IS / 272.1 / 113.1 / 3.76
Hyp / 280.1 / 121.1 / 3.76
Ile/Leu/Nle_IS / 272.2 / 113.1 / 8.01
Ile/Leu/Nle / 280.2 / 121.1 / 8.01
Asn_IS / 273.2 / 113.1 / 3.57
Asn / 281.2 / 121.1 / 3.57
Asp_IS / 274.2 / 113.1 / 3.95
Asp / 282.2 / 121.1 / 3.95
PEtN_IS / 282.1 / 113.1 / 2.75
PEtN / 290.1 / 121.1 / 2.75
Gln_IS / 287.2 / 113.1 / 3.94
Gln / 295.2 / 121.1 / 3.94
Glu_IS / 288.2 / 113.1 / 4.55
Glu / 296.2 / 121.1 / 4.55
Met_IS / 290.1 / 113.1 / 6.65
Met / 298.1 / 121.1 / 6.65
His_IS / 296.2 / 113.1 / 4.04
His / 304.2 / 121.1 / 4.04
Aad_IS / 302.2 / 113.1 / 5.4
Aad / 310.2 / 121.1 / 5.4
Phe_IS / 306.2 / 113.1 / 8.04
Phe / 314.2 / 121.1 / 8.04
1MHis/3MHis_IS / 310.2 / 113.1 / 4.39
1MHis/3MHis / 318.2 / 121.1 / 4.39
Arg_IS / 315.2 / 113.1 / 4.85
Arg / 323.2 / 121.1 / 4.85
Cit_IS / 316.2 / 113.1 / 4.42
Cit / 324.2 / 121.1 / 4.42
Tyr_IS / 322.2 / 113.1 / 6.98
Tyr / 330.2 / 121.1 / 6.98
PSer_IS / 326.1 / 113.1 / 2.46
PSer / 334.1 / 121.1 / 2.46
Hcit_IS / 330.2 / 113.1 / 5.3
Hcit / 338.2 / 121.1 / 5.3
Trp_IS / 345.2 / 113.1 / 8.6
Trp / 353.2 / 121.1 / 8.6
Car_IS / 367.2 / 113.1 / 4.71
Car / 375.2 / 121.1 / 4.71
Ans_IS / 381.2 / 113.1 / 4.87
Ans / 389.2 / 121.1 / 4.87
Orn_IS / 413.2 / 113.1 / 5.62
Orn / 429.2 / 121.1 / 5.62
Lys_IS / 427.3 / 113.1 / 5.97
Lys / 443.3 / 121.1 / 5.97
Asa_IS / 431.2 / 113.1 / 4.41
Asa / 439.2 / 121.1 / 4.41
Hyl_IS / 443.3 / 113.1 / 5.25
Hyl / 459.3 / 121.1 / 5.25
Cth_IS / 503.2 / 113.1 / 5.68
Cth / 519.2 / 121.1 / 5.68
Cys_IS / 521.2 / 113.1 / 5.76
Cys / 537.2 / 121.1 / 5.76
Hcy_IS / 549.2 / 113.1 / 6.99
Hcy / 565.2 / 121.1 / 6.99

Supplemental Data Table 2

Calculated LLOQ, based on the accuracy profile approach.

LLOQ
(µmol/L)
1MHis / 4.2
3MHis / 2.4
Aad / 4.1
Abu / 5.0
Ala / 18.4
Ans / 4.8
Arg / 7.5
Asn / 12.5
Asp / 8.9
bAib / 9.9
bAla / 265.4
Car / 4.7
Cit / 8.5
Cth / 7.4
Cys / 13.5
EtN / 10.0
GABA / 3.2
Gln / 4.5
Glu / 5.3
Gly / 32.3
Hcy / 10.0
His / 14.8
Hyl / 9.3
Hyp / 4.1
Ile / 4.8
Leu / 11.5
Lys / 11.4
Met / 3.1
Orn / 19.4
PEtN / 19.2
Phe / 4.8
Pro / 5.0
PSer / 4.5
Sar / 3.1
Ser / 47.7
Tau / 15.7
Thr / 16.4
Trp / 9.8
Tyr / 5.4
Val / 14.9

Supplemental Data Statistic

Total error

Total error (TE) is the simultaneous combination of systematic and random error. Systematic error is measured by a bias () and random error by a variance .

1.

β-Expectation Tolerance interval

Tolerance intervals are intervals that contain a proportion β of the individual values, such as results, of the population (e.g. 0.95). These intervals allow to describe the entire population. The following formula describes a β-expectation tolerance interval:

2.

where

  • Qt(ν;θ) is the θth percentile of a Student Qt(ν) distribution;
  • n: number of replicates per run (p runs)
  • is the run-to-run variance, and is the within-run or repeatability variance.The overall variability of the analytical method is measured by the intermediate precision variance: .

Measurement Uncertainty

The measurement uncertainty of a result x is estimated by:

3.

where is the estimated intermediate precision standard deviation and is the uncertainty associated with the estimator of the bias δ of the method (expressed in term of standard error). can be estimated as:

4.

where with being an estimate of the repeatability variance.

Dosing Range Index

The dosing range (DR) is the length of the interval in which the method is valid. This dosing range is obtained by calculating the difference between the upper and the lower limits of quantitation. The Dosing Range Index is a dimensionless value varying in [0,1] expressing how much was achieved between the maximum and the minimum, 1 being the best value indicating that the procedure is able to quantify over the whole range envisaged. It's computed as follows:

whereCmaxand Cmin are the highest and the lowest concentrations

Remark: if only one level of concentration is introduced, the Dosing Range index is fixed to 0 or 1.

Precision Index

The precision area corresponds to the area, within the limits of quantitation, between the lower bounds and the upper bounds of the Accuracy Profile. This area is calculated by the trapezoidal rule. The Precision Index is a dimensionless value varying in [0,1] expressing how much was achieved between the maximum and the minimum possible, 1 being the best value and 0 the worst. It's computed as follows:

whereCmax and Cmin are the highest and the lowest concentration, CA is the concentration introduced where the limit1 stops and the limits2 starts, λ1 is the limit1 and λ2 the limit2, area1 corresponds to the area linked to the limit1 and area2 correspond to the area linked to the limit2.

Trueness Index

The sum of square biases (SSB) is calculated as the sum of the squares of the biases estimated at each concentration level. The Trueness Index is a dimensionless value varying in [0,1] expressing how much was achieved between the maximum and the minimum possible, 1 being the maximal and optimal value obtained when no bias is observed. It's computed as following:

where λ1 and λ2 are the accuracy acceptance limits and m1 is the number of concentration levels linked to λ1, m2 is the number of concentration levels linked to λ2.

Computation of the Accuracy Profile

An accuracy profile is obtained by linking on one hand the lower bounds and on the other hand the upper bounds of the β-expectation tolerance intervals calculated at each concentration level. The formula to compute these β-expectation tolerance intervals is:

where

and

andare the estimates of the between-series and within-series variances, respectively;

is the β quantile of the Student's distribution with  degrees of freedom;

is the Satterthwaite's approximation of the degrees of freedom; where

R is the ratio of the between-series over the within-series variance;

p is the number of series and n the number of repetitions per series.

When the design is not balanced, i.e. not the same number of repetition for all series, then n is estimated by the average number of repetitions.

is the estimate of the intermediate precision standard deviation (SD).

The method is considered as valid within the range for which the accuracy profile is within the accuracy acceptance limits.

Risk calculation

The risk of having measurements outside the Acceptance limits is directly derived from the above Tolerance Interval, using the same estimates and t distribution in a different manner, i.e. by computing the probability to be above the upper Acceptance limit plus the probability of being below the lower Acceptance limit instead of computing the interval where it is expected to observe β% of the future measurements.

The probability to have measurements outside the Acceptance limit can be expressed as follows:

where

Xi is the individual result,μT is the considered true value,

p is the number of series and n the number of repetitions per series,

λ is the acceptance limit,

is the Satterthwaite's approximation of the degrees of freedom,

RSDIP is the relative Standard Deviation of the Intermediate Precision.

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