Uncertainty Evaluation for the Quantification of Urinary Amphetamine and 4-Hydroxyamphetamine Using Liquid Chromatography–Tandem Mass Spectrometry: Comparison of the Guide to the Expression of Uncertainty in Measurement Approach and the Monte Carlo Method with R

Estimating the measurement uncertainty (MU) is becoming increasingly mandatory in analytical toxicology. This study evaluates the uncertainty in the quantitative determination of urinary amphetamine (AP) and 4-hydroxyamphetamine (4HA) using a liquid chromatography–tandem mass spectrometry (LC–MS/MS) method based on the dilute-and-shoot approach. Urine sample dilution, preparation of calibrators, calibration curve, and method repeatability were identified as the sources of uncertainty. To evaluate the MU, the Guide to the Expression of Uncertainty in Measurement (GUM) approach and the Monte Carlo method (MCM) were compared using the R programming language. The MCM afforded a smaller coverage interval for both AP (94.83, 104.74) and 4HA (10.52, 12.14) than that produced by the GUM (AP (92.06, 107.41) and 4HA (10.21, 12.45)). The GUM approach offers an underestimated coverage interval for Type A evaluation, whereas the MCM provides an exact coverage interval under an abnormal probability distribution of the measurand. The MCM is useful in complex settings where the measurand is combined with numerous distributions because it is generated from the uncertainties of input quantities based on the propagation of the distribution. Therefore, the MCM is more practical than the GUM for evaluating the MU of urinary AP and 4HA concentrations using LC–MS/MS.