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Horwitz Ratio (HorRat)

Horwitz Ratio (HorRat). as an extended criterion for the assessment of the reproducibility in collaborative trials. Dr. Michael Haustein (on behalf of DAPA) CURRENTA GmbH & Co. OHG Analytics 41538 Dormagen, Germany www.analytik.currenta.de. The Horwitz Equation.

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Horwitz Ratio (HorRat)

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  1. Horwitz Ratio (HorRat) as an extended criterion for the assessment of the reproducibility in collaborative trials Dr. Michael Haustein (on behalf of DAPA) CURRENTA GmbH & Co. OHG Analytics 41538 Dormagen, Germany www.analytik.currenta.de

  2. The Horwitz Equation • In the 1980‘s Horwitz et al. published a relationshipbetweentheprecisionof an analyticalmethodandtheconcentrationoftheanalyteaccordingtothefollowingequation [1]: • Predicted RSDR = 2 (1-0.5 log C) % (empiricallyset) • WithRSDR isthe relative standarddeviation (= coefficientofvariation, CV) underreproducibilityconditions (R)C istheconcentrationoftheanalyteexpressedas a dimensionlessmassfraction • Conclusions: • The RSDRappearsonlytobedependent on theconcentrationandnot on thenatureoftheanalyte, thetest material ortheanalyticaltestmethod/technique • The RSDR increasesby a factoroftwoastheconcentrationoftheanalytedecreasesovertwoordersofmagnitude. So at 100 % concentrationofanalytethe RSDRisabout 2 %, at 1 % itisabout 4 % and at 0.01 % (100 ppm) itisabout8 % ( HorwitzTrumpet) [1] W. Horwitz, L.R. Kamps, K.W. Boyer, J. Assoc. Off. Chem., 63, 1344 (1980)

  3. The Horwitz Trumpet

  4. Horwitz Ratio (HorRat) • Equation: • withRSDR is the reproducibility obtained from the collaborative trialPRSDR is the predicted reproducibility obtained from the Horwitz equation • Translation:HorRat < 1: RSDR of the method is below the predicted valueHorRat = 1: RSDR of the method is equal to the predicted valueHorRat > 1: RSDR of the method exceeds the predicted value

  5. HorRat as a benchmark criterion ? • If HorRat is >> 1, the analytical method is undoubtedly suspect to perform worse than expected/hoped (e.g. due to method deficiencies or due to interferences, contaminations or sample inhomegeneity) • If HorRat is << 1, suspect comes out that the collaborative trial was not performed correctly and it gives precision values that are too optimistic (e.g. due to less participants or prior knowledge of analyte content) • If HorRat is close to 1, method precision in terms of reproducibility is close to the predicted value • Which HorRat value/range is suitable as a performance benchmark ?

  6. DAPA proposal/recommendation

  7. The End……. Thank you for your kind attention

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