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1 From the analytical uncertainty to uncertainty in data interpretation D. Concordet, J.P. Braun d.concordet@envt.fr jp.braun@envt.fr

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2 Biological data vary according several sources of variations Biological - species - status (healthy, sick) - breed - format, age... - inter-individual - intra-individual Metrological - intra- laboratory variations (imprecision) - inter-laboratories variations (bias) controlledof interest not controlled parasitic

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3 Influence of imprecision on the reference interval Pl-creatinine ( mol/L) Population distribution of Pl-Creatinine of healthy dogs

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4 Influence of imprecision on the reference interval Pl-creatinine ( mol/L) Population distribution of Pl-Creatinine of healthy dogs Y = X + with E (

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5 Influence of imprecision on the reference interval Pl-creatinine ( mol/L) Population distribution of Pl-Creatinine of healthy dogs Y = X + with E (

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6 Sampling variations of the reference interval 95% CI of the reference interval Pl-creatinine ( mol/L) N=100 dogs CV=0% CV=10%CV=20%

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7 Use of reference interval Pl-creatinine ( mol/L) 40 135 Effect of large imprecision

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8 Use of reference interval Pl-creatinine ( mol/L) 40 135 When the precision is better

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9 Replicates decrease the influence of imprecision Y 1 = X + Y 2 = X + with E ( i SD(Y i )= SD( i Y p = X + p CV(Y i ) = 20 % pCV(Y) 214.1% 311.5% 410.0%

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10 Influence of inter laboratories variability on the reference interval Pl-creatinine ( mol/L)

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11 Influence of inter laboratories variability on the reference interval Pl-creatinine ( mol/L)

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12 Influence of inter laboratories variability on the reference interval Pl-creatinine ( mol/L)

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13 Reference range of Pl-creatinine 11 books of animal clinical biochemistry 0 25 50 75 100 125 150 175 200 225 250 Pl-Creatinine (µmol/l) [2] [6] [7] [8] [27] [28] [34] [45] [46] [55] [59] Lefebvre HP et al. 1998. 35 µmol/l 245 µmol/l Reference number

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14 A “demographic” source of variation GFR value GFR (mL/kg/min) Mean SD 886 GFR value depends on breed Lefebvre HP unpublished results

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15 Influence of the population’s structure 130 Pl-creatinine ( mol/L)

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16 Influence of the population’s structure 210 Pl-creatinine ( mol/L)

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17 Influence of multiplicity : case of independence Pl-creatinine ( mol/L) 40 135 40 95% of healthy animals 90% of healthy animals

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18 Imprecision and multiplicity Pl-creatinine ( mol/L) 40 135 40

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19 Imprecision and multiplicity Pl-creatinine ( mol/L) 40 135 40 CV= 15 % 82 % of healthy animals CV = 15% 93% of healthy animals

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20 Diagnostic tests : a better way to proceed Diseased animals Without the disease Threshold Considered as sick Pl-creatinine ( mol/L) Considered as healthy Sensitivity :Se Specificity :Sp

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21 Performances of the test Sensitivity = Se % of diseased animals with a result > threshold Specificity = Sp % of animals without the disease with a result < threshold

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22 Several definitions of specificity Specificity = Sp Sp1 :% of healthy animals with a result < threshold Sp2 :% of animals without the disease (healthy + with any other disease) with a result < threshold

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23 Several definitions of specificity Healthy animals Sp1 Threshold Healthy animals + with other diseases Sp2 Sp2<<Sp1

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24 The operational indices : the predictive values Positive Predictive Value (PPV) : Probability that the animal has the disease when its result >threshold Negative Predictive Value (NPV) : Probability that the animal has not the disease when the result < threshold

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25 The clinician experience : Pr Pr = Pre-test probability probability that the animal has the disease Pr = 1 : The clinician is sure that the animal has the disease Pr = 0 : The clinician is sure that the animal has not the disease PPV =1 NPV =0 whatever Se and Sp PPV =0 NPV =1 whatever Se and Sp Positive diagnostic gain : PPV-Pr Negative diagnostic gain : NPV-(1-Pr) Pr = 0.5 : The clinician does not know (coin tossing)

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26 Sp = 80% Influence of imprecision Threshold Pl-creatinine ( mol/L) Se = 92% Sp = 73% CV = 15 % Se = 81% CV = 15%

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27 Consequences on interpretation Pre-test probability PPV/NPV

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28 Sampling variations of sensitivity and specificity Sample size : n 95% confidence interval of Se=0.92, Sp=0.80 Se = 0.92 Sp = 0.80 95% confidence interval of Se/ Sp :

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29 Consequences on interpretation 95% confidence interval of PPV/NPV Pre-test probability N=50

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30 Consequences on interpretation 95% confidence interval of PPV/NPV Pre-test probability N=100

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31 Consequences on interpretation 95% confidence interval of PPV/NPV Pre-test probability N=300

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32 Effects of the biological sources of variation Increase the overall dispersion of the results Improvement possible if Se and Sp are determined for each level of the factors of variation (e.g. breed) decrease Se and Sp decrease PPV and NPV for a fixed pre-test proba

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33 The future ? Individualisation Blood sample when the animal is young and healthy Follow-up of the evolution of the appropriate marker Critical difference Independent of demographic factors (breed, sex…) dependent only on intra-individual variability analytical errors

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34 The end

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