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

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

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

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

4. Influence of imprecision on the reference interval Y = X + e with E (e) = 0 Pl-creatinine (mmol/L) Population distribution of Pl-Creatinine of healthy dogs

5. Influence of imprecision on the reference interval Y = X + e with E (e) = 0 Pl-creatinine (mmol/L) Population distribution of Pl-Creatinine of healthy dogs

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

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

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

9. p CV(Y) 2 14.1% 3 11.5% 4 10.0% Replicates decrease the influence of imprecision Y1 = X + e1 with E (ei) = 0 SD(Yi)= SD(ei) = s Y2 = X + e2 Yp = X + ep CV(Yi) = 20 %

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

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

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

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

14. GFR value A “demographic” source of variation GFR value depends on breed GFR (mL/kg/min) Mean  SD 8 8 6 Lefebvre HP unpublished results

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

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

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

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

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

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

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

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

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

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

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

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

27. Consequences on interpretation PPV/NPV Pre-test probability

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

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

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

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

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

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

34. The end