USE OF THE SAS VARCOMP PROCEDURE TO ESTIMATE ANALYTICAL REPEATABILITY. Anna Caroli Istituto di Zootecnica Veterinaria - Milano - Italy

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1 INTRODUCTION USE OF THE SAS VARCOMP PROCEDURE TO ESTIMATE ANALYTICAL REPEATABILITY Anna Caroli Istituto di Zootecnica Veterinaria - Milano - Italy Researchers often have to assess if an analytical method is repeatable in the same experimental conditions (analytical repeatability) and if it is reproducible among different laboratories (analytical reproducibility). The analysis of the components of variance is a powerful tool in order to achieve this information. Reproducibility and repeatability coefficients, indicating respectively the probability for an analytical measure to be reproduced among different laboratories or repeated within laboratories, can be easily calculated by the SAS Varcomp Procedure (SAS/STAT). For the reproducibility evaluation, the following mixed model can be used: y ijk = µ + trial i + + where: µ is the overall mean; y ijk is the k -th analytical parameter; trial i is the fixed effect of the i -th trial; is the random effect of the j -th referee sample; ε ijk is the residual error. The reproducibility coefficient among laboratories is then calculated by the ratio: ε ijk R = sample + j error ijkl For the repeatability evaluation, the following mixed model can be used: y ijkl = µ + trial i + + ε ijkl where: µ is the overall mean; y ijkl is the l -th analytical parameter; trial i is the fixed effect of the i -th trial; is the random effect of the j -th referee sample within the k -th laboratory; ε ijkl is the residual error. The repeatability coefficient within laboratories is then calculated by the ratio:

2 r = sample jk + error ijkl The models can be obviously simplified if there is no diffent trial factor, by eliminating this effect from both of them.

3 AN EXAMPLE Milk rennet clotting aptidude can be evaluated by the lactodynamographic analysis. In the following study, the rennet clotting time (RCT) of four individual milk samples is evaluated in two different laboratories during two sequencial trials. In the following box, the SAS program used to calculate the repeatability and reproducibility coefficients is reported. BOX 1: SAS PROGRAM data milk; input sample lab $ trial cards; 1 A A A 10 1 A 9 1 B B B 13 1 B 14 A 1 0 A 1 A 19 A 18 B 1 B 1 B 0 B 0 3 A A A 6 3 A 6 3 B B B 8 3 B 8 4 A A A 14 4 A 13 4 B B B 16 4 B 16 ; /******************************************************************** ********* 1) MODEL FOR REPRODUCIBILITY COEFFICIENT EVALUATION (AMONG LABORATORIES) ********************************************************************* *********/ proc varcomp method = reml; class trial sample; model rct = trial sample / fixed = 1; run; /******************************************************************** ********* ) MODEL FOR REPEATABILITY COEFFICIENT EVALUATION (WITHIN LABORATORIES) ********************************************************************* *********/ proc varcomp method = reml; class trial lab sample; model rct = trial sample(lab) / fixed = 1; run;

4 In the following box, the output of the first varcomp procedure is reported: BOX : OUTPUT OF THE MODEL FOR REPRODUCIBILITY COEFFICIENT EVALUATION (AMONG LABORATORIES) Variance Components Estimation Procedure Class Level Information Class Levels Values TRIAL 1 SAMPLE Number of observations in data set = 3 Restricted Maximum Likelihood Variance Components Estimation Procedure Dependent Variable: RCT Iteration Objective Var(SAMPLE) Var(Error) Convergence criteria met. Asymptotic Covariance Matrix of Estimates Var(SAMPLE) Var(Error) Var(SAMPLE) Var(Error) The reproducibility coefficient among laboratories is then calculated by the ratio: R = sample + j error ijkl = = (93%)

5 In the following box, the output of the second varcomp procedure is reported: BOX 3: OUTPUT OF THE MODEL FOR REPEATABILITY COEFFICIENT EVALUATION (WITHIN LABORATORIES) Variance Components Estimation Procedure Class Level Information Class Levels Values TRIAL 1 LAB A B SAMPLE Number of observations in data set = 3 Restricted Maximum Likelihood Variance Components Estimation Procedure Dependent Variable: RCT Iteration Objective Var(SAMPLE (LAB)) Var(Error) Convergence criteria met. Asymptotic Covariance Matrix of Estimates Var(SAMPLE (LAB)) Var(Error) Var(SAMPLE(LAB)) Var(Error) The repeatability coefficient within laboratories is then calculated by the ratio: r = sample jk + error ijkl = = (98%) References: SAS Institute Inc. SAS/STAT User s Guide, Release 6.03 Edition, Cary, NC: SAS Insitute Inc., 1988, 108 pp. Anna Caroli Istituto di Zootecnica Veterinaria Via Trentacoste, 0134 Milano - Italy