Comptes Rendus
Statistique
Plans dʼexpérience pour lʼestimation de la courbe de concentration et de lʼAUC
Comptes Rendus. Mathématique, Volume 350 (2012) no. 13-14, pp. 707-710.

Le problème dʼintérêt est dʼestimer la fonction de concentration et lʼaire sous la courbe (AUC) à travers lʼestimation des paramètres dʼun modèle de régression linéaire avec un processus dʼerreur autocorrélé. On introduit un estimateur linéaire sans biais simple et non paramétrique de la courbe de concentration et de lʼAUC. On montre que cet estimateur construit à partir dʼun plan dʼéchantillonnage régulier approprié est asymptotiquement optimal.

The problem of interest is to estimate the concentration curve and the area under the curve (AUC) by estimating the parameters of a linear regression model with autocorrelated error process. We introduce a simple linear nonparametric unbiased estimator of the concentration curve and the AUC. We show that this estimator constructed from an appropriate regular sampling design is asymptotically optimal.

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DOI : 10.1016/j.crma.2012.07.013

Mohamad Belouni 1 ; Karim Benhenni 2

1 Laboratoire Jean-Kuntzmann (UMR CNRS 5224), université Joseph-Fourier, BP 53, 38041 Grenoble cedex 09, France
2 Laboratoire Jean-Kuntzmann (UMR CNRS 5224), université Pierre-Mendes-France, BP 47, 38040 Grenoble cedex 09, France
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Mohamad Belouni; Karim Benhenni. Plans dʼexpérience pour lʼestimation de la courbe de concentration et de lʼAUC. Comptes Rendus. Mathématique, Volume 350 (2012) no. 13-14, pp. 707-710. doi : 10.1016/j.crma.2012.07.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.07.013/

[1] A.C. Atkinson; K. Chaloner; A.M. Herzberg; J. Juritz Optimum experimental designs for properties of a compartmental model, Biometrics, Volume 49 (1993), pp. 325-337

[2] A.J. Bailer; W.W. Piegorsch Estimating integrals using quadrature methods with an application in pharmacokinetics, Biometrics, Volume 46 (1990) no. 4, pp. 1201-1211

[3] K. Benhenni; S. Cambanis Sampling designs for estimating integrals of stochastic processes, Annals of Statistics, Volume 20 (1992), pp. 161-194

[4] S. Cambanis Sampling designs for time series (E.J. Hannan; P.R. Krishnaiah; M.M. Rao, eds.), Handbook of Statistics, Time Series in Time Domain, vol. 5, North-Holland, Amsterdam, 1985, pp. 337-362

[5] S.B. Duffull; S. Retout; F. Mentré The use of simulated annealing for finding optimal population designs, Computer Methods and Programs in Biomedicine, Volume 69 (2002), pp. 25-35

[6] B. Jones; J. Wang Constructing optimal designs for fitting pharmacokinetic models, Statistics and Computing, Volume 9 (1999), pp. 209-218

[7] D. Katz; D.Z. DʼArgenio Experimental design for estimating integrals by numerical quadrature with applications to pharmacokinetic systems, Biometrics, Volume 39 (1983), pp. 621-628

[8] F.H. Kong; R. Gonin Optimal sampling times in bioequivalence tests, Journal of Biopharmaceutical Statistics, Volume 10 (2000), pp. 31-44

[9] J. Sacks; D. Ylvisaker Designs for regression problems with correlated errors, Annals of Mathematics, Volume 37 (1966), pp. 66-89

[10] Y. Su; S. Cambanis Sampling designs for regression coefficient estimation with correlated errors, Annals of the Institute of Statistical Mathematics, Volume 46 (1993), pp. 707-722

[11] J. Wang Optimal design for linear interpolation of curves, Statistics in Medicine, Volume 20 (2001), pp. 2467-2477

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