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Optimal and Robust Designs for Estimating the Concentration Curve and the AUC

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  • Mohamad Belouni
  • Karim Benhenni

Abstract

type="main" xml:id="sjos12116-abs-0001"> 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 an autocorrelated error process. We introduce a simple linear unbiased estimator of the concentration curve and the AUC. We show that this estimator constructed from a sampling design generated by an appropriate density is asymptotically optimal in the sense that it has exactly the same asymptotic performance as the best linear unbiased estimator. Moreover, we prove that the optimal design is robust with respect to a minimax criterion. When repeated observations are available, this estimator is consistent and has an asymptotic normal distribution. Finally, a simulated annealing algorithm is applied to a pharmacokinetic model with correlated errors.

Suggested Citation

  • Mohamad Belouni & Karim Benhenni, 2015. "Optimal and Robust Designs for Estimating the Concentration Curve and the AUC," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 453-470, June.
    • Handle: RePEc:bla:scjsta:v:42:y:2015:i:2:p:453-470
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    File URL: http://hdl.handle.net/10.1111/sjos.12116
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    References listed on IDEAS

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    1. Leena Choi & Brian Caffo & Charles Rohde, 2004. "Optimal Sampling Times in Bioequivalence Studies Using a Simulated Annealing Algorithm," Johns Hopkins University Dept. of Biostatistics Working Paper Series 1059, Berkeley Electronic Press.
    2. Dette, Holger & Kunert, Joachim, 2006. "Exact optimal designs for weighted least squares analysis with correlated errors," Technical Reports 2006,04, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
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    Cited by:

    1. D. Benelmadani & K. Benhenni & S. Louhichi, 2020. "The reproducing kernel Hilbert space approach in nonparametric regression problems with correlated observations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(6), pages 1479-1500, December.

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