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Monotone Constrained Tensor-product B-spline with application to screening studies

Author

Listed:
  • Yue Wang

    (Vaccine Biometric Research, Merk Co. & Inc.)

  • Jeremy Taylor

    (University of Michigan)

Abstract

When different markers are responsive to different aspects of a disease, combination of multiple markers could provide a better screening test for early detection. It is also resonable to assume that the risk of disease changes smoothly as the biomarker values change and the change in risk is monotone with respect to each biomarker. In this paper, we propose a boundary constrained tensor-product B-spline method to estimate the risk of disease by maximizing a penalized likelihood. To choose the optimal amount of smoothing, two scores are proposed which are extensions of the GCV score (O'Sullivan et al. (1986)) and the GACV score (Ziang and Wahba (1996)) to incorporate linear constraints. Simulation studies are carried out to investigate the performance of the proposed estimator and the selection scores. In addidtion, sensitivities and specificities based ona pproximate leave-one-out estimates are proposed to generate more realisitc ROC curves. Data from a pancreatic cancer study is used for illustration.

Suggested Citation

  • Yue Wang & Jeremy Taylor, 2004. "Monotone Constrained Tensor-product B-spline with application to screening studies," The University of Michigan Department of Biostatistics Working Paper Series 1022, Berkeley Electronic Press.
    • Handle: RePEc:bep:mchbio:1022
    Note: oai:bepress.com:umichbiostat-1022
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    References listed on IDEAS

    as
    1. Stuart G. Baker, 2000. "Identifying Combinations of Cancer Markers for Further Study as Triggers of Early Intervention," Biometrics, The International Biometric Society, vol. 56(4), pages 1082-1087, December.
    2. Martin W. McIntosh & Margaret Sullivan Pepe, 2002. "Combining Several Screening Tests: Optimality of the Risk Score," Biometrics, The International Biometric Society, vol. 58(3), pages 657-664, September.
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