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The optimal linear combination of multiple predictors under the generalized linear models

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  • Jin, Hua
  • Lu, Ying

Abstract

Multiple alternative diagnostic tests for one disease are commonly available to clinicians. It is important to use all the good diagnostic predictors simultaneously to establish a new predictor with higher statistical utility. Under the generalized linear model for binary outcomes, the linear combination of multiple predictors in the link function is proved optimal in the sense that the area under the receiver operating characteristic (ROC) curve of this combination is the largest among all possible linear combinations. The result was applied to analysis of the data from the Study of Osteoporotic Fractures (SOF) in comparison with Su and Liu's approach.

Suggested Citation

  • Jin, Hua & Lu, Ying, 2009. "The optimal linear combination of multiple predictors under the generalized linear models," Statistics & Probability Letters, Elsevier, vol. 79(22), pages 2321-2327, November.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:22:p:2321-2327
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    References listed on IDEAS

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    1. Hua Jin & Ying Lu & Steven T. Harris & Dennis M. Black & Katie Stone & Marc C. Hochberg & Harry K. Genant, 2004. "Classification Algorithms for Hip Fracture Prediction Based on Recursive Partitioning Methods," Medical Decision Making, , vol. 24(4), pages 386-398, August.
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    Cited by:

    1. Kubilay Kaptan & Sandra Cunha & José Aguiar, 2025. "The Effect of Activation Methods on the Mechanical Properties of Cement Mortars with Recycled Powder from Concrete Waste as a Cement Partial Replacement: A Review," Sustainability, MDPI, vol. 17(10), pages 1-50, May.
    2. Yu, Wenbao & Park, Taesung, 2015. "Two simple algorithms on linear combination of multiple biomarkers to maximize partial area under the ROC curve," Computational Statistics & Data Analysis, Elsevier, vol. 88(C), pages 15-27.

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