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Comparison of three-dimensional ROC surfaces for clustered and correlated markers, with a proteomics application

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  • Mst. Papia Sultana and Jialiang Li
  • Jianhua Hu

Abstract

type="main" xml:id="stan12065-abs-0001"> We propose a non-parametric test to compare two correlated diagnostic tests for a three-category classification problem. Our development was motivated by a proteomic study where the objectives are to detect glycan biomarkers for liver cancer and to compare the discrimination ability of various markers. Three distinct disease categories need to be identified from this analysis. We therefore chose to use three-dimensional receiver operating characteristic (ROC) surfaces and volumes under the ROC surfaces to describe the overall accuracy for different biomarkers. Each marker in this study might include a cluster of similar individual markers and thus was considered as a hierarchically structured sample. Our proposed statistical test incorporated the within-marker correlation as well as the between-marker correlation. We derived asymptotic distributions for three-dimensional ROC surfaces and subsequently implemented bootstrap methods to facilitate the inferences. Simulation and real-data analysis were included to illustrate our methods. Our distribution-free test may be simplified for paired and independent two-sample comparisons as well. Previously, only parametric tests were known for clustered and correlated three-category ROC analyses.

Suggested Citation

  • Mst. Papia Sultana and Jialiang Li & Jianhua Hu, 2015. "Comparison of three-dimensional ROC surfaces for clustered and correlated markers, with a proteomics application," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(4), pages 399-418, November.
    • Handle: RePEc:bla:stanee:v:69:y:2015:i:4:p:399-418
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    File URL: http://hdl.handle.net/10.1111/stan.12065
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    References listed on IDEAS

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    1. Peter Hall & Stephen M.‐S. Lee & G. Alastair Young, 2000. "Importance of interpolation when constructing double‐bootstrap confidence intervals," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 479-491.
    2. Li, Gang & Zhou, Kefei, 2008. "A Unified Approach to Nonparametric Comparison of Receiver Operating Characteristic Curves for Longitudinal and Clustered Data," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 705-713, June.
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