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Estimation of the volume under a ROC surface in presence of covariates

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  • To, Duc-Khanh
  • Adimari, Gianfranco
  • Chiogna, Monica

Abstract

A new method to adjust for covariate effects in the estimation of volume under a ROC surface (VUS) is presented. The method is based on the induced-regression methodology, which uses location-scale regression models to explain the relation between the test results and the covariate(s). For the estimation of the models, it is proposed to use a semiparametric generalized estimating equations (GEE) approach if the parametric forms of the mean and variance functions are specified. Alternatively, a nonparametric method is proposed, based on local linear regression (LL). In order to estimate the covariate-specific VUS, a covariate-specific Mann-Whitney representation of VUS is used, and working samples constructed after fitting the location-scale models by the GEE or LL approach. This leads to new MW-GEE and MW-LL covariate-specific VUS estimators. The asymptotic behavior of the new estimators is investigated. More precisely, their mean squared consistency is proved. Moreover, the performance of the estimators in finite samples is explored through several simulation experiments, and an illustration, based on data from the Alzheimer's Disease Neuroimaging Initiative, is provided.

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  • To, Duc-Khanh & Adimari, Gianfranco & Chiogna, Monica, 2022. "Estimation of the volume under a ROC surface in presence of covariates," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:csdana:v:174:y:2022:i:c:s0167947322000147
    DOI: 10.1016/j.csda.2022.107434
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    References listed on IDEAS

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    1. Danping Liu & Xiao-Hua Zhou, 2011. "Semiparametric Estimation of the Covariate-Specific ROC Curve in Presence of Ignorable Verification Bias," Biometrics, The International Biometric Society, vol. 67(3), pages 906-916, September.
    2. Lopez-de-Ullibarri, Ignacio & Cao, Ricardo & Cadarso-Suarez, Carmen & Lado, Maria J., 2008. "Nonparametric estimation of conditional ROC curves: Application to discrimination tasks in computerized detection of early breast cancer," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2623-2631, January.
    3. Wenceslao González‐Manteiga & Juan Carlos Pardo‐Fernández & Ingrid Van Keilegom, 2011. "ROC Curves in Non‐Parametric Location‐Scale Regression Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(1), pages 169-184, March.
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    Cited by:

    1. Ibrahim M. Almanjahie & Zoulikha Kaid & Ali Laksaci & Mustapha Rachdi, 2022. "Estimating the Conditional Density in Scalar-On-Function Regression Structure: k -N-N Local Linear Approach," Mathematics, MDPI, vol. 10(6), pages 1-16, March.

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