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Variable-Domain Functional Regression for Modeling ICU Data

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  • Jonathan E. Gellar
  • Elizabeth Colantuoni
  • Dale M. Needham
  • Ciprian M. Crainiceanu

Abstract

We introduce a class of scalar-on-function regression models with subject-specific functional predictor domains. The fundamental idea is to consider a bivariate functional parameter that depends both on the functional argument and on the width of the functional predictor domain. Both parametric and nonparametric models are introduced to fit the functional coefficient. The nonparametric model is theoretically and practically invariant to functional support transformation, or support registration. Methods were motivated by and applied to a study of association between daily measures of the Intensive Care Unit (ICU) sequential organ failure assessment (SOFA) score and two outcomes: in-hospital mortality, and physical impairment at hospital discharge among survivors. Methods are generally applicable to a large number of new studies that record a continuous variables over unequal domains. Supplementary materials for this article are available online.

Suggested Citation

  • Jonathan E. Gellar & Elizabeth Colantuoni & Dale M. Needham & Ciprian M. Crainiceanu, 2014. "Variable-Domain Functional Regression for Modeling ICU Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(508), pages 1425-1439, December.
    • Handle: RePEc:taf:jnlasa:v:109:y:2014:i:508:p:1425-1439
    DOI: 10.1080/01621459.2014.940044
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    2. Shu Jiang & Yijun Xie & Graham A. Colditz, 2021. "Functional ensemble survival tree: Dynamic prediction of Alzheimer’s disease progression accommodating multiple time‐varying covariates," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(1), pages 66-79, January.
    3. Kraus, David, 2019. "Inferential procedures for partially observed functional data," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 583-603.
    4. Kraus, David & Stefanucci, Marco, 2020. "Ridge reconstruction of partially observed functional data is asymptotically optimal," Statistics & Probability Letters, Elsevier, vol. 165(C).
    5. Maistre, Samuel & Patilea, Valentin, 2020. "Testing for the significance of functional covariates," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    6. Liebl, Dominik & Rameseder, Stefan, 2019. "Partially observed functional data: The case of systematically missing parts," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 104-115.

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