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.
Gellar, Jonathan E.; Colantuoni, Elizabeth; Needham, Dale M.; and Crainiceanu, Ciprian M., "VARIABLE-DOMAIN FUNCTIONAL REGRESSION FOR MODELING ICU DATA" (May 2014). Johns Hopkins University, Dept. of Biostatistics Working Papers. Working Paper 261.