Predicting Kidney Obstruction from Renal Photon Count Curve and Auxiliary Variables

Regression of a scalar response on mixed functional- and scalar-valued predictors, such as medical imaging with auxiliary patient information, intro- duces the new challenge of handling cross-modality correlations. To address this, we propose a hybrid partial least squares (PLS) regression framework that integrates functional and scalar predictors within a unified Hilbert space. We then extend the classical nonlinear iterative PLS (NIPALS) algorithm to this hybrid Hilbert space by iteratively maximizing the empirical cross- covariance between the hybrid predictor and the response. As a result, our method identifies low-dimensional representations that capture both within- and between-modality variation, as well as the response-predictor correla- tion. The procedure is computationally efficient, requiring only the solution of linear systems at each step. We provide theoretical properties to justify our algorithm and demonstrate its effectiveness through simulations and an application to clinical outcome prediction using renal imaging and scalar co- variates from the Emory University renal study.

References

high-dimensional statistics

Hybrid Partial Least Squares Regression with Multiple Functional and Scalar Predictors

Jongmin Mun, and Jeong Hoon Jang

arxiv preprint, Jan 2026

Summary R Package Preprint

Motivated by renal imaging studies that combine renogram curves with pharmacokinetic and demographic covariates, we propose Hybrid partial least squares (Hybrid PLS) for simultaneous supervised dimension reduction and regression in the presence of cross-modality correlations. The proposed approach embeds multiple functional and scalar predictors into a unified hybrid Hilbert space and rigorously extends the nonlinear iterative PLS (NIPALS) algorithm. This theoretical development is complemented by a sample-level algorithm that incorporates roughness penalties to control smoothness. By exploiting the rank-one structure of the resulting optimization problem, the algorithm admits a computationally efficient closed-form solution that requires solving only linear systems at each iteration. We establish fundamental geometric properties of the proposed framework, including orthogonality of the latent scores and PLS directions. Extensive numerical studies on synthetic data, together with an application to a renal imaging study, validate these theoretical results and demonstrate the method’s ability to recover predictive structure under intermodal multicollinearity, yielding parsimonious low-dimensional representations.