Smooth tensor decomposition with application to ambulatory blood pressure monitoring data

Abstract: Ambulatory blood pressure monitoring (ABPM) enables continuous measurement of blood pressure and heart rate over 24 hours and is increasingly used in clinical studies. However, ABPM data are often reduced to summary statistics, such as means or medians, which obscure temporal features like nocturnal dipping and individual chronotypes. Functional data analysis methods better capture these temporal dynamics but typically treat each ABPM measurement separately, limiting their ability to leverage correlations among matched measurements. In this work, we observe that aligning ABPM data along measurement type, time, and patient ID lends itself to a tensor representation--a multidimensional array. Although tensor learning has shown great potential in other fields, it has not been applied to ABPM data. Existing tensor learning approaches often lack temporal smoothing constraints, assume no missing data, and can be computationally demanding. To address these limitations, we propose a novel smooth tensor decomposition method that incorporates a temporal smoothing penalty and accommodates missing data. We also develop an automatic procedure for selecting the optimal smoothing parameter and tensor ranks. Simulation studies demonstrate that our method reliably reconstructs smooth temporal trends from noisy, incomplete data. Application to ABPM data from patients with concurrent obstructive sleep apnea and type 2 diabetes uncovers clinically relevant associations between patient characteristics and ABPM measurements, which are missed by summary-based approaches.