June 2024 Functional concurrent regression with compositional covariates and its application to the time-varying effect of causes of death on human longevity
Emanuele Giovanni Depaoli, Marco Stefanucci, Stefano Mazzuco
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Ann. Appl. Stat. 18(2): 1668-1685 (June 2024). DOI: 10.1214/23-AOAS1853


Multivariate functional data that are cross-sectionally compositional data are attracting increasing interest in the statistical modeling literature, a major example being trajectories over time of compositions derived from cause-specific mortality rates. In this work we develop a novel functional concurrent regression model in which independent variables are functional compositions. This allows us to investigate the relationship over time between life expectancy at birth and compositions derived from cause-specific mortality rates of four distinct age classes, namely, zero to four, five to 39, 40–64 and 65+ in 25 countries. A penalized approach is developed to estimate the regression coefficients and select the relevant variables. Then an efficient computational strategy, based on an augmented Lagrangian algorithm, is derived to solve the resulting optimization problem. The good performances of the model in predicting the response function and estimating the unknown functional coefficients are shown in a simulation study. The results on real data confirm the important role of neoplasms and cardiovascular diseases in determining life expectancy emerged in other studies and reveal several other contributions not yet observed.

Funding Statement

This research was supported by the PRIN 2017 project SELECT (20177BRJXS) and by the MUR-PRIN 2022 project CARONTE (2022KBTEBN), funded by the European Union–Next Generation EU.


The authors thank Emilio Zagheni, Ugofilippo Basellini and other scholars from the Max Planck Institute for Demographic Research for useful discussion during the presentation of earlier versions of this work.


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Emanuele Giovanni Depaoli. Marco Stefanucci. Stefano Mazzuco. "Functional concurrent regression with compositional covariates and its application to the time-varying effect of causes of death on human longevity." Ann. Appl. Stat. 18 (2) 1668 - 1685, June 2024. https://doi.org/10.1214/23-AOAS1853


Received: 1 July 2023; Revised: 1 November 2023; Published: June 2024
First available in Project Euclid: 5 April 2024

Digital Object Identifier: 10.1214/23-AOAS1853

Keywords: Compositional data analysis , Functional data analysis , life expectancy , Mortality by cause , Sparsity

Rights: Copyright © 2024 Institute of Mathematical Statistics


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Vol.18 • No. 2 • June 2024
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