Dynamic Principal Component Analysis for Syndemic Factors in an Extended Lee–Carter Mortality Model

Introduction
The interaction between socioeconomic conditions, lifestyle factors, and mortality is a crucial issue for improving mortality modeling and
forecasting. The traditional Lee–Carter family models capture long-term mortality dynamics through a latent time index but do not explicitly incorporate exogenous determinants. This study proposes an extension of the Lee–Carter framework that integrates a composite
syndemic index derived from multiple socioeconomic and health-related variables. To address multicollinearity and preserve temporal dependence among covariates, a dynamic dimensionality-reduction approach based on Dynamic Principal Component Analysis (dPCA) is introduced.

Methods
Central mortality rates are modeled as a function of age-specific parameters, a latent mortality trend, and an additional exogenous component representing a syndemic index. Identification constraints ensure the uniqueness of the model parameters. A set of socioeconomic,
behavioral, and healthcare indicators for Italy and its regions from 1995 to 2023 is used to determine the multidimensional index. Standard Principal Component Analysis (PCA) and dPCA are applied to reduce the dimensionality of the covariates. While PCA identifies latent factors based on variance maximization, dPCA explicitly accounts for temporal dependence by extracting orthogonal dynamic components from lagged data matrices.

Results
Exploratory analysis reveals a strong clustering of economic and health expenditure variables, with obesity and alcohol consumption associated with higher income levels, while smoking and hospital-based healthcare structures are linked to more traditional socioeconomic contexts. The dPCA-based specification further enhances the robustness of the index by preserving temporal relationships among variables.

Conclusions
Integrating a dynamically derived syndemic index into the Lee–Carter framework improves the representation of mortality dynamics by explicitly linking mortality trends to evolving socioeconomic and health environments. The dPCA approach offers a more robust method for dimensionality reduction, thanks to the preservation of the temporal structure, leading to more stable parameter estimations and a more in-depth interpretation of mortality drivers.