  Principal Component Analysis (PCA) is a widely used technique in exploratory
data analysis, visualization, and data preprocessing, leveraging the concept of
variance to identify key dimensions in datasets. In this study, we focus on the
first principal component, which represents the direction maximizing the
variance of projected data. We extend the application of PCA by treating its
first principal component as a covariate and integrating it with Generalized
Estimating Equations (GEE) for analyzing age-specific death rates (ASDRs) in
longitudinal datasets. GEE models are chosen for their robustness in handling
correlated data, particularly suited for situations where traditional models
assume independence among observations, which may not hold true in longitudinal
data. We propose distinct GEE models tailored for single and multipopulation
ASDRs, accommodating various correlation structures such as independence,
AR(1), and exchangeable, thus offering a comprehensive evaluation of model
efficiency. Our study critically evaluates the strengths and limitations of GEE
models in mortality forecasting, providing empirical evidence through detailed
model specifications and practical illustrations. We compare the forecast
accuracy of our PCA-GEE approach with the Li-Lee and Lee-Carter models,
demonstrating its superior predictive performance. Our findings contribute to
an enhanced understanding of the nuanced capabilities of GEE models in
mortality rate prediction, highlighting the potential of integrating PCA with
GEE for improved forecasting accuracy and reliability.
