Title: Forecasting Mortality Rates: Unveiling Patterns with a PCA-GEE Approach Show Chinese title

Title: 预测死亡率：使用PCA-GEE方法揭示模式

Abstract: 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. Show Chinese abstract

Abstract: 主成分分析（PCA）是一种广泛应用于探索性数据分析、可视化和数据预处理的技术，利用方差的概念来识别数据集中的关键维度。在本研究中，我们专注于第一主成分，它表示投影数据方差最大化的方向。 我们通过将PCA的第一主成分作为协变量，并将其与广义估计方程（GEE）结合，用于分析纵向数据中的年龄特定死亡率（ASDR）。选择GEE模型是因为它们在处理相关数据时具有稳健性，尤其适合于传统模型假设观测值之间独立的情况，而在纵向数据中这种假设可能不成立。 我们提出了针对单一和多人口ASDR的专门GEE模型，考虑了各种相关结构，如独立性、AR(1)和可交换性，从而提供了对模型效率的全面评估。我们的研究批判性地评价了GEE模型在死亡率预测中的优缺点，通过详细的模型规范和实际案例提供了实证证据。 我们将PCA-GEE方法的预测准确性与Li-Lee和Lee-Carter模型进行了比较，展示了其优越的预测性能。我们的发现有助于加深对GEE模型在死亡率预测中细微能力的理解，强调了将PCA与GEE集成以提高预测准确性和可靠性的潜力。