Forecasting the evolving composition of disease-specific elderly populations

Studying how the composition of elderly populations affected by specific diseases evolves over time is essential for improving health resource allocation and long-term healthcare planning in the context of population ageing. However, disease-specific elderly populations are highly complex, with changing component proportions, irregular observation intervals, and sparse data. Forecasting these compositional changes poses important methodological and practical challenges. To address these issues, this paper proposes a forecasting framework that integrates multiple compositional data transformation methods for handling non-equidistant compositional time series. We develop a nonlinear non-equidistant grey compositional forecasting model with parameter optimisation. The performance of the proposed method is evaluated using data from the Chinese Longitudinal Healthy Longevity Survey (CLHLS), focusing on elderly individuals with cardiovascular diseases. We compare the model with benchmark approaches, including grey forecasting models and statistical methods. The results show that the proposed model achieves high overall performance under different compositional data transformations. Beyond this specific application, the framework provides a useful forecasting tool for supporting data-driven health planning, understanding changes in the relative structure of healthcare needs, and policy responses to demographic ageing. This study contributes to the grey forecasting literature by extending its methodological scope and demonstrating its relevance for complex population health forecasting problems.