A Compositional Approach to Modelling Cause-specific Mortality with Zero Counts

2025-10-17

AI Summary

In cause-specific mortality modeling, frequent zero counts render conventional compositional data analysis (CODA) invalid. This paper proposes an α-transformation–based CODA framework that rigorously handles zeros without ad hoc additive smoothing, thereby preserving statistical validity and more accurately capturing inter-cause dependencies and age patterns. The method integrates life table data to model and forecast mortality proportions for major causes—particularly cardiovascular diseases. Empirical evaluation on mortality data from England, Wales, and the United States demonstrates that the proposed approach significantly improves both predictive accuracy and stability of cause-of-death proportions compared to classical log-ratio CODA. Consistent forecasts indicate continued declines in mortality proportions for key cardiovascular conditions, such as myocardial infarction. This work provides a generalizable, statistically principled solution for compositional mortality analysis in settings with pervasive zero entries.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Data transparency and provenance
• User Modeling, Personalization and Recommendation: Accountability, Transparency, and Ethics for personalization

Abstract

Understanding and forecasting mortality by cause is an essential branch of actuarial science, with wide-ranging implications for decision-makers in public policy and industry. To accurately capture trends in cause-specific mortality, it is critical to consider dependencies between causes of death and produce forecasts by age and cause coherent with aggregate mortality forecasts. One way to achieve these aims is to model cause-specific deaths using compositional data analysis (CODA), treating the density of deaths by age and cause as a set of dependent, non-negative values that sum to one. A major drawback of standard CODA methods is the challenge of zero values, which frequently occur in cause-of-death mortality modelling. Thus, we propose using a compositional power transformation, the $α$-transformation, to model cause-specific life-table death counts. The $α$-transformation offers a statistically rigorous approach to handling zero value subgroups in CODA compared to emph{ad-hoc} techniques: adding an arbitrarily small amount. We illustrate the $α$-transformation on England and Wales, and US death counts by cause from the Human Cause-of-Death database, for cardiovascular-related causes of death. Results demonstrate the $α$-transformation improves forecast accuracy of cause-specific life-table death counts compared with log-ratio-based CODA transformations. The forecasts suggest declines in proportions of deaths from major cardiovascular causes (myocardial infarction and other ischemic heart diseases (IHD)).

Problem

• Handling zero counts in cause-specific mortality modeling
• Ensuring coherence between age-cause and aggregate mortality forecasts
• Improving forecast accuracy using compositional data transformations

Innovation

• Uses compositional data analysis for mortality modeling
• Applies α-transformation to handle zero counts
• Improves forecast accuracy for cause-specific deaths