Modelling Malaysian mortality with cause-of-death: a compositional data approach to Lee-Carter extension

Forecasting cause-specific mortality is at the core of actuarial valuation, annuity pricing, and long-term public health planning. In traditional extrapolation frameworks such as the Lee-Carter and Li-Lee models, probability leakage is a structural flaw which causes the independently projected cause death rates to not sum to total mortality and results in implausible trajectory crossovers. To overcome these shortcomings, this study explores the application of Compositional Data Analysis (CoDA) extensions namely CoDA Lee-Carter (CDLC) and CoDA Li-Lee (CDLL) to historical Malaysian cause of death data. We transform cause proportions to the unit simplex using centred log-ratio coordinates. This transformation imposes exact aggregate sum coherence but preserves competing-risk substitution dynamics. Short-term structural changes are captured by standard CDLL, but its unweighted common-factor structure overfits noise in the volatile "Others" residual category, extrapolating temporary administrative changes into an implausible expansion of aggregate mortality over multi-decade horizons. We propose a Weighted CoDA Li-Lee (WCDLL) framework with inverse-variance weights to mitigate this log-ratio sensitivity. Baseline noise is buffered by lower structural weights on high volatility residual components, protecting the common temporal index. Empirical evaluation verifies that WCDLL eliminates aggregate trajectory divergence, recovering a demographically plausible secular decline consistent with national all-cause benchmarks, while maintaining exact unit-simplex sum-coherence. For multi-cause mortality modelling, the suggested WCDLL model offers an actuarially sound and mathematically consistent framework.