Probabilistic Forecasting of Mortality in Kenya Using a Zero-truncated Conway-Maxwell-Poisson Bayesian Generalized Additive Model
Grace Mukami Mwangi *
Department of Mathematics, Multimedia University of Kenya, P.O. Box 15653-00503, Nairobi, Kenya.
Anthony N. Karanjah
Department of Mathematics, Multimedia University of Kenya, P.O. Box 15653-00503, Nairobi, Kenya.
Pius Nderitu Kihara
Department of Mathematics and Statistics, Technical University of Kenya, P.O. Box 52428-00200, Nairobi, Kenya.
*Author to whom correspondence should be addressed.
Abstract
Aims: To develop the Zero-Truncated Conway-Maxwell-Poisson Bayesian Generalized Additive Model (ZTCMP-BGAM) for probabilistic mortality forecasting in Kenya, estimate its parameters, evaluate its performance against three models, and generate probabilistic forecasts of mortality and life expectancy for 2024 to 2053.
Study Design: Quantitative secondary data analysis and mathematical modeling.
Place and Duration of Study: Kenya, 1950 to 2023 (observation); 2024 to 2053 (forecast horizon).
Methodology: UN WPP 2024 graduated death counts and population exposures for Kenya across 101 ages (1950-2023) were used. The ZTCMP-BGAM embeds a zero-truncated Conway-Maxwell-Poisson distribution with an age-specific dispersion parameter within a Bayesian generalized additive model. Parameters were estimated via penalized log-likelihood with a Laplace approximation, implemented in Template Model Builder. The ZTCMP-BGAM was compared against three models in a two-by-two factorial design crossing zero-truncation and flexible dispersion. Performance was evaluated using BIC, in-sample accuracy, an independent dispersion diagnostic, and backtesting over two holdout periods. Forecasts were generated by extrapolating the additive predictor.
Results: The ZTCMP-BGAM achieved the lowest BIC (66,003.42). Flexible dispersion accounted for 99,290 log-likelihood units of improvement; zero-truncation contributed 1.5 and 0.36 units within the equidispersion and flexible-dispersion classes, respectively. Departures from equidispersion were confirmed at 96 of 101 ages. Primary backtesting (2014-2023) yielded errors of 19.5% and 29.2% for equidispersion and flexible-dispersion models, respectively; sensitivity backtesting (1994-2023) reversed the ranking (31.8% vs. 24.5%). Life expectancy was projected to rise from 65.94 (95% CI: 65.75-66.15) to 81.23 years (95% CI: 78.87-83.59) by 2053.
Conclusion: Flexible age-specific dispersion improves distributional fit; equidispersion is inappropriate across most ages. Out-of-sample forecast performance depends on the mortality dynamics in the holdout period. The framework is transferable to any country relying on UN WPP estimates.
Keywords: Mortality forecasting, conway-maxwell-poisson, Bayesian generalized additive model, Kenya, zero-truncated distribution, age-specific dispersion, Template Model Builder, life expectancy