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Adaptive Mortality Drift for Short-Horizon Forecasting of Under-Five Mortality in West Africa: Model Development, Monte Carlo Validation, Robustness, and a 16-Country Application

This paper introduces and validates an Adaptive Mortality Drift (AMD) model that outperforms various statistical and machine learning benchmarks in forecasting short-term under-five mortality trends across 16 West African countries by dynamically estimating mortality persistence and demonstrating robustness through Monte Carlo simulations.

Original authors: Mumini Idowu Adarabioyo

Published 2026-10-12

📖 7 min read🧠 Deep dive

CC BY 4.0

Original authors: Mumini Idowu Adarabioyo

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Every year, millions of children around the world do not survive to their fifth birthday. This tragic reality is measured by a single, stark number: the under-five mortality rate. This figure counts how many children die before age five for every thousand babies born. It is more than just a statistic; it is a mirror reflecting the health of a society, revealing the quality of its hospitals, the safety of its water, and the stability of its economy. In West Africa, this burden is heaviest, with countries facing vastly different challenges despite sharing a region. For governments and health organizations, knowing what the future holds is critical. They need to know if current efforts are working, where resources are most needed, and whether the region is on track to save more lives in the coming years. However, predicting the future of child survival is difficult. Trends can shift suddenly due to disease, conflict, or economic changes, and the path forward is rarely a straight line.

A researcher has developed a new way to look at these trends, focusing on the short term to help leaders make immediate decisions. Instead of relying on complex computer models that try to guess every possible future scenario, they created a method that listens closely to the most recent changes in death rates. They call this approach the Adaptive Mortality Drift model. The core idea is simple yet powerful: it assumes that the change seen in the last year will continue into the next, but not with perfect certainty. It estimates how much of that recent progress or decline will carry forward, adjusting its prediction based on the actual history of the region. By testing this method against sixteen different countries in West Africa, the researcher found that this straightforward approach outperformed far more complicated mathematical systems and machine learning algorithms. Their work suggests that for the near future, the best way to forecast child survival is to trust the momentum of recent years, while gently accounting for the fact that momentum can sometimes slow down.

The study focused on sixteen nations in West Africa, including giants like Nigeria and smaller neighbors like Cabo Verde. The researcher gathered data on child mortality rates from the United Nations and the World Health Organization, looking at the smooth, annual national estimates rather than individual cases. They wanted to see if they could predict what would happen in the next year with high accuracy. To do this, they built their model to watch the "drift" of mortality. Imagine a boat moving down a river; if the water is flowing steadily, the boat continues in that direction. The researcher asked: does the river flow at the same speed every year, or does it speed up and slow down? Their model calculates a specific number that represents how much of last year's change in child deaths is expected to happen again this year. If the number is close to one, the change continues fully. If it is lower, the change is expected to fade slightly. This number is not guessed; it is calculated by looking at the history of all sixteen countries together, allowing the model to learn from the entire region's experience.

To ensure their new method was truly reliable, the researcher put it through rigorous testing. They used a technique called rolling-origin validation, which is like taking a test where you are only allowed to use information available up to a certain date to predict the next year, then moving that date forward and testing again. They compared their new model against standard statistical tools and advanced machine learning programs, including artificial intelligence systems designed to find complex patterns. The results were clear: the new adaptive model made the most accurate predictions. It had the smallest errors when compared to the actual numbers that occurred between 2018 and 2024. The complex machine learning models, which often excel at finding hidden patterns in messy data, actually performed worse. This happened because the annual death rates in these countries are surprisingly smooth and steady; they do not have the chaotic noise that usually requires complex algorithms to untangle. The simpler model, which respected this smoothness, was the superior tool.

The researcher also ran thousands of computer simulations to see how their model would behave under different, difficult conditions. They tested what would happen if the data contained sudden, wild swings, or if some years of data were missing. In these simulations, the model held up well, showing it could handle unexpected bumps in the road without falling apart. However, they also discovered its limits. If a country experienced a sudden, dramatic shift in its mortality trends—perhaps due to a major conflict or a new health crisis that completely changed the pattern—the model, which relies on past history, would be slow to react. In such cases, the model would continue to predict based on the old pattern for a while before catching up. The researcher tested variations of their model that could react faster to these sudden changes, but found that for the specific history of West Africa, the standard, simpler version remained the most accurate. The extra complexity did not improve the predictions for the years they studied.

When the researcher applied their model to the real world, the results painted a picture of both hope and deep inequality. In 2024, the number of child deaths varied wildly across the region. In Cabo Verde, the rate was as low as 11.14 deaths per thousand live births, a sign of significant progress. In Nigeria, the rate was 115.65, indicating a much heavier burden. The model predicted that for all sixteen countries, child mortality would continue to decline through 2030. For Nigeria, the forecast suggested a drop to around 109.42, while Cabo Verde was expected to fall further to 8.70. These numbers represent a statistical extrapolation of recent trends, not a guarantee of what will happen. They do not account for future wars, new diseases, or specific policy changes. Instead, they serve as a benchmark, a transparent way to see if the current pace of improvement is likely to hold.

The study highlights that while the region is moving in the right direction, the gap between the best and worst performers remains vast. Countries like Senegal and Ghana have seen massive reductions in child deaths since the year 2000, while others like Nigeria and Niger have seen slower progress. The model confirms that these disparities are real and persistent. It suggests that a single, uniform approach to saving children will not work for the entire region. High-burden countries need to accelerate their efforts to catch up, while lower-burden countries must ensure their progress does not stall. The researcher emphasizes that their model is not a magic wand that can solve the causes of death. It does not tell policymakers which vaccines to buy or which hospitals to build. Rather, it provides a clear, honest view of where the region is heading based on what has happened recently. By offering a reliable short-term forecast, it gives health leaders a solid foundation to plan their next steps, ensuring that resources are directed where they are needed most to continue the vital work of saving young lives.

Technical Summary: Adaptive Mortality Drift for Short-Horizon Forecasting of Under-Five Mortality in West Africa

Problem Statement
Accurate short-term (less than five years) forecasts of under-five mortality rates (U5MR) are critical for tracking child-survival outcomes and allocating limited health resources. While long-term trends in sub-Saharan Africa are well-documented, the region exhibits sharp heterogeneity in mortality levels and improvement rates across countries. Existing literature includes demographic frameworks, conventional time-series models (e.g., ARIMA, Holt-Winters), and machine learning approaches. However, many machine learning studies focus on individual-level mortality classification rather than smooth, annual national-rate forecasting. The specific methodological challenge addressed is whether the strong persistence observed in annual mortality changes can be captured by a simple, estimable drift mechanism that improves genuine out-of-sample forecasts compared to fixed-persistence or complex non-linear models.

Methodology
The study develops the Adaptive Mortality Drift (AMD) model, applied to a panel of 16 West African countries using UN IGME/WHO data up to 2024.

Model Formulation: The AMD model treats annual mortality change ( $\Delta M_{i,t}$ ) as a continuous process where the most recent change persists into the next period at an estimable rate $\lambda$ . The core equation is:
$\Delta M_{i,t} = \lambda \Delta M_{i,t-1} + \varepsilon_{i,t}$
Unlike local linear drift (which assumes $\lambda=1$ ) or simple forecasts ( $\lambda=0$ ), AMD estimates $\lambda$ as a pooled parameter across the regional panel using the least squares method. The conditional one-step-ahead forecast is:
$\hat{M}_{i,t|t-1} = M_{i,t-1} + \hat{\lambda}(M_{i,t-1} - M_{i,t-2})$
Multi-step forecasts are generated recursively, with the persistence parameter governing the decay of forecasted changes over the horizon.
Estimation and Validation: The pooled estimator $\hat{\lambda}$ is derived via a zero-intercept regression of current changes on lagged changes. The study employs a strict rolling-origin validation design for the period 2018–2024, generating 112 country-year predictions. Performance is measured using RMSE, MAE, MAPE, and MASE.
Robustness and Extensions: The model's reliability is assessed via Monte Carlo simulations (1,000 replications) under various data-generating mechanisms, including heavy-tailed innovations, missing data, country heterogeneity, and structural breaks. To address identified weaknesses (specifically structural breaks and heterogeneity), two targeted extensions are tested:
1. Exponentially Weighted AMD (EW-AMD): Accelerates adaptation to structural changes.
2. Shrinkage AMD (S-AMD): Pulls country-specific estimates toward the pooled mean.

Key Results

Empirical Performance: In the 2018–2024 rolling evaluation, AMD outperformed all benchmarks, including local linear drift, ARIMA(1,1,1), damped Holt, ridge regression, random forest, gradient boosting, and a lag-1 simple benchmark.
- AMD Metrics: RMSE = 0.177, MAE = 0.130, MAPE = 0.208%, MASE = 0.034.
- Comparison: AMD reduced RMSE by approximately 5.5% compared to local linear drift. Machine learning models (Random Forest, Gradient Boosting) performed significantly worse, likely because the smooth annual U5MR series contain dynamics best captured by parsimonious temporal models rather than complex non-linear classifiers.
Parameter Recovery: Monte Carlo experiments demonstrated that the pooled estimator $\hat{\lambda}$ recovers the true parameter with small bias and nominal 95% coverage under stable conditions, heavy-tailed errors, and moderate missingness. The estimated regional persistence was 0.966, indicating strong but slightly muted continuity in mortality changes.
Robustness Limitations: The pooled estimator showed deterioration under country heterogeneity (upward bias, poor coverage) and structural breaks (slow reaction to regime changes). While EW-AMD and S-AMD successfully mitigated these specific stress scenarios in simulations, they did not improve forecast accuracy on the observed West African test period (2018–2024). Consequently, the simpler AMD model was retained.
Country-Level Heterogeneity: While AMD was the best regional pooled model, it did not dominate every single country. It reduced RMSE in 11 of 16 countries (e.g., Sierra Leone, Mali, Ghana) but was outperformed by local drift in others (e.g., Benin, Niger, Nigeria).

Significance and Claims
The paper positions the AMD model not as a causal policy tool or a universally optimal model for every nation, but as a parsimonious regional short-horizon forecasting benchmark.

Methodological Contribution: The study demonstrates that for smooth, persistent annual mortality series, a simple adaptive drift mechanism that estimates the degree of persistence ( $\lambda$ ) outperforms both fixed-persistence linear models and complex machine learning algorithms in short-horizon forecasting.
Policy Implication: The model provides a transparent test of whether observed mortality patterns are continuing, slowing, or diverging from recent regional trends. It highlights that while the region generally continues to decline, significant cross-country disparities persist (e.g., U5MR ranging from 11.14 in Cabo Verde to 115.65 in Nigeria in 2024).
Forecasting Outlook: Projections to 2030 indicate continued declines across the region, but the model explicitly warns that these are statistical extrapolations of recent trends, not guarantees of SDG 3.2 compliance or causal predictions of policy impacts. The author concludes that AMD should be used alongside substantive public health models that explain the determinants of mortality, rather than as a replacement for them.

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