Comparative Analysis of Predictive Models for Under-Five Mortality Rates in Ghana: Integrating Artificial Neural Networks, Bayesian Structural Time Series, and Seasonal Autoregressive Integrated Moving Average

Comparative Analysis of Predictive Models for Under-Five Mortality Rates in Ghana: Integrating Artificial Neural Networks, Bayesian Structural Time Series, and Seasonal Autoregressive Integrated Moving Average

Michael Mensah^1,2*, Sampson Opoku¹, Annabel Aku Anum², Ishmeal Turay³, Selasie Brown⁴, Felix Aninagyei⁵

¹Department of Community Health, Family Health Medical School, Family Health University, Teshie-Accra, Ghana

²Department of Research, Family Health Medical School, Family Health University, Teshie-Accra, Ghana

³Department of Child Health, Family Health Medical School, Family Health University, Teshie-Accra, Ghana

⁴Department of Computer Science, College of Physical Sciences, University of Professional Studies, Accra, Ghana

⁵Department of Medicine, College of Health Sciences, Angelicin University, Nkoranza, Bono East Region, Ghana

^*Corresponding Author

DOI: https://dx.doi.org/10.47772/IJRISS.2025.906000012

Received: 17 May 2025; Accepted: 21 May 2025; Published: 26 June 2025

ABSTRACT

Introduction

Under-five mortality remains a critical public health concern in Ghana, with numerous efforts aimed at understanding its drivers and predicting future trends. This study aims to perform a comparative analysis of predictive models for under-five mortality rates, integrating Artificial Neural Networks (ANN), Bayesian Structural Time Series (BSTS), and Seasonal Autoregressive Integrated Moving Average (SARIMA) models.

Methods

This study used a dataset of Ghana’s under-five mortality rate from 1964 to 2017, obtained from the World Bank. Data was analyzed using R software. Missing values were imputed, outliers were treated, and stationarity ensured through transformations. The SARIMA model was fitted using ACF/PACF analysis and seasonal parameters, while ANN was trained with optimized hyperparameters on a train-test split. The BSTS model incorporated trend and seasonal components, estimated via Bayesian inference. Model performance was compared using metrics like MSE, MAE, and R², with forecasting accuracy evaluated across all models.

Results

The median value was 127.4, and the under-5 mortality rate in Ghana is higher than the median for all 241 countries in the exploratory analysis. The mean value of 132.2 and the standard deviation of 54.96 indicated a significant amount of variability in the data. The SARIMA model, despite being a good fit with no significant autocorrelation in residuals, is outperformed by the BSTS model. ANN Model Performance: The ANN model performs better than SARIMA but is not as effective as BSTS. The forecast values of BSTS were chosen for predicting under-5 mortality.

Conclusion

Comparing advanced models like BSTS with ANN and SARIMA, we can better predict under-five mortality rates in Ghana. BSTS was the best model for the prediction of under 5 mortality. Findings on reliable predicted values help improve child health outcomes and inform policies. Further studies can be conducted combining modern machine learning techniques with statistical methods to obtain more robost findings.

INTRODUCTION

The global under-5 mortality rate declined by 59% from 93.0 deaths per 1,000 live births in 1990 to 37.7 in 2019.^1,2,3 The annual number of global under-5 deaths declined from 12.5 million in 1990 to 5.2 million in 2019, a 58% reduction.^1,4 However, despite this progress, under-5 mortality remains a significant public health challenge, with 4.9 million children under 5 dying in 2022.^1,2 Sub-Saharan Africa and South Asia account for over 80% of global under-5 deaths in 2019. Around 75% of countries at risk of missing the Sustainable Development Goal (SDG) target on under-5 mortality are in sub-Saharan Africa.^3,4 Ghana’s under-5 mortality rate declined from 140 deaths per 1,000 live births in 1990 to 73 deaths per 1,000 live births in 2017.^5,6 Under-five mortality rates (U5MRs) in Ghana continue to pose significant public health challenges. Despite efforts to reduce these rates, the country still faces substantial disparities in child survival across different regions, socioeconomic groups, and demographic factors.^7,8 Accurate forecasting of U5MRs is crucial for effective planning and resource allocation in Ghana’s healthcare system. Traditional statistical methods, such as Seasonal Autoregressive Integrated Moving Average (SARIMA) models,⁹ have been widely used to forecast U5MRs in Ghana and other low- and middle-income countries (LMICs). However, these methods have limitations in capturing the complex, non-linear patterns and relationships inherent in child mortality data.^10,11 The data is often characterized by high levels of noise, uncertainty, and non-stationarity, making it difficult for conventional time series models to achieve accurate long-term forecasts. Bayesian Structural Time Series (BSTS) models such as Artificial Neural Networks (ANNs) and Bayesian Structural Time Series (BSTS) models, have emerged as promising alternatives to improve the accuracy of U5MR forecasting.^9,12,13 ANNs are particularly adept at capturing non-linear relationships and complex patterns in the data, while BSTS models can incorporate prior knowledge and uncertainty into the forecasting process. Several studies have explored the application of ANNs and BSTS models in the context of population health and epidemiology.^14–16 These models have demonstrated superior performance compared to traditional statistical methods in forecasting various health outcomes, including disease incidence, mortality rates, and healthcare utilization. However, the comparative evaluation of these advanced models in the specific context of U5MR forecasting in Ghana remains limited. This study aims to fill this gap by conducting a comprehensive comparative analysis of SARIMA, ANN, and BSTS models in forecasting U5MRs in Ghana. The study will assess the performance of these models in capturing the complex patterns and non-linear relationships inherent in the U5MR data, as well as their ability to provide accurate long-term forecasts. The findings of this study will contribute to the existing literature by providing valuable insights into the strengths and limitations of each modeling approach in the context of U5MR forecasting in Ghana. This information can inform healthcare policymakers and practitioners in Ghana, enabling them to make more informed decisions about resource allocation and the implementation of targeted interventions to address the persistent challenges in child survival.

METHODS

Data collection

The dataset used in this study comprises the historical aggregated yearly under-five mortality rate (U5MR) of Ghana from 1964 to 201, providing a total of 54 observations. This dataset was obtained from the official website of the World Bank and is based on reconciled country-level estimates from various data sources by the United Nations Inter-Agency Group for Child Mortality Estimation (UN IGME).

Data Preprocessing

Handling Missing Values: Appropriate imputation methods, such as linear interpolation or moving average, were used to handle any missing values. Statistical techniques like Z-score and IQR method were employed to detect and treat outliers through capping, transformation, or imputation.: Stationarity of the time series was ensured by performing stationarity tests (e.g., Augmented Dickey-Fuller test) and applying necessary transformations like differencing or log transformation. Data normalization was performed to facilitate better model performance, especially for the Artificial Neural Network (ANN) models.

Model Fitting and Evaluation

SARIMA Model

Model Identification: Autocorrelation function (ACF) and partial autocorrelation function (PACF) analyses were conducted to identify the orders of the autoregressive (AR), integrated (I), and moving average (MA) components. Seasonal Components: Seasonal parameters (P, D, Q, m) were determined based on observed seasonal patterns. Parameter Estimation: Model parameters were estimated using maximum likelihood estimation (MLE). Model Diagnostics: The goodness-of-fit was evaluated using residual diagnostics and model selection criteria such as Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). Validation: Model performance was assessed using in-sample and out-of-sample validation metrics.

ANN Model

The data was split into training (70%), and test sets (30%). The ANN architecture was designed, including the number of hidden layers, neurons per layer, and activation functions (e.g., ReLU, sigmoid).  Training: The ANN model was trained using the training data, optimizing hyperparameters such as learning rate, batch size, and number of epochs using the validation set. Evaluation: Model performance was evaluated on the test set using metrics such as mean squared error (MSE), mean absolute error (MAE), and R-squared (R²).

BSTS Model

Model Specification: The BSTS model structure was specified, incorporating trend, seasonal, and regression components as necessary. Parameter Estimation: Model parameters were estimated using Bayesian inference techniques, such as Markov Chain Monte Carlo (MCMC) sampling. Model Diagnostics: Diagnostic checks were performed using posterior predictive checks and model fit was evaluated using metrics like log-predictive density. Validation: The model’s performance was assessed on the test set using MSE, MAE, and R² metrics.

Model Comparison and Selection

The forecasting accuracy of the SARIMA, ANN, and BSTS models was compared using metrics such as MSE, MAE, and R² on the test set.

RESULTS

From table 1, The statistics on under-5 mortality in Ghana show that there is still work to be done to reduce child mortality rates. With a median value of 127.4, the under-5 mortality rate in Ghana is higher than the median for all 241 countries in the exploratory analysis. The mean value of 132.2 and a standard deviation of 54.96 indicated a significant amount of variability in the data. The 95% confidence interval of the median is 127.4 (107.2-164.0), and the 95% confidence interval of the mean is 132.2 (118.2-146.3). These findings highlight the need for continued efforts to improve access to healthcare, education, and other resources for children in Ghana.

Figure 1Global burden of under 5 mortality

Figure 2 Trend of Under 5 mortality

Model Residual Diagnostics

Ljung-Box Test for SARIMA Residuals, Q* = 5.2865, df = 5, p-value = 0.3819 This indicates that the residuals from the SARIMA (3,1,2) model do not show significant autocorrelation, suggesting that the model is well-specified.

Table 2 Model performance

Model performance

MSE: BSTS has the lowest MSE, followed by ANN, with SARIMA having the highest MSE. This suggests that BSTS has the best fit of the three models. MAE and MAPE: BSTS also has the lowest MAE and MAPE, indicating that it makes the smallest average errors in both absolute and relative terms. BSTS Model Performance: The BSTS model outperforms both the SARIMA and ANN models in terms of lower error metrics, making it the best choice for this dataset.

SARIMA Model Suitability: The SARIMA model, despite being a good fit with no significant autocorrelation in residuals, is outperformed by the BSTS model. ANN Model Performance: The ANN model performs better than SARIMA but is not as effective as BSTS.

Forecasted values of models   

SARIMA (Seasonal Autoregressive Integrated Moving Average), ANN (Artificial Neural Network), and BSTS (Bayesian Structural Time Series) are pivotal for predicting future values based on historical data. Each model provides unique insights into future trends, and their forecasted values can significantly influence strategic decisions. The predicted values range from approximately 31.42 to 43.08using SARIMA. The forecasted range spans from around 42.46 to 44.19. The projected values oscillate between approximately 44.82 and 45.09. The SARIMA model forecasts a significant and steady decline in values over the forecast period. Starting at 43.08 in 2021, the value decreases annually, reaching 31.42 by 2026. This downward trajectory suggests that the underlying factors driving the historical data are expected to continue their influence, leading to further decline.  The ANN model, on the other hand, predicts a more moderate decline. Starting at 44.19 in 2021 and decreasing to 42.46 by 2026, the ANN model indicates a less severe downward trend compared to SARIMA. In contrast to SARIMA and ANN, the BSTS model forecasts relatively stable values. The projected value begins at 45.04 in 2021 and fluctuates slightly, ending at 44.93 in 2026.

DISCUSSION

Under-five mortality remains a significant public health challenge in Ghana, where the median rate of 127.4 deaths per 1,000 live births exceeds global averages. This disparity reveals the urgent need for targeted interventions to address regional disparities and improve child survival outcomes across the country. The high variability in under-five mortality rates, as indicated by a mean of 132.2 deaths per 1,000 live births with a standard deviation of 54.96, further emphasizes the complex and multifaceted nature of this issue, requiring tailored approaches to healthcare delivery and policy formulation. The application of the SARIMA(3,1,2) model to the under-five mortality data in Ghana demonstrated robust performance, as evidenced by the Ljung-Box test results indicating no significant autocorrelation in the residuals.^9,17 This finding suggests that the SARIMA model effectively captured the underlying temporal dependencies and removed serial correlations, thereby providing reliable forecasts. The model’s ability to maintain residuals that behave like white noise supports its suitability for forecasting applications in public health. In contrast to traditional statistical methods, artificial neural networks (ANNs) offer a powerful alternative for modeling complex non-linear relationships in under-five mortality data.^18–21 Studies such as those by Adeyinka et al. have demonstrated the superior predictive accuracy of ANNs over conventional regression models, highlighting their potential to enhance forecasting precision in healthcare settings. Integrating ANNs alongside SARIMA and Bayesian Structural Time Series (BSTS) models could provide a comprehensive framework for understanding and predicting under-five mortality trends in Ghana.^9,22

The Bayesian principles and structural time series analysis represent another advanced approach capable of incorporating prior information and handling dynamic temporal patterns. A recent study illustrated the efficacy of BSTS models in capturing spatial and temporal variations in under-five mortality, making the model relevant for predictive modeling in resource-constrained settings like Kenya.¹⁵ In assessing model performance in this study, the BSTS model consistently outperformed SARIMA and ANN models based on key error metrics such as Mean Squared Error (MSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE). This superior performance suggests that BSTS effectively accounts for the complex dynamics inherent in under-five mortality data, providing more accurate forecasts crucial for evidence-based policy decisions.^15,23,24 While ANNs demonstrated competitive predictive capabilities compared to SARIMA, their performance fell short of BSTS in terms of forecast accuracy. The ANN’s ability to capture intricate non-linear relationships may offer advantages in certain contexts but requires careful consideration of model complexity and computational resources.

The SARIMA model, despite its well-specified residuals and effective handling of temporal dependencies, exhibited comparatively higher forecast errors. This indicates potential limitations in capturing the full complexity of under-five mortality dynamics, particularly those influenced by non-linear and seasonal factors. The findings from this comparative analysis align with previous studies, highlighting the BSTS model as the preferred method for forecasting under-five mortality in Ghana.^11,17,25 This recommendation is based on the model’s ability to generate stable and accurate predictions, thereby supporting targeted interventions and enabling effective monitoring of progress towards the Sustainable Development Goal (SDG) targets.

In conclusion, comparing the performance of BSTS with SARIMA and ANN models provides valuable insights into the strengths and limitations of each method, guiding the selection of appropriate modeling techniques for specific forecasting objectives. Also, by leveraging advanced modeling techniques such as BSTS alongside ANN and SARIMA, the capacity to accurately predict under-five mortality trends in Ghana will be enhanced. The approach would not only improve child health outcomes but also strengthen the evidence base for policy development and implementation, ultimately advancing towards global health goals. Future research should focus on refining these models with additional data and exploring novel methodologies to further enhance forecasting precision in public health contexts.

REFERENCES

1. Irimu G, Gupta P, bmj ME, 2024 undefined. Global child mortality falls to historic low. bmj.com. Accessed July 15, 2024. https://www.bmj.com/content/385/bmj.q1077
2. Mohammed A, Dwomoh D, Nonvignon J. The impact of maternal and child health and nutrition improvement project on maternal health service utilization in Ghana: An Interrupted time series analysis. PLOS Glob Public Heal. 2022;2(4 April). doi:10.1371/journal.pgph.0000372
3. Barwe T. Multilevel determinants of under-five deaths in South Africa: evidence from 2016 Demographic Health Survey. Published online 2023. Accessed July 15, 2024. https://repository.nwu.ac.za/handle/10394/42349
4. Amir M, Khan A. Child Malnutrition and Mortality in South Asia: A Comparative Analysis. researchgate.net. Accessed July 15, 2024. https://www.researchgate.net/profile/Mohammad-Amir-29/publication/378862216_Child_Malnutrition_and_Mortality_in_South_Asia_A_Comparative_Analysis/links/65eecac8b1906066b28c4503/Child-Malnutrition-and-Mortality-in-South-Asia-A-Comparative-Analysis.pdf
5. Siakwa M, Kpikpitse D, Laryea T, … AAIJPC, 2014 undefined. A five-year neonatal mortality trend in a Ghanaian Teaching Hospital after the implementation of strategies to achieve the Millenium Development Goal (MDG) 4. researchgate.net. 2014;2(1):43-049. Accessed July 15, 2024. https://www.researchgate.net/profile/Amandus-Ankobil/publication/273462535_A_five-year_neonatal_mortality_trend_in_a_Ghanaian_Teaching_Hospital_after_the_implementation_of_strategies_to_achieve_the_Millennium_Development_Goal_MDG-4/links/55eb662308ae3e1218469e83/A-five-year-neonatal-mortality-trend-in-a-Ghanaian-Teaching-Hospital-after-the-implementation-of-strategies-to-achieve-the-Millennium-Development-Goal-MDG-4.pdf
6. Aregawi M, Malm KL, Wahjib M, et al. Effect of anti-malarial interventions on trends of malaria cases, hospital admissions and deaths, 2005-2015, Ghana. Malar J. 2017;16(1). doi:10.1186/s12936-017-1828-6
7. Kanmiki EW, Bawah AA, Agorinya I, et al. Socio-economic and demographic determinants of under-five mortality in rural northern Ghana. BMC Int Health Hum Rights. 2014;14(1). doi:10.1186/1472-698X-14-24
8. Rahman MM, Alam K. The Role of Socio-economic and Female Indicators on Child Mortality Rate in Bangladesh: A Time Series Analysis. Omega (United States). 2023;86(3):889-912. doi:10.1177/0030222821993616
9. Onambele L, Guillen-Aguinaga S, Guillen-Aguinaga L, et al. evidence of health inequity in child survival: spatial and Bayesian network analyses of stillbirth rates in 194 countries. Published online 2019:322-351. Accessed July 15, 2024. https://www.nature.com/articles/s41598-019-56326-w
10. Helleringer S, Arhinful D, Abuaku B, et al. Using community-based reporting of vital events to monitor child mortality: Lessons from rural Ghana. PLoS One. 2018;13(1). doi:10.1371/journal.pone.0192034
11. Agbadi P, Agbaglo E, Tetteh JK, Adu C, Ameyaw EK, Nutor JJ. Trends in under-five mortality rate disaggregated across five inequality dimensions in Ghana between 1993 and 2014. Public Health. 2021;196:95-100. doi:10.1016/j.puhe.2021.04.024
12. Onovo A, Atobatele A, Kalaiwo A, et al. Using Supervised Machine Learning and Empirical Bayesian Kriging to Reveal Correlates and Patterns of COVID-19 Disease Outbreak in Sub-Saharan Africa: Exploratory Data Analysis. SSRN Electron J. Published online 2020. doi:10.2139/ssrn.3580721
13. Adedia D, Nanga S, Appiah SK, Lotsi A, Abaye DA. Box-Jenkins’ Methodology in Predicting Maternal Mortality Records from a Public Health Facility in Ghana. Open J Appl Sci. 2018;08(06):189-202. doi:10.4236/ojapps.2018.86016
14. Nyoni SP, Nyoni T. Prediction of Infant Mortality Rate in Gambia Using Artificial Neural Networks. Int Res J Innov Eng Technol. 2021;5(3):587-591. Accessed July 15, 2024. https://search.proquest.com/openview/2a14bfbd31c46e1025ada1c11a39bbab/1?pq-origsite=gscholar&cbl=5314840
15. Khagayi S, Amek N, Bigogo G, Odhiambo F, Vounatsou P. Bayesian spatio-temporal modeling of mortality in relation to malaria incidence in Western Kenya. PLoS One. 2017 Jul 13;12(7):e0180516.
16. Nyoni SP, Nyoni T. Forecasting Infant Mortality Rate in Madagascar Using Artificial Neural Networks. Int Res J Innov Eng Technol. 2021;5(3):576-580. Accessed July 15, 2024. https://search.proquest.com/openview/a59fe92ceb57cd5b8c47280e55ced993/1?pq-origsite=gscholar&cbl=5314840
17. Siamba S, Otieno A, Koech J. Application of ARIMA, and hybrid ARIMA Models in predicting and forecasting tuberculosis incidences among children in Homa Bay and Turkana Counties, Kenya. PLOS Digit Heal. 2023;2(2):e0000084. doi:10.1371/journal.pdig.0000084
18. Singh K, Brodish P, Speizer I, et al. Can a quality improvement project impact maternal and child health outcomes at scale in northern Ghana? Heal Res Policy Syst. 2016;14(1). doi:10.1186/S12961-016-0115-2
19. Dwomoh D, Amuasi S, Agyabeng K, Incoom G, Alhassan Y, Yawson AE. Understanding the determinants of infant and under-five mortality rates: A multivariate decomposition analysis of Demographic and Health Surveys in Ghana, 2003, 2008 and 2014. BMJ Glob Heal. 2019;4(4). doi:10.1136/bmjgh-2019-001658
20. Avoka JA, Dun-Dery EJ, Seidu I, et al. Time series analysis of the relationship between diarrhea in children and Rota 2 vaccine in the Fanteakwa District of the eastern region of Ghana. BMC Pediatr. 2021;21(1). doi:10.1186/S12887-021-02540-3
21. DerSarkissian M, … CTJEC, 2013 undefined. Time series analysis of maternal mortality in Africa from 1990 to 2005. jech.bmj.com. Accessed July 15, 2024. https://jech.bmj.com/content/67/12/992.short
22. Adeyinka DA. Social determinants and child survival in Nigeria in the era of Sustainable Development Goals: Progress, challenges, and opportunities. 2020;(September). Accessed July 15, 2024. https://harvest.usask.ca/bitstream/handle/10388/13065/ADEYINKA-DISSERTATION-2020.pdf?sequence=1
23. Nyoni SP, Nyoni T. Forecasting Infant Mortality Rate in Madagascar Using Artificial Neural Networks. Int Res J Innov Eng Technol. 2021;5(3):576-580. Accessed July 15, 2024. https://search.proquest.com/openview/939d4bde84c313cd389ac1daf2ca0fe9/1?pq-origsite=gscholar&cbl=5314840
24. Nyoni SP, Nyoni T. Prediction of Infant Mortality Rate in Gambia Using Artificial Neural Networks. Int Res J Innov Eng Technol. 2021;5(3):587-591. Accessed July 15, 2024. https://search.proquest.com/openview/0c6b84e04afa980e6c8765eccf2f546d/1?pq-origsite=gscholar&cbl=5314840
25. Nyoni SP, Nyoni T. Forecasting Infant Mortality Rate in Ghana Using a Machine Learning Algorithm. Int Res J Innov Eng Technol. 2021;5(3):622-626. Accessed July 15, 2024. https://search.proquest.com/openview/62cac18bbe9acf08d62cd6f5df5fe957/1?pq-origsite=gscholar&cbl=5314840