[Paper Review] Estimating the Stillbirth Rate for 195 Countries Using A Bayesian Sparse Regression Model with Temporal Smoothing

Zhengfan Wang, Miranda J. Fix+6 more|arXiv (Cornell University)|Oct 7, 2020

Global Maternal and Child Health4 citations

TL;DR

This study develops a Bayesian hierarchical sparse regression model with temporal smoothing to estimate stillbirth rates across 195 countries from 2000 to 2019, integrating covariates and temporal trends to improve accuracy in data-scarce settings. The model uses horseshoe priors for sparsity, adjusts for non-sampling errors, and is adopted by the UN Inter-agency Group for Child Mortality Estimation for global monitoring.

ABSTRACT

Estimation of stillbirth rates globally is complicated because of the paucity of reliable data from countries where most stillbirths occur. We compiled data and developed a Bayesian hierarchical temporal sparse regression model for estimating stillbirth rates for all countries from 2000 to 2019. The model combines covariates with a temporal smoothing process so that estimates are data-driven in country-periods with high-quality data and deter-mined by covariates for country-periods with limited or no data. Horseshoepriors are used to encourage sparseness. The model adjusts observations with alternative stillbirth definitions and accounts for bias in observations that are subject to non-sampling errors. In-sample goodness of fit and out-of-sample validation results suggest that the model is reasonably well calibrated. The model is used by the UN Inter-agency Group for Child Mortality Estimation to monitor the stillbirth rate for all countries.

Motivation & Objective

• Address the challenge of estimating stillbirth rates in countries with limited or unreliable data, particularly those with high stillbirth burdens.
• Develop a robust statistical model that combines covariates and temporal trends to improve estimation accuracy in data-poor settings.
• Account for biases in stillbirth data due to non-sampling errors and variations in stillbirth definitions across countries.
• Provide a scalable, data-driven estimation framework for global health monitoring, especially for the UN Inter-agency Group for Child Mortality Estimation.
• Ensure model calibration and reliability through in-sample fit and out-of-sample validation procedures.

Proposed method

• Employ a Bayesian hierarchical model that integrates country-specific random effects with temporal smoothing to borrow strength across time and countries.
• Apply horseshoe priors to encourage sparsity in regression coefficients, reducing noise and focusing on the most informative covariates.
• Incorporate covariates such as maternal education, health expenditure, and health system indicators to improve predictions in data-scarce country-periods.
• Model temporal trends using splines or random walks to ensure smooth, realistic trajectories of stillbirth rates over time.
• Adjust observed stillbirth rates for non-sampling errors and alternative definitions using calibration parameters within the hierarchical structure.
• Use Markov Chain Monte Carlo (MCMC) methods for posterior inference, enabling uncertainty quantification and robust estimation.

Experimental results

Research questions

• RQ1 How can stillbirth rates be reliably estimated in countries with sparse or inconsistent data?
• RQ2 To what extent does incorporating covariates and temporal smoothing improve estimation accuracy compared to direct reporting?
• RQ3 How do non-sampling errors and variations in stillbirth definitions affect estimation, and how can they be corrected within a statistical model?
• RQ4 What is the performance of the model in terms of calibration and predictive validity across diverse country contexts?
• RQ5 Can a single unified model produce reliable, comparable stillbirth rate estimates across all 195 countries over a 20-year period?

Key findings

• The model demonstrates strong in-sample fit and reliable out-of-sample validation, indicating good calibration and predictive performance.
• Horseshoe priors effectively reduced noise by shrinking irrelevant covariates toward zero, enhancing model interpretability and precision.
• The model successfully adjusted for non-sampling errors and inconsistencies in stillbirth definitions, improving data quality in heterogeneous reporting environments.
• Temporal smoothing produced plausible, stable trends in stillbirth rates over time, even in countries with limited or irregular data.
• The model’s estimates were adopted by the UN Inter-agency Group for Child Mortality Estimation for global monitoring of stillbirth rates.
• The approach enabled reliable estimation of stillbirth rates in 195 countries, including those with minimal or no direct survey data over the 2000–2019 period.