Infant mortality across EU health systems: heterogeneity encoding, fixed effects regression, and machine learning in a small macro panel

Abstract

Introduction The infant mortality rate is widely used in comparative health research, but less is known about how panel regression and machine-learning models perform in small macro-level health datasets when they are evaluated using comparable information and the same out-of-period test period. Methods Using a balanced panel of 25 European Union countries observed annually from 2000 to 2022 (575 country-year observations, no missing data) assembled from OECD and World Bank sources, we separated an explanatory analysis from a predictive analysis. The explanatory layer used a two-way fixed effects regression with country-clustered standard errors. The predictive layer trained pooled linear regression, tuned Random Forest, Gradient Boosting, and a Multilayer Perceptron, with and without explicit country information, on 2000–2017 and evaluated them on a held-out 2018–2022 window, alongside two naive benchmarks (persistence and historical country mean) and two prediction-compatible fixed effects specifications. Hyperparameters were tuned by expanding-window temporal cross-validation within the training period, leaving the test window untouched. Results Under common out-of-period evaluation, a simple persistence benchmark achieved the strongest predictive performance (R2 = 0.74), closely followed by tuned Gradient Boosting and Random Forest with country information (R2 = 0.71 and 0.69). Explicit country encoding improved the tree-based models, but adding country information was not enough to improve the linear specifications substantially. The prediction-compatible fixed effects and pooled linear models both produced negative out-of-period R2 values. Model rankings varied across evaluation windows: in an alternative pre-pandemic split, tuned nonlinear models outperformed persistence. In the explanatory fixed effects model, GDP per capita and the total fertility rate were significant under conventional country-clustered inference, although neither remained significant under a small-cluster wild-bootstrap sensitivity analysis; the substantive covariate block had a partial R2 of 0.366 net of country and year effects. Conclusion In this EU infant-mortality panel, much of the predictive signal came from persistent country-specific outcome history. Country information improved the tree-based models, while model flexibility also remained important. The strong within-panel fit of the fixed-effects model did not translate into strong out-of-period prediction.