Comparative machine learning survival models for under-five mortality in Southern Africa with frailty modelling

Child survival remains central to achieving Sustainable Development Goals (SDGs) 3 and 10, particularly in sub-Saharan Africa where inequalities in health outcomes persist. This study aimed to predict under-five survival in Southern Africa using advanced machine learning survival models and to examine the influence of household composition, maternal care giving, and unobserved community-level heterogeneity on child mortality outcomes.

A retrospective cohort was constructed using Demographic and Health Survey (DHS) birth-history data from Malawi, South Africa, Zambia, and Zimbabwe. Survival time was measured from birth until death before age five or censoring at the time of interview, with a maximum follow-up period of 59 months. Three survival modelling approaches were evaluated: Random Survival Forests (RSF), DeepHit, and DeepFrailty. The DeepFrailty model incorporated DHS cluster identifiers to account for unobserved community-level heterogeneity. Model performance was assessed using the concordance index (C-index) and Integrated Brier Score (IBS), while calibration analyses and five-fold cross-validation were used to evaluate predictive reliability and model robustness.

Survival probabilities remained consistently high across all four countries, exceeding 0.97 throughout the follow-up period. South Africa generally demonstrated the most favourable survival outcomes and lowest mortality risk, whereas Zambia showed comparatively lower survival probabilities and higher cumulative hazard levels over time. Among the evaluated models, RSF achieved the strongest predictive performance across countries, with C-index values ranging from 0.8890 to 0.9458 and IBS values ranging from 0.0062 to 0.0097. DeepHit demonstrated slightly lower predictive performance (C-index: 0.5889-0.8943; IBS: 0.0085-0.0140), while DeepFrailty produced comparatively lower predictive accuracy (C-index: 0.8385-0.9159; IBS: 0.0164-0.0212). However, DeepFrailty provided clearer separation of survival and cumulative hazard curves across countries by capturing latent community-level heterogeneity through the frailty component. Important predictors of under-five survival included "births in the past year", "total number of living children", "total children ever born", "currently breastfeeding", and "birth order", highlighting the importance of household composition, fertility behaviour, and maternal caregiving practices in child survival.

The findings demonstrate the potential of machine learning survival models for improving under-five mortality prediction and risk stratification in Southern Africa. RSF emerged as the most accurate and robust predictive model, while DeepFrailty provided valuable insights into unobserved socioeconomic and community-level heterogeneity influencing child survival. The results further emphasise the importance of targeted, context-specific interventions focusing on maternal healthcare, family planning, breastfeeding promotion, and household-level support to improve child survival outcomes. Future work should focus on improving the interpretability of deep learning survival models and incorporating additional contextual information to support evidence-based public health interventions aligned with SDGs 3 and 10.