Comparisons of cox semi-parametric and parametric shared frailty models: application for under-five children survival in sub-Saharan Africa

Abstract

Abstract Background The under-five child mortality in sub-Saharan African (sSA) countries is a persistent problem with limited effort being made to explore the determinants of disparities across countries and their lower administrative districts. A child’s survival may depend on several known and unknown covariates and vary across the study areas. The main objective of this study is to assess the time to death of under-five children and its associated risk factors by comparing the performance of semiparametric and parametric frailty models across sSA regions. Methods We used a dataset from the Demographic and Health Survey (DHS) across 33 sSA countries. The semiparametric and parametric models with different frailty distributions were used to model the under-five survival time of children across the administrative districts of 33 sSA countries. Results A total of 330,373 under-five children were included in the study, of whom 19,893 (6.02%) died before reaching their 5th birthday. Unobserved country-level variance $$\:\left(0\:.421\right)$$ and district-level variance (0.183) effects considerably impacted the survival time of under-five children in sSA countries. Under-five children born to mothers aged 25–29 and 30–49 were 16% and 20% less likely to die compared to children born to mothers younger than 24 years. Moreover, children born in rural areas were 8.3% more likely to die than those who were born in urban areas. Children who were born from mothers with better access to improved water sources and clean fuel were 9% and 11% less likely to die than their counterparts, respectively. Conclusions The exponential shared frailty hazard model with lognormal frailty distribution demonstrated better performance compared to the Cox semiparametric model for identifying risk factors for under-five children across sSA countries. Place of residence, wealth index, media exposure, birth order, birth interval, access to improved water, and use of clean fuels for cooking were the significant risk factors on time to death of under-five children in sSA.

Keywords

• Demographic and health survey
• Frailty models
• Under-five mortality
• Parametric models
• Random effects
• Unobserved heterogeneity