Modeling Under-Five Mortality Using Advanced Count Regression Techniques: Evidence from Water, Sanitation, and Hygiene Indicators in Ethiopia

Background: Under-five mortality remains a critical public health challenge in Ethiopia, with water, sanitation, and hygiene (WASH) conditions playing a substantial role. Methodologically, under-five mortality data derived from household surveys are characterized by count outcomes, overdispersion, and excess zero observations, which violate the assumptions of conventional regression approaches. Robust statistical modeling is therefore essential to ensure valid inference and policy relevance. Objective: This study aimed to model under-five mortality using advanced count regression techniques and to quantify the effects of water, sanitation, and hygiene indicators on under-five mortality in Ethiopia, while systematically evaluating model adequacy and fit. Methods: Data were obtained from the 2019 Ethiopian Mini Demographic and Health Survey (EMDHS), comprising 5,753 women of reproductive age with under-five children. The outcome variable was the number of under-five child deaths per household. A sequence of count regression models—including Poisson, Negative Binomial, Zero-Inflated, and Hurdle models—were fitted. Overdispersion diagnostics, likelihood-based tests, and information criteria (AIC) were employed to guide model selection. Model parameters were estimated using maximum likelihood methods, and results were interpreted using incidence rate ratios. Results: The Poisson regression model exhibited significant overdispersion (residual deviance/df > 1), indicating violation of the equidispersion assumption. Among the competing models, the Negative Binomial regression model provided the best fit (lowest AIC). After adjustment for covariates, rural residence was associated with a significantly higher rate of under-five mortality compared with urban residence (IRR ≈ 1.30, p < 0.01). Households lacking improved sanitation facilities, including those with no toilet facility or bush/field defecation, experienced substantially higher mortality rates (IRR > 1.50, p < 0.05). Reliance on unsafe drinking water sources, particularly surface water such as rivers and lakes, was also significantly associated with increased under-five mortality (IRR ≈ 1.18, p < 0.05). In addition, households sharing toilet facilities had higher mortality rates than those with private facilities (IRR ≈ 1.21, p < 0.01). Conversely, female-headed households showed a reduced rate of underfive mortality (IRR ≈ 0.88, p < 0.05). Household radio ownership was significantly associated with under-five mortality, reflecting differential exposure to health-related information (p < 0.05). Conclusion: Advanced count regression modeling provides a statistically robust framework for analyzing under-five mortality data in Ethiopia. The findings highlight the critical role of WASH-related factors and demonstrate the importance of appropriate model selection when addressing overdispersed health count data. These results offer both methodological and policy-relevant insights for reducing under-five mortality in low-resource settings.