Alpha Power Transformed Beta Regression with Application on Antenatal Care Visit Proportions Among Ethiopian Women

This study introduces a novel regression model based on the Alpha Power Transformed Beta (APTBeta) distribution to analyze maternal antenatal care (ANC) utilization among 2913 eligible women from the Mini Ethiopian Demographic Health Survey 2019 dataset. Implemented within the Generalized Additive Model for Location, Scale, and Shape (GAMLSS) and Bayesian frameworks, the APTBeta model enhances traditional beta distributions by incorporating a shape controlling parameter, improving flexibility in modeling skewed, bounded outcomes like ANC utilization rates. The APTBeta model demonstrated superior performance with an AIC of − 5427.932 and BIC of − 5051.38, outperforming alternatives such as Top-Lione and Beta distributions. Simulation studies confirmed that Maximum Likelihood Estimation (MLE) improved parameter recovery, with estimates for parameter a approaches to true parameter 0.4 from 0.99 (MSE = 2.63) at n = 75 to 0.38 (MSE = 0.015) at n = 1500. Bayesian estimation with n = 2500 yielded posterior estimates $$\widehat{a}$$ = 0.98, $$\widehat{b}$$ =0.37, and $$\hat{\alpha }$$ =16.74, with effective sample sizes exceeding 4500 and $$\widehat{R}$$ = 1.00. Key predictors of ANC utilization identified in both frameworks include maternal age at first birth, economic status, educational level, age group, place of residence, and regional disparities. Specifically, older maternal age at first birth was associated with a 1.41 times increase in ANC usage, while higher education correlated with a 25% increase. Urban residency and improved household wealth contributed to an 18% increase in ANC utilization; however, rural residence and regions like Gambela and Somali were linked to lower rates. The scale parameter (σ) indicated increased shape in ANC usage with a coefficient of 0.035875 for age at first birth, while rural women showed lower shape (coefficient of − 0.20379). The shape parameter (α) was estimated at 0.01749, indicating a more symmetric distribution of ANC visits with increasing maternal age, whereas rural women exhibited a skewed distribution (coefficient of − 0.10309). These findings underscore the necessity of targeted interventions to enhance access to maternal health services in rural areas, improve women's education, and address economic inequalities. The study demonstrates the utility of user-defined distributions in modeling complex healthcare behaviors and contributes to statistical methodologies in public health research.