Modelling count data on timie to first antenatal care visit using truncated betageometric distribution

Abstract

Understanding the timing of the first antenatal care (ANC) visit requires statistical methods capable of handling bounded, skewed, and heterogeneous count outcomes subject to truncation. Conventional count models such as the Poisson and Negative Binomial are often inadequate in this setting due to their limited ability to accommodate simultaneous truncation and dispersion effects. This paper introduces the Truncated Beta-Geometric (TBG) distribution as a flexible modelling framework for truncated discrete data. The TBG model, derived by truncating the standard Beta-Geometric distribution, accommodates overdispersion, underdispersion, and bounded count outcomes, addressing heterogeneity in healthseeking behavior. Key statistical properties of the TBG distribution, including its probability mass function, mean, and variance, are presented along with a numerical parameter estimation method using maximum likelihood. A Monte Carlo simulation study evaluated the performance of the model under different sample sizes, truncation intervals, and parameter settings, demonstrating that estimator bias stems more from structural features than sample size. The model is applied to data from the 2000 Oman National Health Survey, where timing to first ANC visit was recorded across 1,299 women having ANC visits. The results demonstrate that TBG outperformed the untruncated Beta-Geometric, in terms of AIC, BIC, and goodness-of-fit. The model is further extended to a regression framework, allowing covariate inclusion. The results demonstrate significant associations of ANC timing with maternal age, education, parity, and urban residence. The TBG regression model demonstrated superior flexibility and interpretability, establishing it as a robust tool for modeling truncated count outcomes in public health research.

Journal of Statistical Research 2026, Vol. 60, No. 1, pp. 91-111.