Analysis of Birth Growth: Using a Mixture Cure Frailty Model.

Background: The birth rate is important in population growth. Concerns are growing over declining birth rates in Iran, as a developing country in the past decade. The present study aimed to examine population growth in Hamadan and the factors influencing the birth rate.

Methods: This retrospective cohort study utilized data from 633 families with their first child in 2012 in Hamadan-information updated in 2022. The Kaplan-Meier plateau indicates a curing pattern; therefore, a mixture cure frailty model was employed to estimate the probability and hazard rate of having different numbers of children. This model comprises 2 components: the first estimates the probability of birth (or nonbirth, indicating cure), while the second component calculates the birth hazard rate for having different number of children.

Results: Mothers with high school diploma (odds ratio [OR], 0.049; = 0.004) and under diploma (OR, 0.449; < 0.001) education levels and fathers with under diploma (OR, 0.802; = 0.021) education levels were linked to a lower risk of birth and a higher chance of a cure. Moreover, high school diploma (hazard ratio [HR] = 0.668; < 0.001) and under diploma (HR = 0.821; < 0.001) education levels in mothers significantly decreased the birth hazard rate. The shape parameter in the hazard function (μ = 0.933; SE = 0.049) indicates that the hazard rate of birth was decreasing during the follow-up time.

Conclusion: The study found that the mixture cure frailty model was effective in analyzing birth rates, with couples showing a decreased inclination to have more than 2 children. One contributing factor to this trend is the mothers' education and employment.