Analysing First Birth Interval by A CART Survival Tree

Document Type : Original Article


National Population Studies and Comprehensive Management Institute, Statistical Methods and Population Modeling Group, Tehran, Iran


Background: Birth spacing, especially the first birth interval (FBI), is a suitable index to investigate the delayed fertility
that results in a low fertility pattern. Non-parametric familiar alternatives to the Cox proportional hazard regression
(CPH) model include survival trees that can automatically discover certain types of covariate interactions according to
the survival length. The aim of this research is to study FBI influential factors by applying survival trees.
Materials and Methods: In this cross-sectional study, 610 married women (aged 15-49 years), were selected from
different regions of Tehran, Iran in the Winter and Spring of 2017. Classification and regression trees (CART) for the
FBI survival tree were fitted by taking into consideration the predictors of each woman’s age, age at first marriage,
educational level, partner’s educational level, activity, region, house ownership, kinship, partner’s race, marriage time
attitude, and expenditure using R packages.
Results: Since the PH assumption of the CPH model was not confirmed for the covariates of age at first marriage (P=0.001),
kinship (P=0.000), partner’s race (P=0.001), and marriage time attitude (P=0.042), the results of this model were not valid.
Thus, a CART survival tree was fitted. The validity of the fitted model in assessing FBI was confirmed by the significant
result of the log rank test (p <0.01) for the terminal nodes and the value of the separation measure, which was greater than
1. The fitted tree had 13 terminal nodes and the most vital FBI predictor was women’s age. The longest FBI belonged to
educated and employed women, ages 30-37 years.
Conclusion: Analysing patterns of birth spacing by selecting the appropriate statistical method provides important information
for health policymakers. In order to formulate appropriate demographic policies, it is essential to take into consideration
age, educational level and job status of the women, all of which have essential roles on their decision to have children.