Analysing First Birth Interval by A CART Survival Tree

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.

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.

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.

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.