Statistical analysis

The large sample size allowed for independent training and validation cohorts. The overall sample was divided randomly into a training cohort (70%) and a validation cohort (30%), stratifying by ePTB status to ensure a balanced partition. Descriptive statistics were summarized to compare the demographic and pre-pregnancy information between the two cohorts of data. The training sample was used to build models via both logistic regression and CART and the validation sample was used to evaluate the models obtained from the training cohort.

In order to investigate the association of ePTB with the potential risk factors, a multivariate logistic regression model was applied to estimate odds ratios (OR) and the corresponding 95% confidence intervals (CI). All predictors entered the model and they were selected via backward elimination. We set the significance level to stay in the model for a predictor to 0.05. A further simplified logistic regression model was fitted using 10 covariates to explore risk subgroups of ePTB. The predicted probabilities were calculated for the validation cohort based on the simplified model obtained from the training cohort. Based on the validation cohort, the calibration plot was generated to compare the average predicted probabilities and the average observed probabilities. The c-index was calculated to identify the model discriminatory capacity in terms of the training and validation cohorts.

CART model can be a very useful complement to a logistic regression model because the CART model can identify unknown interactions among the risk factors of ePTB. CART is a nonparametric method that derives hidden patterns in data by constructing a series of binary splits on the outcome of interest [27–29]. The most discriminating predictor is selected to form the first partition based on the ability of the variables to minimize the within-group variance of the dependent variable, so the observations within each subgroup share the same characteristics that influence the probability of belonging to the interested response group [30]. This step is executed repeatedly to each partition until the sample size of each subgroup (i.e., a terminal node) is at or below a pre-specified level. In this study, the terminal node was specified as 0.5% of the total sample (either the training sample or the validation sample). A maximum tree first was constructed and standard pruning strategies were then applied to arrive at a parsimonious tree with a low misclassification rate and a high discriminatory capacity [31]. The final CART model can be visualized as an upside-down tree with the parent node of the tree containing the entire sample. Additional child nodes can be created using the Gini splitting rule for binary outcomes [32], and the terminal nodes are where predictions and inferences are made. The training cohort was used to generate an appropriate CART tree, and the validation cohort was utilized to evaluate the CART tree via the C-index and the misclassification rate.

All statistical tests were two-tailed with p ≤ 0.05 as the statistically significant level. The CART analysis was executed in SAS Enterprise Miner Workstation 13.1 [32], and all other statistical analyses and the data management were conducted with SAS 9.4.