Key variables

Bishop score components

Patient-level characteristics

Table 1. Patient-level summary by median (inter-quartile range; IQR)
C-section (N=18) Vaginal delivery (N=114) p-value*
Age (years) 24.5 (23, 28) 24 (23, 27) 0.627
GA (weeks) 39.7 (39, 40) 39.6 (39.1, 39.9) 0.950
Bishop score 5 (4, 6) 6 (5, 8) 0.027
Cervical length (cm) 3.1 (2.9, 4) 2.6 (2, 3.3) 0.010
SWS^-2 (5mm) 0.42 (0.31, 0.57) 0.42 (0.32, 0.57) 0.377
SWS^-2 (10mm) 0.49 (0.32, 0.59) 0.47 (0.39, 0.61) 0.155

*Wilcoxon rank sum test.

Location and push side of SWS

For each patient, we take the median SWS\(^{-2}\) for each combination of location (5 or 10mm) and push side (R or L). To see whether location or push side matters, we fit logistic regression models for induction and intervention against SWS\(^{-2}\) and its interactions with location and push side (see below). Because the interaction terms are non-significant, we conclude that location and push side do not significantly affect the relationships between SWS\(^{-2}\) with the outcomes. We thus take the median SWS\(^{-2}\) within each patient across locations and push sides.

Table 2a. Logistic regression of induction
Estimate Std. Error z value Pr(>|z|)
(Intercept) 1.2266896 0.3960911 3.0969888 0.0019550
inversesws_sq 1.2996282 1.2950871 1.0035064 0.3156166
inversesws_sq:X -0.0007143 0.1201708 -0.0059442 0.9952573
inversesws_sq:pushSideR -0.1464662 0.6021954 -0.2432203 0.8078347
Table 2b. Logistic regression of intervention
Estimate Std. Error z value Pr(>|z|)
(Intercept) 1.0060314 0.2982505 3.3731088 0.0007432
inversesws_sq -0.4972082 0.8948527 -0.5556313 0.5784629
inversesws_sq:X -0.0619567 0.0825767 -0.7502929 0.4530783
inversesws_sq:pushSideR 0.3113852 0.4127800 0.7543612 0.4506324

Predictive performance of BS, CL, and SWS individually

ROC analyses below show

Predictive performance of BS, CL, and SWS combined

Logistic regression models are built to combine multiple predictors. The AUC is assessed objectively using \(K\)-fold cross-validation (\(K=3\) for induction and 5 for intervention by sample size considerations). Its 95% confidence interval (CI) is calculated by the bootstrap. Wald tests are used to assess whether each variable can be dropped from the model (even if a variable is tested signicant, it may not improve predictive performance due to the possibility of overfitting).

BS + CL

Combining BS and CL does not improve upon either variable alone in predicting successful induction, nor does it improve upon BS alone in predicting intervention.

Table 3a. Wald-test p-values in logistic regression models with BS and CL.
Induction Intervention
BS 0.5736960 0.0001104
CL 0.0472303 0.0775713

BS + SWS\(^{-2}\)

Adding SWS\(^{-2}\) to BS does not improve predictive performance for induction or intervention.

Table 3b. Wald-test p-values in logistic regression models with BS and SWS.
Induction Intervention
BS 0.0637214 0.0000003
inversesws_sq 0.4660471 0.5698568

BS + CL + SWS\(^{-2}\)

Adding SWS\(^{-2}\) to BS \(+\) CL does not improve predictive performance for induction or intervention either.

Table 3c. Wald-test p-values in logistic regression models with BS, CL, and SWS.
Induction Intervention
BS 0.5857862 0.0001379
CL 0.0676183 0.0922736
inversesws_sq 0.9402412 0.9970362

Conclusion

The best performing model for successful induction is CL alone; the best performing model for intervention is BS alone (or in combination with CL).

Components of Bioshop score

ROC analyses of individual components of BS are shown below (AUCs of BS for induction and intervention are 0.665 and 0.813, respectively; see above).

Logistic regression of induction (Table 4a) shows that the most important component is dilation. Likelihood ratio test (LRT) of a dilation-only model against the full model produces a \(p\)-value of 0.2992, suggesting that dilation alone provides adequate fit.

Table 4a. Logistic regression of induction.
Estimate Std. Error z value Pr(>|z|)
(Intercept) 0.3559124 1.0257322 0.3469837 0.7286036
Pos -0.6588257 0.5286873 -1.2461537 0.2127080
Consist -0.5603197 0.5061718 -1.1069754 0.2683046
Efface 0.2748333 0.5443419 0.5048910 0.6136354
Dil 1.7067896 0.6099443 2.7982713 0.0051377
Station 0.9476943 0.5135459 1.8453937 0.0649803

Logistic regression of intervention (Table 4b) shows that the most important components include consistency, effacement, and dilation.

Table 4b. Logistic regression of intervention.
Estimate Std. Error z value Pr(>|z|)
(Intercept) 6.8708800 1.3665354 5.0279559 0.0000005
Pos 0.0019060 0.4142638 0.0046008 0.9963291
Consist -1.1083116 0.4675144 -2.3706470 0.0177570
Efface -0.7939827 0.4714412 -1.6841605 0.0921507
Dil -2.4997555 0.7648904 -3.2681224 0.0010826
Station -0.3926729 0.3891249 -1.0091180 0.3129181

We refit the model with these components only (Table 4c; LRT against full model $p=$0.5883). Given the other two, effacement is only borderline significant.

Table 4c. Logistic regression of intervention - submodel.
Estimate Std. Error z value Pr(>|z|)
(Intercept) 6.9050557 1.3585869 5.082528 0.0000004
Consist -1.1589758 0.4574850 -2.533364 0.0112974
Efface -0.8969403 0.4500048 -1.993180 0.0462418
Dil -2.5543894 0.7637605 -3.344490 0.0008243

ROC analyses with “Consist + Dil” and “Consist + Dil + Efface” are shown below.

Conclusion

The main predictor of successful induction is dilation; the main predictors of intervention are consistency + dilation (+ effacement).