External validation of calculator for cesarean delivery during induction of labor

Abstract

Objective

To validate a published risk calculator to predict cesarean delivery (CD) among singletons undergoing induction of labor.

Methods

Our retrospective cohort study included singletons undergoing induction of labor. A predicted CD score was calculated for each individual based on a previously developed calculator. External validation of the calculator was assessed by the discriminative power of the model by using the area under the receiver operating characteristic curve, and by a calibration curve. The score was categorized as less than 10%, 10% to less than 30%, and 30% or greater. The primary outcome was CD. The secondary outcomes were a composite maternal adverse outcome (CMAO) and composite neonatal adverse outcome (CNAO). Multivariable Poisson regression models with robust error variance were used to estimate the association; adjusted relative risks with 95% confidence interval (CI) were calculated.

Results

Among 548 women, 159 (29%) had CD. The area under the curve was 0.77 (95% CI 0.73–0.81), and the calibration curve and its 95% confidence band demonstrated good calibration. The likelihood of having a CD was higher in those with a score from 10% to less than 30% (adjusted relative risk [aRR] 2.65, 95% CI 1.58–4.45) and 30% or greater (aRR 5.73, 95% CI 3.55–9.25). The risk of CMAO was higher in those with a score between 10% and less than 30% (aRR 1.64, 95% CI 1.08–2.48) and 30% or greater (aRR 1.81, 95% CI 1.20–2.73). The risk of CNAO was similar across groups.

Conclusions

The previously developed prediction model demonstrated good external validity in our cohort. Our analyses suggest that a higher predicted CD score was associated with an increased likelihood of CD and CMAO.

1. INTRODUCTION

The rate of induction of labor has steadily increased from 12.5% in 1997 to 23.9% in 2018 ¹ , ² with the primary goal being the achievement of a safe vaginal delivery. ³ The likelihood of cesarean delivery (CD) during induction has varied from 9% to 59%. ³ , ⁴ , ⁵ , ⁶ , ⁷ , ⁸ A clinically useful shared decision making tool with an acceptable predictive value would help to guide discussions about induction and the risks of adverse outcomes. ⁹

Predictive models have been developed to identify individuals undergoing induction who are at high risk of needing CD. These prognostic models, focusing on low‐risk nulliparous to high‐risk preterm inductions, have sample sizes varying from 264 to 4.1 million. ⁹ , ¹⁰ , ¹¹ , ¹² , ¹³ , ¹⁴ , ¹⁵ , ¹⁶ However, few of these models have been validated in an external population or linked with adverse outcomes. ⁹ We sought to validate a published risk calculator derived from a national population‐based cohort in the USA. This was chosen because it can be used during the antepartum period, applies to nulliparous and parous women, does not require physical or sonographic examination, and applies to preterm inductions. ¹²

The primary objective of our study was to validate the risk calculator proposed by Rossi et al. ¹² at our large academic level IV center, which as a tertiary referral institution manages a diverse urban population with a significant proportion of high‐risk pregnancies and consistently has high induction rates often exceeding over 40%. ¹⁷ The secondary purpose was to assess if the predicted likelihood of CD is associated with adverse outcomes. We hypothesized that the predictive model based on US live‐birth records would be applicable to our practice and that the risk of composite adverse outcomes will increase as the likelihood of CD increases.

2. MATERIALS AND METHODS

We performed a retrospective cohort study among pregnant women undergoing labor induction at our level IV academic hospital from March 2020 to September 2020. Our study population included consecutive women with singleton, non‐anomalous pregnancies with no previous CD, who underwent labor induction, delivered at 32 weeks or more of pregnancy, and had a live birth. We excluded individuals with previous CD who were being induced because for a trial of labor after CD, the existing calculator from the Maternal‐Fetal Medicine Units Network was used at our institution. ¹³ Induction was defined as an attempt to achieve a vaginal delivery by using mechanical or pharmacologic agents before the onset of spontaneous labor. ³ Our study was approved by the institutional review body (HSC‐MS‐21‐0383). All delivery records during the study timeframe were accessed from the electronic medical record system and relevant data points, including patient demographics, obstetrical history, and outcomes were abstracted directly from the electronic medical record into a secure REDCap database. All data abstraction was performed by physicians with ample clinical knowledge and familiarity with the electronic medical record platform. Additionally the individual responsible for inputting the calculator variables was blinded to the study outcomes (CD vs. vaginal delivery) during this data abstraction process.

We conducted a sample size calculation for external validation of a predictive model with a binary outcome. Based on the results of Rossi et al. ¹² with area under the receiver operating curve (AUC) of 0.78, we targeted an outcome event proportion (rate of CD) of 20% for our sample size calculation. This 20% figure was chosen as a conservative estimate, reflecting the approximate overall CD rate reported in the original Rossi et al. study cohort. ¹² A total sample size of 512 participants (about 102 events) was required to achieve an expected 95% confidence interval (CI) of the AUC (0.73–0.83), with a targeted CI width of 0.1. ¹⁸

In this study, the explanatory variable was the predicted CD score, which was calculated based on the results of Rossi et al. ¹² (Appendix A, Table A1). The prediction model included seven variables: maternal age, gestational age, maternal height (in), maternal weight at delivery (lb), maternal race and ethnicity, previous CD, and previous vaginal delivery. To evaluate if a higher predicted CD score was associated with a higher risk of CD, composite maternal adverse outcomes (CMAO) and composite neonatal adverse outcomes (CNAO), the score was further categorized as three mutually exclusive CD score groups (<10%, 10% to <30%, and ≥30%), this categorization was used because this score distribution would generate study groups of roughly equal sizes.

The primary outcome was the rate of CD. For the purpose of this study, the definitions for arrest of labor and failed induction adhered to the guidelines of the American College of Obstetricians and Gynecologists. Specifically, arrest of active phase of labor was diagnosed for individuals who had reached more than 6‐cm cervical dilation with ruptured membranes and subsequently experienced either: more than 4 h of adequate uterine contractions with no cervical change or more than 6 h without adequate uterine contractions. Arrest of descent was diagnosed in individuals when the head was engaged (>0 station) and there was no further descent after more than 4 h in nulliparous individuals or more than 3 h in parous individuals. ¹⁹ Failed induction was defined as the inability to achieve active labor after at least 12–18 h of oxytocin administration following membrane rupture (either spontaneous or artificial), provided that cervical ripening efforts had been completed. ²⁰ The secondary outcomes were the rate of CMAO, which included estimated / quantitative blood loss greater than 1000mL, uterotonic use other than oxytocin usage, mechanical tamponade, surgical techniques (including O'Leary, B‐Lynch, uterine artery embolization), ²¹ transfusion of red blood cells, hysterectomy, deep venous thrombosis, pulmonary embolism, admission to the intensive care unit, and maternal death, and the rate of CNAO, which included 5‐min APGAR score less than 7, bronchopulmonary dysplasia, intraventricular hemorrhage, necrotizing enterocolitis, seizures, sepsis, meconium aspiration syndrome, ventilation for more than 6 h, brachial plexus palsy, hypoxic‐ischemic encephalopathy, and neonatal death.

Using our cohort data, we first examined the external validation of the calculator from Rossi et al. ¹² by assessing: (1) the discriminative power of the model AUC, with 95% CI, and (2) the model calibration, which was examined by graphically displaying a calibration curve to determine whether the predicted risks were similar to the observed risks.

Differences in the maternal and obstetrical characteristics stratified by predetermined CD score groups (<10%, 10% to <30%, and ≥30%) were examined using χ ² or Fisher exact tests for categorical variables, and one‐way analysis of variance test for continuous variables. The missing maternal and obstetrical characteristics were categorized and analyzed as an “unknown” group. Multivariable Poisson regression models with robust error variance were used to estimate the association between predicted CD score groups (using <10% as referent) and the primary and secondary outcomes, while adjusting for potential confounders identified in the univariate analysis, including diabetes, hypertensive disorders, and private insurance. Because the predicted CD score was generated using the seven variables listed above, we did not adjust for these variables to avoid over‐correction. The results were reported as adjusted relative risk (aRR) with 95% CI. All statistical analyses were conducted using STATA software version 17 (StataCorp LP, College Station, TX, USA). The STROBE guidelines for reporting observational studies were followed. ²²

3. RESULTS

During the study period, there were 2145 deliveries, 677 (31.6%) were induced, while 1468 (68.4%) were not. We further excluded 129 (6.0%) inductions because they met one of the exclusionary criteria. The final study sample contained 548 consecutive inductions; of these, 389 (71.0%) had a vaginal birth and 159 (29.0%) had a CD (our primary outcome, Figure 1).

FIGURE 1.

Flow diagram of the study population.

When we examined the external validation of the predictive model of CD after induction in our study population, our results noted a good discriminative power (AUC 0.77, 95% CI 0.73–0.81; Figure 2a). The calibration results with the estimated curve and its 95% confidence band confirmed that the predicted probabilities for CD were consistent with the empirical probabilities (Figure 2b). As illustrated, the predicted probability of CD largely adhered to the observed probability of CD, with narrow CIs, along a large range of predicted probability values. It only began to deviate when the chance of CD was more than 70% (at which point there were very few individuals with such probabilities). Appendix A, Figure A1 demonstrates the distribution of the predicted probabilities of the outcome for individuals with and without the outcome (CD).

FIGURE 2.

Model validation. (a) Receiver operating characteristic curve of the prediction model. The area under the receiver operating characteristic curve (AUC) = 0.77 (95% confidence interval = 0.73‐0.81). (b) Calibration curve (with 95% confidence interval) of model validation. The grey straight line is the line of perfect calibration. The blue line is the calibration curve generated by the prediction model, which is surrounded by light blue area that represent the 95% confidence band of the calibration curve.

According to the calculator, 185 (33.8%) of our cohorts had a predicted CD score of less than 10%, 190 (34.7%) had a score between 10% and less than 30%, and the remaining 173 (31.6%) individuals had a score of 30.0% or greater. Of the seven variables used in the calculator, all variables were significantly different among the three CD risk groups, except gestational age, maternal race and ethnicity, and previous CD, as our sample was limited to individuals without previous CD. Of the non‐calculator variables examined, diabetes (P = 0.01), hypertensive disorder (P < 0.01), and private insurance (P = 0.02) were maternal characteristics that differed significantly among the three groups (Table 1).

TABLE 1.

Maternal characteristics of women undergoing induction of labor. ^a

Characteristics	Predicted CD score			P‐value
	<10% (n = 185)	10% to <30% (n = 190)	≥30% (n = 173)
Calculator variables
Maternal age, years	29.1 ± 5.2	27.0 ± 6.2	29.2 ± 6.6	0.001
Maternal height, in	64.4 ± 2.7	64.6 ± 3.0	63.1 ± 2.7	<0.001
Maternal weight, lb	186.5 ± 34.9	193.8 ± 48.8	211.2 ± 44.4	<0.001
Gestational age, weeks	38.1 ± 1.3	38.1 ± 1.4	38.2 ± 1.7	0.888
Maternal race/ethnicity				0.252
White	56 (30.3)	60 (31.6)	36 (20.8)
Black	65 (35.1)	55 (28.9)	65 (37.6)
Hispanic	30 (16.2)	35 (18.4)	33 (19.1)
Other	34 (18.4)	40 (21.1)	39 (22.5)
Previous vaginal birth				<0.001
No	0 (0.0)	137 (72.1)	171 (98.8)
Yes	185 (100.0)	53 (27.9)	2 (1.2)
Previous cesarean birth	0 (0.0)	0 (0.0)	0 (0.0)	x
Non‐calculator variables
Marital status				0.806
Single	83 (44.9)	97 (51.1)	83 (48.0)
Married	90 (48.6)	83 (43.7)	83 (48.0)
Divorced/separated/widowed	2 (1.1)	3 (1.6)	1 (0.6)
Unknown	10 (5.4)	7 (3.7)	6 (3.5)
Smoking during pregnancy				0.061
No	181 (97.8)	189 (99.5)	166 (96.0)
Yes	4 (2.2)	1 (0.5)	7 (4.0)
Diabetes in pregnancy				0.010
No	156 (84.3)	176 (92.6)	143 (82.7)
Yes	29 (15.7)	14 (7.4)	30 (17.3)
Hypertensive disorders				0.001
No	135 (73.0)	110 (57.9)	97 (56.1)
Yes	50 (27.0)	80 (42.1)	76 (43.9)
Private insurance				0.017
No	105 (56.8)	94 (49.5)	72 (41.6)
Yes	80 (43.2)	96 (50.5)	101 (58.4)
Prenatal care provider				0.387
Academic Faculty and Residents	62 (33.5)	70 (36.8)	62 (35.8)
Private OB‐GYN	113 (61.1)	106 (55.8)	106 (61.3)
None	4 (2.2)	2 (1.1)	0 (0.0)
Unknown	2 (1.1)	4 (2.1)	3 (1.7)
Public clinic	4 (2.2)	8 (4.2)	2 (1.2)
Intrapartum care provider				0.674
Academic Faculty and Residents	95 (51.4)	106 (55.8)	91 (52.6)
Private	90 (48.6)	84 (44.2)	82 (47.4)

Abbreviations: CD, cesarean delivery.

^a Data are presented as mean ± standard deviation or as number (percentage).

The rate of CD differed significantly between the three groups: 9.2%, 25.3%, and 54.3% for individuals in less than 10%, 10% to less than 30%, and 30% or greater groups, respectively (P < 0.01). The CMAO varied significantly between the three groups (P < 0.01), as did the rate of postpartum hemorrhage (P < 0.01). The CNAO did not differ significantly between the three groups (Table 2).

TABLE 2.

Composite and individual adverse outcomes. ^a

Outcomes	Predicted CD score			P‐value
	<10% (n = 185)	10% to <30% (n = 190)	≥30% (n = 173)
Primary outcome
Cesarean delivery	17 (9.2)	48 (25.3)	94 (54.3)	<0.001
Secondary outcomes
Composite maternal adverse outcome	29 (15.7)	49 (25.8)	50 (28.9)	0.008
EBL/QBL ≥1000	6 (3.2)	8 (4.2)	24 (13.9)	<0.001
Uterotonic use b	26 (14.1)	41 (21.6)	39 (22.5)	0.080
Mechanical tamponade	1 (0.5)	5 (2.6)	1 (0.6)	0.229
Surgical technique (O'Leary, B‐Lynch UAE)	1 (0.5)	0 (0.0)	1 (0.6)	0.546
Transfusion	3 (1.6)	9 (4.7)	6 (3.5)	0.221
Hysterectomy	0 (0.0)	3 (1.6)	0 (0.0)	0.110
DVT/PE	0 (0.0)	1 (0.5)	0 (0.0)	1.000
Admission to ICU	0 (0.0)	0 (0.0)	0 (0.0)	x
Maternal death	0 (0.0)	0 (0.0)	0 (0.0)	x
Composite neonatal adverse outcome	3 (1.6)	5 (2.6)	5 (2.9)	0.778
5‐min APGAR score <7	1 (0.5)	4 (2.1)	1 (0.6)	0.380
Bronchopulmonary dysplasia	0 (0.0)	1 (0.5)	1 (0.6)	0.765
Intraventricular hemorrhage	0 (0.0)	0 (0.0)	1 (0.6)	0.316
Necrotizing enterocolitis	0 (0.0)	0 (0.0)	0 (0.0)	x
Seizures	1 (0.5)	0 (0.0)	0 (0.0)	0.653
Sepsis	0 (0.0)	0 (0.0)	0 (0.0)	x
Meconium aspiration syndrome	0 (0.0)	0 (0.0)	0 (0.0)	x
Ventilation >6 h	1 (0.5)	2 (1.1)	3 (1.7)	0.532
Brachial plexus palsy	0 (0.0)	0 (0.0)	0 (0.0)	x
Hypoxic ischemic encephalopathy	0 (0.0)	1 (0.5)	0 (0.0)	1.000
Neonatal death	0 (0.0)	0 (0.0)	0 (0.0)	x

Abbreviations: CD, cesarean delivery; DVT, deep venous thrombosis; EBL, estimated blood loss; ICU, intensive care unit; PE, pulmonary embolus; QBL, quantitative blood loss; UAE, uterine artery embolization; x, not calculable.

^a Data are presented as number (percentage).

^b Excluding initial routine use of oxytocin.

After multivariable adjustment, compared with the referent group (<10%), the risk for CD was significantly higher for the 10% to less than 30% group (aRR 2.65; 95% CI 1.58–4.45) and the 30% or greater group (aRR 5.73; 95% CI 3.55–9.25). Similarly, compared with the referent group (<10%), the risk of the CMAO was higher in the other two groups (10% to <30%: aRR 1.64; 95% CI 1.08–2.48; and ≥30%: aRR 1.81; 95% CI 1.20–2.73). Though the crude risk of the CNAO was not significantly different among the three groups, multivariable adjustment was not performed because of the small number of cases (Table 3).

TABLE 3.

Association between predicted cesarean delivery score and adverse outcomes.

Outcomes	Predicted CD score	Total	n	%	Crude RR (95% CI)	Adjusted RR a (95% CI)
Primary outcome
Cesarean delivery	All	548	159	29.0
	<10%	185	17	9.2	1.00	1.00
	10% to <30%	190	48	25.3	2.75 (1.64–4.6)	2.65 (1.58–4.45)
	≥30%	173	94	54.3	5.91 (3.68–9.49)	5.73 (3.55–9.25)
Secondary outcomes
Composite maternal adverse outcome	All	548	128	23.4
	<10%	185	29	15.7	1.00	1.00
	10% to <30%	190	49	25.8	1.65 (1.09–2.49)	1.64 (1.08–2.48)
	≥30%	173	50	28.9	1.84 (1.23–2.77)	1.81 (1.20–2.73)
Composite neonatal adverse outcome	All	548	13	2.4
	<10%	185	3	1.6	1.00	x
	10% to <30%	190	5	2.6	1.62 (0.39–6.70)	x
	≥30%	173	5	2.9	1.78 (0.43–7.36)	x

Abbreviations: CD, cesarean delivery; CI, confidence interval; RR, relative risk.

^a Adjusted for diabetes, hypertensive disorders, and private insurance; x, adjusted RR is not calculated due to small case numbers. Values in bold type indicate statistical significance.

In individuals with a predicted CD score less than 10%, most CDs were due to nonreassuring fetal heart tones (64.7%). For those individuals with a score of 30% or greater, the majority of the CDs were due to arrest disorders (Table 4).

TABLE 4.

Indication for cesarean delivery. ^a

	Predicted CD score
	<10%	10% to <30%	≥30%	All
n	17	48	94	159
Arrest	5 (29.4)	24 (50)	58 (61.7)	87 (54.7)
NRFHTs	11 (64.7)	21 (43.8)	31 (33)	63 (39.6)
Other	1 (5.9)	5 (10.4)	12 (12)	18 (11.3)
Malpresentation	0	3 (6.3)	1 (1.1)	4 (2.5)

Abbreviations: CD, cesarean delivery; NRFHT, nonreassuring fetal heart tones.

^a Data are presented as number (percentage).

4. DISCUSSION

In our study population, we were able to externally validate the risk calculator proposed by Rossi et al. ¹² among individuals being induced. The AUC for our population (0.77) was akin to that in the original model (0.78).The rate of CD differed significantly for the three groups of predicted CD score, and the rate of the CMAO was also significantly different in the three groups. The CNAO occurred infrequently and the rate did not differ significantly among the three groups. Our cohort encompassed both elective and medically indicated inductions, reflecting the real‐world population managed at a tertiary center. We observed that individuals with a predicted CD score greater than 30% were more likely to have comorbidities such as diabetes and hypertensive disorders. These observed differences were accounted for through multivariable adjustment in our analysis. Additionally, the observed CD rate among induced labors in our cohort was 29%, higher than the 20% used for the sample size calculation, and consistent with our institution's profile as a level IV tertiary referral center managing a significant proportion of high‐risk pregnancies and maintaining high overall institutional primary CD rates of 31%.

A correlative of externally validating the predictive model is that it should be used in practice. There are several reasons to use the risk calculator for labor induction. When indicated, the majority of patients accept induction and up to 40% of low‐risk pregnancies accept induction. ²³ Given these high rates, a risk calculator permits shared decision making about the risks and chances of successful induction. Most clinicians are comfortable using calculators for counseling ¹³ , ²⁴ and the calculator of Rossi et al. is publicly available (https://ob.tools/iol‐calc). This calculator does not require a physical or sonographic examination, which means an individual can use the calculator for their own risk prediction, or this tool could be adapted for telemedicine consultations. The Rossi et al. calculator, while suggested for use “in addition to the Bishop score,” offers a key advantage as it was developed without Bishop score data but achieved comparable predictive accuracy (AUC 0.787) to calculators that include it. ¹⁰ , ¹² Our external validation (AUC 0.77) confirms this independent utility and its association with maternal adverse outcomes, thereby enhancing pre‐induction risk assessment. Given the recent publication of the multi‐center, randomized trial of elective induction at 39 weeks in low‐risk pregnancies, the safety of induction has been demonstrated. ²⁴ When counseling on inductions for potential maternal risk reduction, the ability to individualize counseling for chances of success, as well as risks and benefits of induction, better allows individuals to give informed consent. Additionally, as with the vaginal birth after CD calculator, ²⁵ we found that the CMAO increases as the likelihood of CD increases. This may be additional information to guide decision making, and may even be reassuring to women considering CD by maternal request.

Notwithstanding the reasons for using the risk calculator for CD during the induction, there are justifications for the cautious scaling up of the tool. It may not be feasible to provide a risk‐benefit analysis to all high‐ and low‐risk pregnancies about their likelihood of vaginal or cesarean delivery and the associated adverse outcomes. Our study provides an additional look into morbidity from the initial design of Rossi et al., ¹² and information on potential risk with induction, like hemorrhage, may improve outcomes. ⁹ As Hamm et al. ⁹ suggested, it may not reflect the same results at other sites because of differences in obstetrical practices. A critical consideration for clinical implementation is the potential for altering provider behavior. The Rossi et al. calculator, especially at very high predicted CD rates (e.g. >70%), exhibited decreased accuracy in our study. While over‐reliance on calculators might inadvertently lead to more frequent and potentially avoidable CDs, they are designed as adjuncts for counseling and shared decision making, not replacements for clinical judgment. Individuals with a higher predicted CD risk, as identified by the calculator, inherently present with elevated obstetric risk factors that predispose them to both CD and higher incidence of complications like postpartum hemorrhage, which was our primary significant CMAO. These adverse outcomes are multifactorial, driven by underlying complexities such as prolonged labor, uterine atony, or chorioamnionitis. Therefore, these findings should not deter medically indicated inductions of labor, rather, it highlights the need for heightened clinical vigilance and proactive management for these high‐risk individuals. Successful integration of these predictive tools requires comprehensive provider education.

Our findings are a nidus for additional research. The model uses socially constructed variables of race and ethnicity, which may perpetuate health disparities. ²⁶ Hence, a calculator for the likelihood of CD during induction that does not use race and ethnicity as a predictor is warranted. Once such a calculator is developed, it needs to be externally validated in different populations. Rubashkin et al. ²⁷ described how patients approach the use of the trial of labor after cesarean (TOLAC) calculator; a similar exploratory open‐ended interview study, which ascertains how individuals navigate the result of induction calculator, is needed.

We acknowledge the multiple strengths of our study. Our cohort was racially and ethnically diverse, with the majority being non‐White individuals. The data for all the individuals were abstracted by trained clinicians. The individuals in the study included high‐ and low‐risk pregnancies, nulliparous and parous, term and preterm inductions, and those managed by house staff, faculty as well as private attendings. We ascertained the association between the composite maternal and neonatal adverse outcomes and the predictive CD score calculated from the model, which was not done previously. ¹² Finally, the predictive risk calculator was developed by a large cohort study on more than 4 000 000 US pregnant women, which makes the model generalizable to our population.

The limitations of our analysis are notable. This was an observational study, so the findings only indicate association and causal relationships should not be inferred. We aligned our cohort characteristics with those used to developed the initial calculator by Rossi et al. ¹² However, a notable difference in our validation approach was our exclusion of individuals with a previous CD undergoing induction of labor. This decision was driven by the aim of clinically validating the Rossi calculator within our practice. Pragmatically, our institution routinely uses the already validated Grobman et al. TOLAC calculator ¹³ for counseling patients with a previous CD who want to undergo a trial of labor. Applying the Rossi calculator to this already‐counseled and potentially selected cohort (who may have been deemed more likely to achieve a vaginal delivery based on previous counseling) could have introduced selection bias into our validation study and potentially misrepresented the Rossi et al. ¹² model's performance in a more general induction population. Given the existing clinical tool for TOLAC, and the ongoing need for a predictive tool specifically for individuals without a previous CD, our study thus provides an external valiation of the Rossi calculator for this crucial subset of the induced population. While the Rossi calculator includes “previous CD” as a predictor variable, it remains unclear if its performance and utility for this specific goup can be considered interchangeable with the Grobman et al. TOLAC calculator. ¹³

Though the sample size was calculated for external validation, the post‐hoc power analysis showed that our sample size had more than 98% power to detect the primary outcome. However, the study may be underpowered to examine the association with the secondary adverse outcomes. In this study, we used three predicted CD score groups (<10%, 10% to <30%, and ≥30%). These thresholds were chosen based on the data distribution of the predicted CD score in our sample, as we aimed to present if a higher predicted CD score was associated with a higher risk of outcomes. Nonetheless, other thresholds may be considered in a different population.

Each individual factor from the calculator is listed in Appendix A, Table A1. Although several of the coefficients are independent risk factors for CD, the one that carried the greatest weight on the predicted probability was previous vaginal delivery. Induction by gestational age in weeks had also different coefficients, with preterm and post‐term having a negative effect on the calculation and term inductions having a greater impact. Even though we used consecutive inductions at our institution, the mean gestational age did not differ significantly between the three groups (38.1–38.2 weeks). Additionally, given this was a validation study from the original calculator by Rossi et al., ¹² we were unable to test if fewer variables were equally as predictive.

Finally, our cohort study timeframe coincided with the early phase of the COVID‐19 pandemic. Although our institution's overall induction rate remained high, the overall induction rate we observed during this period may reflect the temporary constraints of the pandemic. Despite potential shifts, our institution, given its high volume, continued medically indicated and ARRIVE trial‐based inductions. A recognized limitation is our decision not to include specific induction parameters (e.g. agents, dosages, mechanical methods) or the precise reasons for induction (elective vs. medical) in our analysis. Although our single‐institution setting and electronic medical record access provided the opportunity for such detail, the primary aim of this study was the external validation of the existing Rossi et al. calculator, which does not incorporate these variables. Integrating them would have constituted a new model development, beyond our current scope. We acknowledge that future research could leverage such detailed induction of labor parameters to provide more specific insights for identifying individuals at higher risk of CD. However, we included both academic and private patients to reflect the potential different practice patterns during this time. ¹²

In conclusion, at our level IV center, we externally validated the calculator ¹² that provides the probability of CD during induction. Moreover, there was an increased risk of the CMAO as the likelihood of CD increased.

AUTHOR CONTRIBUTIONS

CJI contributed to data collection, resources, conceptualization, and writing and editing of the original draft; RLW contributed to data collection, conceptualization, methodology, and editing of the original draft; H‐YC contributed to data curation, data analysis, and review and editing of the draft; EG and IG contributed to data collection, and review and editing of the draft; HM‐F contributed to conceptualization, methodology, and editing of the original draft; and SPC contributed to conceptualization, methodology, and writing the original draft. All authors read and approved the final manuscript.

CONFLICT OF INTEREST STATEMENT

The authors have no conflicts of interest.

APPENDIX A.

A.1.

TABLE A1.

Calculating a predicted probability of cesarean delivery (CD) using the calculator developed by Rossi et al ¹² .

Variable	Variable name	Coefficient
Prior vaginal birth	prior_va	–2.117016
Prior cesarean birth	prior_cs	1.255777
Maternal weight at delivery, lb	weight	0.0109185
Maternal height, in	height	–0.1538638
Maternal age	age	0.0571224
Maternal race/ethnicity
White	race_w	0
Black	race_b	0.4661974
Hispanic	race_h	0.1079402
Other	race_o	0.1474727
Gestational age, weeks
32	ga_32	0
33	ga_33	–0.2417164
34	ga_34	–0.8054884
35	ga_35	–0.8010319
36	ga_36	–0.9520646
37	ga_37	–1.125466
38	ga_38	–1.154707
39	ga_39	–1.175031
40	ga_40	–1.002833
41	ga_41	–0.8081131
42	ga_42	–0.6372783
Constant		6.364138

Note: Predicted probability of CD = exp (w)/(1 + exp (w)) × 100.

$$\begin{array}{c}w=6.364138+\left(–2.117016\right)\times \text{prior}\_\mathrm{va}+\left(1.255777\right)\times \text{prior}\_\mathrm{cs}+\hfill \\ \left(0.0109185\right)\times \text{weight}+\left(–0.1538638\right)\times \text{height}+\left(0.0571224\right)\times \hfill \\ \mathrm{age}+\left(0\right)\times \text{race}\_\mathrm{w}+\left(0.4661974\right)\times \text{race}\_b+\left(0.1079402\right)\times \text{race}\_h+\hfill \\ \left(0.1474727\right)\times \text{race}\_\mathrm{o}+\left(0\right)\times \mathrm{ga}\_32+\left(–0.2417164\right)\times \mathrm{ga}\_33+\hfill \\ \left(–0.8054884\right)\times \mathrm{ga}\_34+\left(–0.8010319\right)\times \mathrm{ga}\_35+\left(-0.9520646\times \right)\hfill \\ \mathrm{ga}\_36+\left(–1.125466\right)\times \mathrm{ga}\_37+\left(–1.154707\right)\times \mathrm{ga}\_38+\left(–1.175031\right)\times \hfill \\ \mathrm{ga}\_39+\left(-1.002833\right)\times \mathrm{ga}\_40+\left(–0.8081131\right)\times \mathrm{ga}\_41+\left(–0.6372783\right)\times \hfill \\ \mathrm{ga}\_42\hfill \end{array}$$

FIGURE A1.

Calibration plot with c‐statistic and distribution of the predicted probabilities for individuals with and without the outcome. Groups represent 10ths of predicted risk with 95% confidence intervals. The spike plot illustrates the events and non‐events according to predicted risk.

DATA AVAILABILITY STATEMENT

Data available on request due to privacy/ethical restrictions.