The evolution of the labor curve and its implications for clinical practice: the relationship between cervical dilation, station, and time during labor

Abstract

The assessment of labor progress is germane to every woman in labor. Two labor disorders - arrest of dilation and arrest of descent - are the primary indications for surgery in close to 50% of all intrapartum cesarean deliveries and often contributing indications for cesarean deliveries for fetal heart rate abnormalities.

Beginning in 1954 the assessment of labor progress was transformed by Friedman. He published a series of seminal works describing the relationship between cervical dilation, station of the presenting part and time. He proposed nomenclature for the classification of labor disorders. Generations of obstetricians used this terminology and the normal labor curves to determine expected rates of dilation and fetal descent and to decide when intervention was required.

The analysis of labor progress presents many mathematical challenges. Clinical measurements of dilation and station are imprecise and prone to variation especially with inexperienced observers. Many interrelated factors influence how the cervix dilates and how the fetus descends. There is substantial variability in when data collection begins and in the frequency of examinations. Statistical methods to account for these issues have advanced considerably in recent decades. In parallel, there is growing recognition among clinicians of the limitations of using time alone to assess progress in cervical dilation in labor. There is wide variation in patterns of dilation over time and most labors do not follow an average dilation curve.

Reliable assessment of labor progression is important because uncertainty leads to both over-use and under-use of cesarean delivery and neither of these extremes is desirable. This review will trace the evolution of labor curves, describe how limitations are being addressed to reduce uncertainty and to improve the assessment of labor progression using modern statistical techniques and multi-dimensional data, and discuss the implications for obstetrical practice.

The Importance of Labor Disorders in Clinical Practice

Cesarean delivery is second only to cataract removal as the most common surgery in the US.¹ In a recent review of contemporary practice in the US, slow progress in labor was the reported indication for surgery in close to half of all intrapartum cesarean deliveries.² Labor disorders are often listed as a contributing indication in cesarean deliveries for fetal heart rate abnormalities. In addition, a labor disorder resulting in cesarean delivery is often considered a potentially recurring condition leading the decision to opt for a repeat cesarean rather than a trial of labor in later pregnancies. Thus, directly or indirectly, labor disorders are by far the leading indication for cesarean delivery.

Disorders of labor progression impart a high burden on women, their families and healthcare services. WHO statistics from 2014 attribute 9% of global maternal deaths and a large portion of serious birth-related morbidities to obstructed labor. ^3–5 Although serious maternal and fetal trauma related to prolonged labor are uncommon in modern obstetrics in high income countries, they do occur. Prolonged labor is associated with adverse outcomes such as infection, low Apgar scores, shoulder dystocia and trauma. ^6–12

Cesarean delivery is associated with post operative complications and undesirable sequelae in later pregnancies related to abnormal placentation. ^13–16 In 1960, the frequency of placenta accreta was approximately 1 in 30,000 pregnancies. ¹⁷ More recent studies report rates of 1 in 533 in 1982–2002 and around 1 in 300 pregnancies in 2010–2013. ^17–19 In a 2011 review of a series of births with confirmed placenta accreta, the median number of units of blood transfused was 5, 28% of patients experienced disseminated intravascular coagulation, 50% required admission to the NICU and 88% underwent hysterectomy. ²⁰ Although complication rates vary among studies, placenta accreta is universally seen as an important contributory factor for severe fetal and maternal morbidity. Moreover, its incidence has shown a near logarithmic rise as the number of cesarean deliveries has increased.

Uncertainty in the assessment of labor progress leads to both over-use and under-use of cesarean delivery and neither of these extremes is desirable. Thus, the ramifications and actions related to labor assessment touch many women, often do so more than once and can have serious consequences.

Original Time-based Labor Curves

With introduction of oxytocin and the development of safer cesarean operations, better assessment of labor progress became germane as obstetricians could intervene when progress did not occur as expected. The seminal work of Emmanuel Friedman transformed labor assessment from qualitative and vague - like counting sunsets - to quantitative and objective.

Between 1954 and 1969 Friedman described the relationship between cervical dilation, station of the presenting part and time, and proposed nomenclature for the classification of labor disorders. This body of work began when Friedman, a young obstetrical resident, spent a night on call recording dilation and station observations on a series of laboring women, at the behest of the attending anesthesiologist Dr. Virginia Apgar, who wanted to know the effect of caudal anesthesia on labor. By the next morning, he observed that his cervical dilation versus time recordings showed a sigmoid (S)-shaped curve. ²¹ These observations had a marked affect on his subsequent analytical methods and publications.

A series of landmark publications followed. In 1954 in The Graphic Analysis of Labor he described this sigmoid shaped pattern of dilation based on data from 100 primipara.²² At that time, the rate of cesarean delivery was 1%, and rate of forceps use was 68%. ²² He characterized the first stage of labor as a process with 4 phases: a latent phase - little change in dilation, an acceleration phase - a brief transition period, a phase of constant maximal dilation rate and a deceleration phase. In 1955 the dilation curve was updated slightly with data from 500 primigravida. ²³ In 1965 the first curves of descent were published based on observations from 421 nulliparae and 389 multiparae. ²⁴

In scientific parlance, these curves of dilation or descent are models. In general, models are simplified ways to represent a process, an entity or a concept. They are useful because it may be difficult to interact directly with the original subject matter. Pediatric growth charts for the height and weight of children are examples of graphic time-based models. The Friedman labor curves are graphic models that embodied the experience of hundreds of births. They were reproduced in numerous publications around the world. Generations of obstetricians used these normal labor curves and terminology to determine expected rates of dilation and fetal descent and to decide when intervention was required.

In 1969 Friedman moved one step forward by providing a mathematical equation for the relationship between dilation and time. ²⁵ That is, the graphic model was expressed as a mathematical model or equation. Examples of mathematical models in obstetrics include estimating fetal weight based on several fetal measurements taken by ultrasound or estimating the likelihood of trisomy 21 based on biochemical and ultrasound markers.

The report by Friedman and Kroll on their modelling approach, describes their choice to use the structure of an existing formula known as the Gompertz function, and how they derived its coefficients from data in the National Collaborative Perinatal Project. ²⁵ Benjamin Gompertz, an actuary, published a function in 1825 to describe mortality rates with increasing age. ²⁶ The Gompertz function, produces a sigmoid shaped curve:

$$y_{\left(t\right)}=ae{\mathrm{ }{\mathrm{ }}^{-be}}^{-ct}$$

Later this function was seen to describe some biological systems, such as bacterial cell growth in an environment with finite nutrition. Once cell doubling had produced a substantial number of bacteria, growth of the colony became extremely rapid until limited resources caused the growth rate to flatten. The function also described tumor expansion where cell growth eventually slows as it outstrips its vascular supply.

The National Perinatal Collaborative dataset included labor information from 58,831 births between 1959–1965 in 19 US hospitals. Using this data and the Gompertz function, Friedman and Kroll published the following equation linking dilation (y) to time (x):

$$y_{\left(x\right)}=2.30+7.70\mathrm{ }\left(0.016\right){{\mathrm{ }}^{0.34}}^x$$

Inspecting this equation shows that dilation can only begin its upward turn when the time variable (x) exceeds 0. Time₀ not necessarily observed but estimated from a graph of dilation versus time by extrapolating a straight line through the phase of maximal constant dilation downward to find where it crossed a horizontal line drawn at 2.5 cm. Times before this point were given negative numbers. ²⁵

In short, the model was built in on several assumptions. The 4 most notable are:

1. Cervical dilation was related to a single variable - time

2. The course of dilation over time had a sigmoid shape. The Gompertz function will always produce a sigmoid shaped curve regardless of the data that it is based on.

3. All women had a discernable point in time (time₀) where dilation transitioned relatively quickly from the latent phase to a faster rate. A specific time₀ was determined for all women even if one could not be observed.

4. Time ₀ occurred when dilation was around 2.5 cm dilation. The extrapolation method to find time₀ was anchored to dilation = 2.5 cm.

The formula constant of 2.3 means that on average, the transition from the latent phase begins at 2.3 cm.

The Friedman curves of dilation and descent and related terminology were widely welcomed as they brought structure and order to the analysis of labor. They appeared in textbooks and shaped labor management guidelines across continents and partograms with Alert and Action Lines based on the dilation curves were formally recommended by the WHO from 1987 to 2020. ^27–31 Debates ensued about the presence or absence of a deceleration phase, and what dilation values defined the onset of the acceleration phase. ^32–36

Second Generation Time-based Labor Curves

The sections that follow are intended to expand on key aspects of mathematical modelling that are pertinent to the problem of labor assessment. Statistical terms are linked to a glossary.

The Friedman curves strongly influenced researchers studying labor progression more than five decades later.^37–45 They asked the same basic question - how does cervical dilation change over time? However, later scientists could approach this problem with the benefit of the considerable advances in mathematical modeling and computerization.

Labor data presents challenges to developing an accurate model. Women have repeated measurements of dilation and descent over time. There is variation in when they enter hospital and, in the number, and frequency of examinations. Dilation assessment is imprecise and sometimes erroneous. Dilation at a previous examination is likely to affect the value at the next examination. Each of these challenges can be addressed in part by longitudinal statistical methods to produce curves which are more accurate.

Contemporary mathematical methods let the data determine the optimal shape of the curve rather than forcing the data to fit a presumed shape. Resulting models are evaluated with statistical tests to measure how well they represent the data. Rather than debating what kind of curve is the best representation of labor, it is possible to measure their goodness of fit and assess with statistical confidence which curve has the best fit, is the most parsimonious or the most robust.

The first of several publications using longitudinal statistical methods was published by Zhang et al in 2002. ³⁷ It was based on an examination of 1162 term nullipara with a spontaneous onset of labor and vaginal birth in the US. The cesarean delivery rate in the parent dataset was 12.5%. Forceps were used in 9.8% of the births. A repeated-measures mixed-effects model was used to take into account serial measurements. Representing the response variable (dilation) as a polynomial function of time in their approach, allowed the average population curve to have bends (inflection points). The general shape of curves of both dilation and descent versus time were different from the classic Friedman curves. These differences are illustrated in Figure 1.

Figure 1.

Curves of nulliparous dilation and station

The curve in red was calculated by Friedman et al²⁴ and the curve in black was by Zhang et al.³⁷

Reasonable speculation arose that differences in the two study groups could account for the differences in the shapes of the labor curves. Cesarean rates were much higher in later years, and hence the number of labors removed from consideration were very different. In addition, there were substantial changes in the rates of epidural/caudal anesthesia, oxytocin administration, forcep delivery, as well as differences in maternal age and BMI.

When Zhang et al³⁷ applied the same repeated-measures mixed-effect modeling techniques based on a polynomial function to the National Perinatal Collaborative data from 1959 to 1965 (the same data source used in the 1969 report by Friedman and Kroll²⁵), the resulting curve was another nearly exponential curve that was similar to the earlier work.³⁸ In short, the mathematical techniques appear to be a major source of the differences in the shapes of the Friedman and Zhang curves. Zhang et al³⁷ applied the same modeling method on another large dataset from women who delivered between 2002–2008 in 19 US hospitals, and again obtained a similar curve.³⁸ The three average dilation curves for nullipara by Zhang et al³⁷ from these 3 different sources are similar as is shown in Figure 2. ^37–39

Figure 2.

Three US-based mixed-effects models of nulliparous dilation over time^37–39

Reports of labor curves of dilation over time soon followed from other regions in the US, and from different countries including Japan, Nigeria and Uganda, Sweden, Israel, and China.^40–48 Despite anthropometric differences in these populations, some differences in inclusion/exclusion criteria and background cesarean rates, the nulliparous curves based on repeated-measures and polynomial modeling techniques were similar to those shown in Figure 2.^37–39 Other studies have confirmed differences in station compared to the Friedman descent curve.^49–52

The final equation (or curve) from any modeling procedure depends upon the mathematical techniques in use as well as the characteristics of the dataset under study.^53–54 Figure 3 shows four models of nulliparous cervical dilation from three continents.^{37, 40, 42} The blue and black curves are similar. They were constructed using a 10th degree polynomial equation with data from different countries. The black curve was based on US data and the blue curve was based on data from Japanese women. The same modeling technique and data from different populations has produced similar average curves.

Figure 3.

Models of nulliparous dilation over time from three continents^39,40,42

The solid and dashed orange curves are different. They are based on the same dataset from Uganda and Nigeria but use different modeling methods.⁴² The solid orange line is the result of a Markov multistate modeling method. The dashed orange line is from a non-linear mixed-effect approach. Different modeling techniques have produced different average curves despite being based on the same dataset.

Figures 1–3 show average curves of dilation vs. time using a variety of modeling methods and datasets. ^{24,37–39,40,42} They do not show the ranges that cover 90% of the study population or provide goodness of fit measures to help determine if one method is significantly better than another. All these studies noted that there was wide variation among individuals and that many patients progress slowly. Wide variation limits the clinical usefulness of a labor curve.

Limitations of Time-Based Labor Curves

Mathematical models of labor serve two main clinical purposes that are closely related yet distinct. The following section will describe how wide variation and low central tendency reduce their clinical usefulness.

One purpose of labor models is to characterize normal progress in dilation and descent over time. Another goal is to identify labors where progress is sufficiently abnormal that cesarean delivery is warranted to avoid complications, without causing an undue number of unnecessary cesarean deliveries. This goal presents a far greater challenge.

An ideal diagnostic test clearly separates the normal and abnormal groups. Results from the normal group cluster around an average and do not overlap with the results from the abnormal group. Central tendency refers to the clustering of most results around the average. An obstetrical example of a measure with good central tendency is fetal weight at each gestational age. Fetal weights do cluster around the average and the range of values in the normal group is relatively small. The average fetal weight at a given gestational age is a clinically useful number because most fetuses will be close to it, and few will have a fetal weight that is far from the average. Furthermore, rates of complications do increase with very deviant weights.

Poor central tendency and wide variability is a feature of normal dilation as shown in Figure 4. Each graph shows dilation patterns for a random set of nulliparous women from different countries. ^42,44 Each colored line is an individual dilation course starting at 3 cm. The Alert Line, shown by the dashed black line, derived from the Friedman curves, is supposed to identify the slowest 10% of labors. All women had spontaneous onset of labor and delivered vaginally without adverse outcomes. It is evident, that there is no clustering of the lines and wide variability is observed. Although a mathematical average can always be calculated, it does not actually represent the measurements from many individuals. Recent reports including a systematic review also report wide variation among individuals and that labor complications did not cluster at the periphery or even below the Alert line.^55–57

Figure 4.

A random sample of nulliparous dilation patterns from three countries

Individual dilation patterns (colored lines) and the Alert Line (dashed black line) from a random sample of nulliparous women from Sweden,⁴⁴ Uganda and Nigeria,⁴² and the United States.

A large study from Sweden also showed that an average curve of dilation over time does not represent labor well due to poor central tendency and wide variation within the normal population.⁴⁴ Wide variation with the time-based labor curves is also apparent when examining the time it takes for dilation to advance by one centimetre. Table 1 shows the number of hours taken to advance 1 cm in dilation, depending on the dilation level in nulliparous women at term from several countries.^37–45 Characteristics of these studies are summarized in Table 2. These studies all showed long transit times and wide ranges at early dilation. In the two largest studies, the 95^th percentile of time to advance from 3 to 4 cm was 8.1 and 5.0 hours.^39,44 The range of transit times was less at higher dilations. In the same two studies, the 95^th percentile of time to advance from 8 to 9 cm was 1.4 and 3.0 hours.

Table 1.

Median (95^th percentile) time in hours to advance 1 cm in dilation in nulliparae at term

Change in dilation	Zhang et al 2002 37	Zhang et al 2010 38	Zhang et al 2010 39	Suzuki et al 2010 40	Oladapo et al 2018 42	Inde et al 2018 43	Lundborg et al 2020 44	Shi et al 2016 41	Shindo et al 2021 45
2 −3 cm	3.2 (15.0)			7.5 (21)		2.62 (8.31)		2.7(7.2)
3–4 cm	2.7(10.1)	1.2 (6.6)	1.8 (8.1)	6.2 (17.7)	2.82 (13.33)	2.24 (8.00)	0.83 (4.97)	2.0 (4.2)
4–5 cm	1.7 (6.6)	0.9 (4.5)	1.3 (6.4)	4.8 (15.7)	1.72 (7.83)	1.83 (5.81)	0.89 (5.26)	1.7 (4.0)
5–6 cm	0.8 (3.1)	0.6 (2.6)	0.8 (3.2)	3.3 (10.7)	1.19 (6.17)	1.31 (4.67)	0.68 (4.55)	1.0 (2.5)	3.6 (5.2)
6–7 cm	0.6 (2.3)	0.5 (0.8)	0.6 (2.2)	2.6 (9.3)	0.66 (4.92)	1.05 (3.13)	0.48 (3.82)	1.0 (2.3)	1.1 (1.3)
7–8 cm	0.5 (1.5)	0.4 (1.4)	0.5 (1.6)	1.8 (6.8)	0.25 (3.10)	1.0 (3.31)	0.33 (3.62)	0.92 (2.1)	0.75 (0.85)
8–9 cm	0.4 (1.3)	0.4 (1.3)	0.5(1.4)	1.0 (4.4)		0.76 (2.17)	0.24 (3.0)	1.0 (2.5)	0.58 (0.60)
9–10 cm	0.4 (1.4)	0.4 (1.2)	0.5 (1.8)	0.9 (2.6)		0.52 (2.19)	0.18 (2.66)	0.33 (1.0)	0.46 (0.9)
8–10 cm					0.87 (4.19)

Table 2.

Characteristics of studies describing models of cervical dilation

	Zhang et al 2002 37	Zhang et al 2010 38	Zhang et al 2010 39	Suzuki et al 2010 40	Oladapo et al 2018 42	Inde et al 2018 43	Lundborg et al 2020 44	Shi et al 2016 41	Shindo et al 2021 45
Country	USA	USA	USA	Japan	Nigeria, Uganda	Japan	Sweden	China	Japan
Number of subjects	1,162	8,690	25,624	2,369	2,166	1,047	44,813	1,200	4,215
Birth yr.	1992–96	1959–65	2002–08	2001–05	2014–15	2008 −15	2008–14	2013–14	2011–19
Background % Cesarean	20.7–22.3% CDC	5.6%	30.2–31.8% CDC	17.4% 2005 WHO	1.8–3.1% 2008 WHO	17.4% 2005 WHO	17.3% 2006 WHO	24.7% 2007–13	19.7% 2014 WHO
Model Variables	dilation, time	dilation, time	dilation, time	dilation, time	adilation, time bdilation, time, oxytocin use	dilation, time	dilation, time	dilation, time	dilation, time
Model methods	repeated-measures, 10th order polynomial	repeated-measures, 8th order polynomial	repeated-measures, 8th order polynomial	smoothing B-spline and 10th order polynomial	non liner mixed model (3 parameter logistic growth model) ~ or a multi state Markov modela	repeated-measures, 6th order polynomial	quintile logistic regression	repeated-measures, 8th order polynomial	smoothing B-spline

CDC: Centers for Disease Control and Prevention; WHO, World Health Organization

^aNon-linear mixed model (3 parameter logistic growth model)

^bMulti-state Markov model*

In the largest US based study, it was only at dilation ≥5 cm that an interval of time defining arrest such as 4 hrs was beyond the 95^th percentile in normal labors.³⁹ That is, a reasonable definition of arrest of dilation can be used only at ≥5 cm because if it were applied earlier, it incorrectly would have labeled many labors that ultimately ended with vaginal delivery as abnormal. In contrast, 4 hours of arrest is well beyond the 95^th percentile for dilations ≥6 cm. As stated by Zhang et al regarding the definition of arrest of dilation, “…a 2-hour threshold may be too short before 6 cm whereas a 4-hour limit may be too long after 6 cm”.³⁷

In keeping with these observations, the WHO has adopted a sort of sliding scale regarding alert criteria for unchanged dilation as outlined in Table 3. Higher dilations require less time of unchanged dilation to trigger the alerts.⁵⁸

Table 3.

World Health Organization alert criteria with increasing dilation

Cervical Dilation	WHO Alert Criteria re Duration of Unchanged Dilation
5 cm	≥6 h
6 cm	≥5 h
7 cm	≥3 h
8 cm	≥2.5 h
9 cm	≥2 h

WHO: World Health Organization

Labor Curves Based on Multiple Factors

Fortunately, there are established ways to achieve better central tendency and reduce variation. A leading technique is to identify the top sources of variation and to account for their influence in the model. For example, a weather prediction model based solely on a single time factor, say the month of the year, will cover wide range of possibilities. The precision of weather prediction is improved by considering additional factors like changes in barometric pressure, wind patterns, as well as yesterday’s measurements and weather in neighboring regions. Likewise, additional factors can be considered when modeling labor progression.

The factors that influence dilation and fetal descent are well known to clinicians. The very definition of labor, “Presence of uterine contractions resulting in cervical change (dilation and/or effacement)”, underscores the important role of contractions.⁵⁹ In addition, the role of contractions is key to the definition of first stage arrest. ACOG/SMFM guidelines defining arrest of dilation are conditional on the frequency and strength of uterine contractions. The arrest definition requires no change in dilation over 4 hours when Montevideo units are high and no change over 6 hours when Montevideo units are low.⁶⁰

Clinicians have believed that cervical dilation is a direct response to contractions but that is an oversimplification. The response is modified by several other factors such as cervical compliance, abnormal positions of the fetal head, or pelvic size and shape. Numerous publications have measured the impact of various maternal and fetal factors on the rates of cervical dilation.^61–66

The complexity of labor calls for a modeling approach that can identify and incorporate multiple factors, account for how they interact with each other and adapt as they change over the course of labor. Clinicians do this mentally when they modify general practice guidelines according to the specific characteristics of an individual in question. There are mathematical techniques to find the most influential factors and determine how best to incorporate them in an equation or labor curve. Customized models refer to equations that include static personal factors. Examples of customized models include fetal growth curves that consider ethnic origin, maternal height, weight, and parity in addition to gestational age.⁶⁷ Models to predict preterm birth based on cervical length can be customized and improved by including terms for maternal parity, height, and weight.⁶⁸ Customized models mitigate the problems of a “one size fits all” approach.

A “Stimulus-Response” system is another attractive construct because it could describe the relationship between contractions (the stimulus) and cervical dilation (the response) and how this relationship is modified by other clinical factors. Furthermore, it can adapt as these factors, such as contraction strength and frequency change over the course of the labor. An adaptive labor model that adjusts for changing influences can mitigate inconsistencies with the ad hoc mental adjustments that clinicians make when assessing labor progression.

Previous reports have indicated that it is feasible to develop a mixed-effects model of cervical dilation or station that includes terms for many factors, including contraction activity, cervical effacement, dilation level, station, and epidural usage.^69,70 An individual woman’s dilation and station can be compared to the expected ranges defined by the model and her results expressed in percentile rankings. This method reflects how clinicians assess labor and it can adjust the assessment in a standardized fashion. In essence, it is a mathematical restatement of the obstetrical adage to consider, “power, passage and passenger” when assessing labor progression.

The models mentioned so far generally fall into the category of statistical models. Machine learning refers to another group of methods that is well suited to complex biological processes. Machine learning algorithms use existing data to generate models that can classify or make predictions on future data. The models “learn” from training data without making assumptions about the mathematical nature of the relationship. Neural networks, one machine learning approach in widespread use across many domains, is an approach that provides full mathematical expressiveness. They can approximate any mathematical function to characterize complex relationships between predictors and responses.

To model normal labor, neural networks could “learn” the relationship between dilation and covariates from a training set of data from patients with normal labor. Given sufficient data this modeling technique could account for patient characteristics, noisy data and interactions among covariates.

Another machine learning approach would be to model normal vs abnormal labor without explicitly constructing a normal curve but simply feeding the learning algorithm with exemplars from both categories. Drawbacks of machine learning approaches are the need for large datasets to create them and their more limited transparency/interpretability regarding how a given prediction is obtained.⁷¹

The Use of Labor Curves to Diagnose Complications of Parturition

A major use of labor curves is to help clinicians identify when labor progress is sufficiently abnormal that cesarean delivery is warranted to avoid parturition-related complications. However, there are several challenges with this goal. Three problems merit further discussion.

The intervention paradox

The first problem is that an avoided complication is usually unobservable. Generally, there is no post-delivery test that confirms the presence of dystocia or an impending dystocia-related complication. The following extreme example demonstrates the paradox of intervention to prevent a complication. Suppose there is a perfect test of a labor disorder that if left untreated, always causes death of the fetus. Further, also assume that timely cesarean delivery always prevents fetal death. With proper use, the abnormal test would be associated with a normal outcome. When evaluating this test, it would appear to have a 100% false positive rate and a 0% sensitivity rate because the intervention (cesarean delivery) prevented all intrapartum deaths. Intervention paradox is not unique to labor curves. It affects the evaluation of other tests where the objective is prevention of complications such as the use of NSTs or biophysical profiles.

This paradox must be remembered when evaluating intervention thresholds from labor curves. It is still useful to compare different intervention guidelines on the same dataset because they will be equally affected by this paradox. However, the observed values of sensitivity and specificity will underestimate their potential true value.

Multiple outcomes with a spectrum of severity

A second problem in the evaluation of labor curve utility is related to the outcome definition. Exactly what outcome are we trying to prevent? Dystocia related complications cover a wide spectrum of severities.^{3–19, 72–77} At one extreme are complications like death, and severe morbidities. Long term complications such as pelvic floor disorders and placenta accreta are important sequelae. Pain and suffering are other considerations.

The problem of defining abnormal based on the study of normal

The third problem relates to defining abnormality based on studies where abnormality was largely excluded. All labor curves outlined in Tables 1 and 2 have been developed on data from women with spontaneous labor onset and vaginal delivery. Patients where clinicians performed a cesarean for any reason were excluded. Furthermore, each study had additional exclusion criteria to remove other adverse outcomes. Thus, the study groups were largely “normal”. Limits such as the 5^th or 95^th percentile of the study groups do identify outliers, but they are “normal” outliers. While this information is helpful to estimate the potential effect on unnecessary cesarean rates, it does not provide any information on the potential impact on adverse outcomes. For the sake of argument, suppose a cesarean intervention was recommended for the slowest 5% as identified by the model of normal labor. This policy could potentially add an extra 5% to the cesarean rate because it will likely identify 5% of those women who would deliver vaginally. The potential benefit regarding the reduction in long labor-related complications is not obvious without at least knowing how often labors with such complications fell below that same threshold. Furthermore, it is not certain that cesarean intervention at that time would truly have prevented a complication.

For these reasons labor-related intervention criteria cannot be evaluated in the same retrospective way that the performance of classic diagnostic tests in oncology can be assessed against definitive histology. Nevertheless, it is important to examine historical data and determine how often criteria to define labor abnormalities would have been met in patients with complications and in those without complications before prospective trials are undertaken. Despite wide variation in normal labor lengths, long labors are not without consequences. Recent reports continue to show that longer lengths of labor are related to more complications and more operative interventions.^72–77

Outcome Studies with Guidelines Based on Friedman or Zhang curves

Over the years most, but not all, studies have reported that lowering the cesarean rate is feasible and safe. Several randomized studies on labor related interventions have reported small reductions in cesarean rates with no increase in complication rates.^78–80 In addition, many observational studies have demonstrated safe and substantial reductions in cesarean rates after introducing new clinical management policies.^81–90 These studies usually introduce a group of interventions, often referred to as a bundle, including education, defined management guidelines, heightened awareness, and ongoing clinician feedback. Any of these interventions could contribute to the outcome.

A recent large prospective cluster-randomized clinical trial showed no significant difference in cesarean rates using intervention guidelines based on the Zhang curve compared to WHO guidelines which are based on the Friedman curves.⁹¹ This study, completed in 2017, included 14 Norwegian centers and 11,615 nulliparae at term. The Cesarean delivery rate was not different in the group using guidelines based on the Zhang curve (6.8%) versus the rate in the group using the WHO guidelines (5.9%) The adjusted relative risk was 1.17 (95% CI 0.98–1.4) There was no difference is secondary outcomes related to maternal transfusion, low Apgar scores or fetal acidemia.

In both groups, cesarean rates fell from their pre-study levels, from 9.3% to 6.8% in the Zhang curve-guided group and from 9.5% to 5.9% in the WHO-guided group. This observation supports the position that focus on labor management can lower cesarean rates irrespective of what labor curve is used. The successes of “before and after” studies further reinforce the importance of education, audit, and feedback.

After the publication of the newer labor curves, some professional societies have proposed management strategies to reduce the cesarean delivery rate; however, there is no prospective clinical trial evidence that the use of the WHO labour scale or the Zhang curve modifies the cesarean delivery rate when compared to the Friedman curve.^{58, 60,80,91}

Outcome Studies with Multifactor Labor Models

The relationship between labor-related complications with percentile rankings from the multifactorial mixed-effect models described earlier was evaluated on a retrospective analysis of 4703 cephalic presenting singleton term births.⁷⁰ The multifactorial method showed substantially more discrimination for the complications than duration of arrest at a cervical dilation of 6 cm or more.

Duration of arrest at dilation ≥6cm showed poor levels of discrimination for cesarean delivery for a first stage labor disorder (AUC=0.65) or cesarean for concern about fetal heart rate patterns (AUC=0.55) and no significant relationship to obstetrical hemorrhage (AUC=0.52) or neonatal depression (AUC=0.52). The dilation and station percentiles from the multifactorial adaptive models showed much higher discrimination for the cesarean delivery groups (AUC 0.78–0.93; P <0.01) and better albeit low discrimination for the clinical outcomes of hemorrhage and neonatal depression (AUC, 0.58–0.61; P < 0.01).

An assessment of labor curves developed by machine learning is not feasible as they are not yet present in the literature.

Conclusions

The assessment of labor progress is a global health care challenge. There are 140 million births per year in the world. Labor disorders can have very serious consequences.

Labor curves have a role in the assessment of labor progression, however an average labor curve of dilation based solely on time has limited clinical utility because of low central tendency and wide variation in labor progression even in patients who deliver vaginally.

More complex/customized models that consider several factors that affect dilation and descent are available and more are under development.^69–70 They can improve the precision of labor assessment, and hence potential utility. As larger and larger datasets become available from electronic medical records it will be feasible to account for the effect of more factors such as maternal ethnicity, BMI, or fetal head position. The amount of data needed grows almost exponentially with the number of factors under study. Data requirements can become excessive very quickly in order to find sufficient examples of all factor values.

Establishing intervention guidelines for labor disorders will remain a challenge. It is straightforward to create guidelines for diagnostic tests with reproducible performance measures determined against an irrefutable gold standard. Labor disorders are much harder to define. The intervention paradox makes it more difficult to select reasonable intervention thresholds based on retrospective data. Cesarean delivery usually prevents the adverse outcome, making it hard to tell postoperatively if the intervention was warranted and successful or unnecessary. Accumulating evidence from clinical trials, prospective studies, and retrospective simulations also assist in developing more practical and effective policies.

Childbirth is complex and so is the decision-making of healthcare professionals providing labor care. There is a growing expectation for precision medicine, namely health care that is optimized for an individual but is also standardized. Labor models using modern statistical techniques and multi-dimensional data can advance this goal. There has been a rapid rise in the number of FDA-cleared devices with Machine-Learning-based technologies, that complement human judgement and support the delivery of personalized healthcare.⁹² They exist in many medical specialities from radiology to oncology to general medicine. With large datasets available for training these techniques can be successfully applied to help assess labor progression.

It is unlikely that any labor curve will account for all factors that influence labor in every patient. Although better labor curves can reduce the ad hoc mental adjustments that clinicians must do when assessing labor progression, critical thinking and clinical judgment will always be needed.

Glossary

Goodness of fit

refers to how well a model represents actual observed data. There are many statistical methods to measure the discrepancy between observed values and the values expected from the model in question. Smaller discrepancies indicate better goodness of fit.

Longitudinal statistical methods

are a group of statistical methods used on data where subjects have multiple measurements over time. Repeated measures taken on an individual may be correlated. For example, dilation at one time is related to what dilation was at the previous examination. It may also be correlated with other measurements for that individual. One woman may have examinations at different and irregular intervals compared to another. Longitudinal statistical techniques account for such correlations and unbalanced observation points.

Models

are simplified representations of an object, a system, a process or even a concept. Models are efficient approximations of the targeted entity; however, they can have limitations related to the assumptions and methods used in their creation. A model can be expressed mathematically, by equations that describe the object or process of interest.

Physiological processes can be difficult to model because there are many interrelated factors, and they change as the process evolves over time. Factors may wax and wane as the process evolves or when the body invokes compensatory mechanisms to achieve homeostasis. Some factors be inaccessible or difficult to measure accurately. Finally, there is biological variation. Given the same stimulus there will be variation in response from person to person. All these issues need to be addressed when constructing models of human labor.

Mixed-effects models

are statistical models containing both fixed effects and random effects. It is also designed for analyzing the relationship between the dependent variables and covariates with repeated-measures.

Fixed effects

refer to the population level effects (change in response for one unit change in the explanatory variable). This is a quantity expected to have the same meaning in similar studies.

Random effects

refer to subject-specific contributions due to sources other than those considered (e.g., biological variation, unmeasured factors, and measurement imprecision).

Multi State Markov models

use statistical methods for modeling a process with a sequence of states where the probability of transitioning from one state to the next is dependent on the current state.

Non-linear mixed model (3 parameter logistic growth model)

This model is based on the equation:

$f\left(x\right)= \frac{L}{1+{e }^{-k(x-x_0)}}$

with assumptions about the maximum potential dilation, a dilation value for a point of inflection and a dilation value for its asymptote. It produced the curve shown in Figure 3.

Polynomial functions

are mathematical processes whereby a number (x) is raised to a power (y), such as x^y, squared x², cubic x³, quadratic x⁴, 10th order x¹⁰ etc.

Polynomial regression

is a form of regression analysis in which the relationship between the dependent variable (y) and the independent variable (x) and is modelled as an n-th degree polynomial of x.

A polynomial expression permits the relationship to be curved with critical points (maxima and minima) and inflection points (where the concavity changes).

A second order polynomial equation will have at least one variable raised to the power of 2 (x²). The curve can have one critical point.

An n-th order polynomial will have a variable raised to the power of n (xⁿ) and can have at most n-1 critical points and at most n-2 inflection points.

Regression analysis

is a set of statistical processes for characterizing the relationship between a dependent variable (y) and one or more independent predictor variables (x) (also called ‘factors’ or ‘covariates or ‘explanatory’ variables). For example, in the classic labor curves, the dependent variable is dilation, and the sole predictor variable is time.

Repeated-measures

refer to multiple assessments of the same variable taken on the same subject under different conditions or over time.