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Obstetric Anesthesiology: Research Report

The Development and Validation of a Dynamic Model to Account for the Progress of Labor in the Assessment of Pain

Conell-Price, Jessamyn BA; Evans, Jennifer B.; Hong, Daewha MS; Shafer, Steven MD; Flood, Pamela MD

Editor(s): Wong, Cynthia A.

Author Information
doi: 10.1213/ane.0b013e31816d14f3
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Parturition is among the most painful experiences of a woman's lifetime.1–3 Although many women have very high levels of pain during labor, there is wide variability in the amount of pain experienced.3–6 Pain during early labor typically increases with time and cervical dilation.7,8 Although many physical and physiological factors have been linked to the amount of labor pain women experience, it is difficult to discern the contribution of individual factors because the painful stimuli change rapidly as labor progresses.6,9 We sought to create a model for labor pain as a dynamic process that can potentially be used to assess the contributions of specific physiological and anatomical correlates of pain over the course of labor. In addition, we tested the utility of our model by using it to assess whether oxytocin administration affects labor pain.


This retrospective study was approved by the IRB of Columbia University Medical Center. The requirement for informed consent was waived. Two hundred eligible parturients were identified by screening sequential delivery records at the Sloane Hospital for Women (New York Presbyterian Hospital) from October 2006 to January 2007. The inclusion criteria were (1) healthy nulliparous parturients aged 18–49 yr; (2) gestational age of 37–42 wk; (3) vaginal delivery of a singleton infant; and (4) infant birth weight 2.5–4.0 kg. Patients with preeclampsia and chronic pain syndromes were excluded.

Cervical dilation, pain scores in the first stage of labor before analgesic treatment, gestational age, spontaneous or induced labor, use of oxytocin and/or cervical ripening drugs, the type of vaginal delivery (normal spontaneous vaginal delivery or assisted) and birth weight were extracted from the care providers’ notes in the electronic medical record. The time and date of each event or observed data point were recorded including time of admission, pain score, cervical dilation, first administration of oxytocin, first administration of analgesia, and the time of delivery. Numerical rating scale (NRS) scores with contractions were recorded by obstetrical nurses and physicians using an 11-point scale (0 is no pain and 10 is the worst pain imaginable). Because NRS scores of 0 are sometimes recorded for patients not yet in labor, NRS reports of 0 were not included in our analysis. Cervical dilation measurements are reported in 1 cm increments from 0 cm (closed cervix) to 10 cm (fully dilated cervix). When concurrent NRS scores and cervical dilations were not available, the closest chronological cervical examination was substituted. When used, oxytocin was administered according to a standard hospital protocol (initial infusion of 1 mU/min, increased 1 mU/min every 15 min until contraction duration was 40–60 s, with a maximum dose of 40 mU/min).

Data Analysis

To provide a meaningful way to compare time data, all times were converted to the number of hours before the first measurement of full dilation. The first 100 consecutive parturients drawn from the hospital delivery records were defined as the training set. The next 100 women were defined as the validation set. The two data sets were combined, parturients with only pain scores of 0 were omitted, and pain scores from the remaining women were used for the main model.

For each pain score, we noted whether or not oxytocin administration had begun. Pain scores taken after a patient had received any oxytocin were counted as “with oxytocin.” The pain scores reported while patients were receiving oxytocin (with oxytocin) and pain scores reported when patients had not received oxytocin (no oxytocin) were compared with an unpaired t-test.

Pain Model

The pain model makes the single a priori assumption that pain begins in early labor and increases in intensity with increasing cervical dilation. This assumption was tested by determining the number of pain scores that decreased with increasing cervical dilation in the absence of anesthesia. The NRS pain response to dilation was fit to a sigmoid equation with floating variables for minimum pain value, maximum pain value, cervical dilation at half of the maximum pain value, and rate of increase using NONMEM (Nonlinear Mixed-Effects Modeling; Globomax, Ellicott City, MD)

where CD is the cervical dilation, NRSMIN is the minimum reported pain score, NRSMAX is the maximal reported pain score, CD50 is the cervical dilation associated with 50% of maximal pain, and γ is the steepness of the linear portion of the curve. The NONMEM control stream is provided in the Appendix.

The cervical dilation and NRS pain data from the first 100 subjects were used for the training data set. The applicability of the model was tested by applying the equation derived from our training set to the data from the next 100 subjects (validation set). The model was validated based on the model performance errors (PE), which were calculated as the difference between the measured pain score and the predicted pain score

Specifically, we calculated two metrics for the validation set: the median PE (a measure of bias of the estimated model), and the median absolute PE (the median of the absolute values of the PEs, a measurement of the typical inaccuracy of the model).

Data from all parturients (the training and validation sets combined) were used to develop the full model and to test a sample covariant. For the main model, we allowed for interindividual variation on NRSMIN, NRSMAX, and CD50. To determine the potential utility of this model, we tested the hypothesis that oxytocin treatment increased the pain of labor. We tested each parameter (NRSMIN, NRSMAX, and CD50) individually using log likelihood minimization in NONMEM to assess whether oxytocin treatment significantly affected each variable. Log likelihood determinations of nested models were compared using a χ2 distribution. Oxytocin effect was included in the final model based on a statistically significant improvement as measured by the likelihood ratio test. The accuracy of the parameters determined by the model was evaluated with log likelihood profiling; one parameter at a time was fixed at values ranging from 10% to 1000% of the model's optimal value for that parameter. The changes in log likelihood that resulted from altered parameter values were transformed with a χ2 distribution. This method allowed us to determine 95% confidence intervals for each parameter.

To determine whether there were pain differences in subjects treated with oxytocin, and whether the time course of labor could explain these differences, we compared the time course of the early (cervical dilation 0 to 4 cm) and late phases (cervical dilation 5 to 10 cm) of labor with a linear regression similar to that described by Friedman and others.10 Values reported are mean ± sd. P < 0.05 is considered significant.


Population Characteristics

Gestational age, infant birth weight, and time from admission until full cervical dilation are summarized in Table 1. Ninety-one percent of women received epidural analgesia. Four women were treated with systemic opioid analgesia. Between 0 and 11 pain scores were obtained from each parturient with a median of two pain scores from each woman before analgesia was initiated. Seventy-three percent of women were treated with oxytocin at some point during their parturition. Twenty-four percent of all parturients were admitted for the induction of labor. Ten percent of all parturients received dinoprostone or misoprostol for cervical ripening. Ninety-three percent of parturients (91 in the training set and 95 in the validation set) had nonzero pain scores and scores from these women were included in the training, validation, and main model.

Table 1
Table 1:
Study Subjects’ Characteristics

Validity of the Model

Demographic variables, characteristics of labor, and average NRS scores did not differ between the training and validation sets (data not shown). Figure 1A shows the NRS scores versus cervical dilation from the first 91 subjects (the training set) and the subsequent 95 subjects (the validation set). PE is shown in Figure 1B. Median NRS score PE for the training set was 0.39 NRS units. Absolute median PE was 2.02 NRS units. When the model was tested in the validation set, median PE was −0.27 NRS units, and median absolute PE was 2.2 NRS units.

Figure 1.
Figure 1.:
Development of the model. The data from a training set of 91 parturients (+) was fit with the sigmoid equation (numeric rating scale [NRS] = NRSMIN + (NRSMAX − NRSMIN) * CDγ/(CDγ+ CD50 γ)). The resulting function was used to predict the data from a validation set (•) of 95 parturients. A, The values obtained for the training set are: NRSMIN = 4.1, NRSMAX = 8.4, CD50 = 3.6 cm, and γ = 2.8 (r = 0.43, n = 209 data points, P < 0.001). When this function is applied to the validation set (r = 0.41, n = 211 data points, P < 0.001). B, The residuals or performance errors (PEs) (measured NRS scores − predicted NRS scores) are plotted against cervical dilation for the training set (•) and the validation set (+). The upper and lower bounds show two standard deviations from zero based on the training set data (±5.5 NRS).

Main Model

There was large variation in pain scores during nulliparous labor in our population (Fig. 2). The relationship between NRS and cervical dilation was modeled as a sigmoid function with data from the 186 subjects with nonzero pain scores (Table 2). The median PE for the main model was 0.14 NRS units and the absolute PE was 2.2 NRS units.

Figure 2.
Figure 2.:
A model for predicting pain scores with the progress of nulliparous labor with oxytocin treatment as a covariant. Data for numeric rating scale (NRS) versus cervical dilation for subjects receiving oxytocin (SYMBOL) and not receiving oxytocin (•) were fit with the sigmoid equation NRS = NRSMIN + (NRSMAX − NRSMIN) * CDγ/(CDγ+ CD50 γ). The fit was significantly improved with oxytocin use as a covariant on NRSMIN (P < 0.001), but not improved by varying NRSMAX, γ or CD50. NRSMIN was 48% higher for the parturient population who received oxytocin.
Table 2
Table 2:
Calculated Model Parameters for Training and Validation Sets and in Subjects Receiving and Not Receiving Oxytocin

Reported pain scores during uterine contractions increased with progressive cervical dilation and only 7% of women reported a decrease in pain scores at any point in labor. The average pain score in the early phase of labor was 5.6 ± 2.7 NRS units (n = 350 scores) and increased to 7.8 ± 2.2 NRS units in late labor (n = 69 scores). Eighty-four percent of the pain scores were from the early phase of labor, due to increasing use of analgesia over the course of labor.

Oxytocin Effect

Treatment with oxytocin significantly affected the relationship between pain scores and cervical dilation. The average pain scores reported when parturients were not receiving oxytocin (6.2 ± 2.8 NRS units) were not significantly different from the pain scores recorded while parturients were receiving oxytocin (5.6 ± 2.7 NRS). However, the model demonstrated a significant effect of oxytocin on the relationship between cervical dilation and reported pain. NRS scores at NRSMIN or the beginning of labor were 48% higher in subjects who received oxytocin compared with those who did not. Among scores taken with oxytocin, the NRSMIN parameter estimate was lower with induced labor than with augmented labor. Although this difference in pain scores did not reach significance, it indicates that the increase of NRSMIN with oxytocin cannot be attributed to induction.

The maximum levels of pain and the steepness of the curve were not significantly affected by oxytocin administration (Table 2). The model's predictions were unbiased (neither positively nor negatively skewed) and were accurate to within 2 NRS in patients receiving and not receiving oxytocin (not receiving oxytocin: median PE = 0.05 NRS units, absolute median PE = 2.05 NRS units; receiving oxytocin: median PE = 0.25 NRS units, median absolute PE = 2.02 NRS units). Figure 3 shows probability estimates of values for each model parameter.

Figure 3.
Figure 3.:
Log likelihood profiling to determine the accuracy of calculated variables. Log likelihood profiling evaluates a range of values for each variable and the probability of each parameter being correct. Here the x-axis represents a potential value for a parameter and the y-axis represents the probability that the value represents the true mean. These log likelihood profiling graphs show values without (black) and with oxytocin (red) for (A) numeric rating scale (NRS)MIN (the red dotted line at NRSMIN parameter estimate for oxytocin falls outside the 95% confidence interval for the black curve without oxytocin and the black dotted line parameter estimate without oxytocin falls outside the red oxytocin curve) (B) NRSMAX, (C) CD50, and (D) γ (steepness).

Labor Curve Comparison

There was an exponential increase in cervical dilation over time, with a slowly increasing early phase followed by a rapidly increasing late phase. Figure 4 shows the progress of cervical dilation over time for the group of 200 parturients. To approximate a comparison with Friedman's description of the progress of labor, the early and late phases of labor were fit with separate linear equations for women who were treated with oxytocin and who were not treated with oxytocin. During the early phase of labor, the women treated with oxytocin had slower progress of labor than women not treated with oxytocin (P < 0.001). The pattern reversed in the late phase where women treated with oxytocin had a steeper slope (P < 0.001).

Figure 4.
Figure 4.:
Comparison to the standard labor curve for nulliparas with and without oxytocin treatment. Cervical dilation as a function of time for the cohort of 200 parturients who were receiving oxytocin (SYMBOL) and who were not being treated with oxytocin (•). According to the method of Friedman's,10 the early (cervical dilation 0–4 cm) and late phases of labor (cervical dilation 5–10 cm) were fit separately with linear equations. The rate of change in early labor was slower for the patient population treated with oxytocin (P < 0.001) but the rate of change in late labor was faster (P < 0.001). Early labor without oxytocin, y = 3.1 + 0.07x (r = 0.32, n = 548 data points, P < 0.001). Early labor with oxytocin, y = 3.1 + 0.04x (r = 0.32, n = 354, P < 0.001). Late labor without oxytocin, y = 8.7 + 0.43x (r = 0.70, n = 214, P < 0.001). Late labor with oxytocin y = 9.3 + 0.59x (r = 0.76, n = 383, P < 0.001).


We have developed and validated a model for predicting pain during the progress of labor using data from 186 nulliparous parturients. Although pain scores were highly variable in both the early and late phases of labor, we found that pain scores are positively related to cervical dilation during the first stage of labor. The definition of the early phase of labor used in the current study (cervical dilation <5 cm) corresponds to the range of cervical dilation that Friedman observed during the latent phase of labor in most women, and the late phase roughly corresponds to the active phase of labor.10 We were also able to successfully use our model to assess the effect of oxytocin on labor pain in nulliparous women.

Previous studies have evaluated the average amount of pain women experience over the entire course of labor or have been restricted to a comparison of a few points during labor.9,11–15 These authors have also found high pain scores, variability and a positive correlation with pain and cervical dilation. For example, Dannenbring et al. reported an average visual analog score during labor of 6.5 ± 2.5.9 Brown et al. reported a visual analog score of 6.0 ± 2.2 in latent labor and 8.4 ± 2.4 in active labor.15 Our population had average pain scores similar to those previously reported. The pain scores that women reported before analgesia in this study were similar to the pain scores reported by a population of women who elected not to receive analgesia during childbirth.16

Parturient populations often report high levels of pain during the first stage of labor. Factors that have been repeatedly linked to higher levels of pain are nulliparity,1,8 request for analgesic treatment,8,17 and uterine contraction duration and rate.12,18 Other factors are more controversial and include position,12,14,19 birth preparation classes and expectation of pain level,20,21 feelings of control,7 history of dysmenorrhea,3,5 education level and socioeconomic class.20 When factors are closely related, such as previous pain experience and parity,3 or maternal fatigue and cervical dilation,13 it has been difficult to discern the relative influence of each factor on perceived pain. These factors and their potential covariance could be analyzed with our model in the future.

The progress of labor in our population is similar to the typical labor progress previously reported for nulliparas.22 However, the rate of change of cervical dilation during the early phase of labor in our model was shallower than Friedman's. This may be due to the inclusion of women undergoing induction of labor in our model.23 We found that women treated with oxytocin had a longer early phase than women who were not treated with oxytocin. Since this is a retrospective study, the difference likely reflects the fact that obstetricians prescribed oxytocin for both induction of labor and augmentation of labor in women with prolonged latent phases. Conversely, the late phase of labor was more rapid in women treated with oxytocin than in those who were not. This finding suggests that oxytocin effectively increases uterine contractility and the speed of parturition. The only significant difference in pain between the two groups was higher minimum pain among women receiving oxytocin; there was no difference in maximum pain or in the rate of increase in pain with oxytocin treatment. Our finding supports a previously reported correlation between abnormal progress of labor and pain.24

There are some constraints inherent to the data set used to develop this model. First, there is left censoring of data; women may not present to the hospital at the onset of labor before their pain is significant. Second, there is right censoring of data. In our health care setting, all parturients have access to analgesia on demand. We would consider it unethical to construct a prospective study in any other way. When labor pain becomes significant, many women receive analgesia; it is likely that those with the highest pain scores early in labor will be excluded. In addition, parturients who do not request labor analgesia may be different from those who do. Given these constraints, it would be useful to validate our model in a different population without such high penetration of analgesia use. A drawback to using a retrospective database is that measurements of cervical dilation and NRS pain scores were not always obtained concurrently and were not taken at the same rate and time intervals for all women in the study.

Another challenge with the model's application is the large prediction error of the model (±2 NRS), which is due to the wide variation of pain scores in any parturient population; this is the biological variation that we seek to explain. The point is not that the model is very predictive; the purpose of the model is to remove the variable of labor progress so that other factors can be quantitatively evaluated, independent of the progress of labor. In this population, cervical dilation explained 16%–20% of the variability in reported pain. Since parity affects the amount and pattern of labor pain, limiting pain scores to nulliparous parturients may have also increased the accuracy of the model. This preliminary model was able to describe a significant difference in pain at low cervical dilations related to oxytocin use that was not detected by comparing average pain values. The fact that this difference was present in early labor may suggest mechanistic information about the effect of oxytocin on the progress of labor. Patients whose labors were induced with oxytocin reported lower pain scores at early dilations (NRSMIN) than patients whose labors were augmented with oxytocin. This suggests that the higher NRSMIN in patients receiving oxytocin compared with patients not receiving oxytocin is not driven by induction per se, but rather by oxytocin treatment or by a confounding attribute of both induced and augmented labor that requires treatment with oxytocin.

In conclusion, we hope that this modeling technique, if validated, will be useful for prospective studies that seek to determine the effect of variables on labor pain. Our model provides a quantitative method for comparing pain throughout the first stage of labor that is suited to statistical analysis. Both accurate knowledge of what to expect and effective pain relief25,26 have a strong positive effect on patients’ satisfaction with labor. Understanding the reasons that underlie variability in labor pain may provide some guidance to women in terms of “what to really expect while expecting.”


$PROB Sigmoidal PD Data

$DATA laborpainfull.txt



E0=THETA(1)*EXP(ETA(1)); Baseline


IF(OXY.EQ.1) E0=(1 + FAC1/100) * E0; Factor 1 is

% change in E0 induced by OXY

EMAX=THETA(2)*EXP(ETA(2)); Max Effect


IF(OXY.EQ.1) EMAX=(1 + FAC2/100) * EMAX;

Factor 2 is % change in EMax induced by OXY

C50=THETA(3)*EXP(ETA(3)); C50


IF(OXY.EQ.1) C50=(1 + FAC3/100) * C50; Factor 3 is

% change in C50 induced by OXY

GAM=THETA(4); There is no ETA on Gamma

since it is very hard to fit


IF(OXY.EQ.1) GAM=(1 + FAC4/100) * GAM;

Factor 4 is % change in GAM induced by OXY





(0,3.59); E0 isn't a factor

(0,8.74); Emax

(0,3.07); CD50

(.5,4.29,10); Gamma

48.1; FAC1 on E0, This control stream tests the

parameter E0


0 FIX; FAC3 on C50

0 FIX; FAC4 on GAM








METHOD=1; FOCE method




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