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Pain Medicine  |   August 2010
Determination and Comparison of Graded Dose–Response Curves for Epidural Bupivacaine and Ropivacaine for Analgesia in Laboring Nulliparous Women
Author Affiliations & Notes
  • Warwick D. Ngan Kee, M.B., Ch.B., M.D., F.A.N.Z.C.A., F.H.K.A.M.
    *
  • Floria F. Ng, R.N., B.A.Sc.
  • Kim S. Khaw, M.B.B.S., F.R.C.A., F.H.K.A.M.
  • Anna Lee, M.P.H., Ph.D.
  • Tony Gin, M.B., Ch.B., M.D., F.R.C.A., F.A.N.Z.C.A., F.H.K.A.M.
    *
  • * Professor, † Research Nurse, ‡ Associate Professor, Department of Anaesthesia and Intensive Care, The Chinese University of Hong Kong, Hong Kong, China.
Article Information
Pain Medicine / Obstetric Anesthesia / Pain Medicine / Pharmacology
Pain Medicine   |   August 2010
Determination and Comparison of Graded Dose–Response Curves for Epidural Bupivacaine and Ropivacaine for Analgesia in Laboring Nulliparous Women
Anesthesiology 8 2010, Vol.113, 445-453. doi:10.1097/ALN.0b013e3181bdf9da
Anesthesiology 8 2010, Vol.113, 445-453. doi:10.1097/ALN.0b013e3181bdf9da
What We Already Know about This Topic
  • ❖ The dose of epidural ropivacaine is greater than bupivacaine to achieve adequate labor analgesia in 50% of women, but there is little full dose-response data
What This Article Tells Us That Is New
  • ❖ Using randomized dosing in 300 parturients, ropivacaine was 25% less potent than bupivacaine to achieve analgesia in 50% of women
  • ❖ At a more clinically relevant dose to achieve analgesia in 90% of women, bupivacaine and ropivacaine were equipotent
SEVERAL recent studies have compared the potencies of bupivacaine and ropivacaine when given epidurally for labor analgesia.1,2 Almost exclusively, these studies have used up-and-down methodology (UDM) and have been designed to determine and compare values for the EC50—the concentration that produces an effective response (however defined) in 50% of the population, which has also been referred to as the minimum local anesthetic concentration.3 Using this methodology, the potency ratio of ropivacaine:bupivacaine has been estimated to be 0.6.1,2 Similar estimates of comparative potency have been made for other local anesthetic pairs.3,4 However, UDM has a number of important limitations. For example, EC50values are not of as much interest to clinicians as values at higher points (quantiles) on the dose–response curve such as EC90or EC95; furthermore, UDM studies provide no information on the shapes of the dose–response curves, and differences in relative potency at higher quantiles may not be the same as at the EC50. Furthermore, UDM studies and random allocation dose–response studies that use methods such as probit and logit analyses are based on binary or quantal outcomes that do not fully use data such as pain scores, which are frequently measured on continuous scales.
In this study, we have performed a graded dose–response study of bupivacaine and ropivacaine given epidurally to nulliparous women for analgesia in the first stage of labor. Rather than a sequential UDM design, we used the more traditional technique of blinded random allocation to a range of doses of each local anesthetic and rather than using a binary outcome, the response to each local anesthetic dose was quantified in terms of the proportional decrement in Visual Analog Scale (VAS) pain score. Data were analyzed using nonlinear regression. Our objectives were to characterize the complete dose–response curves of epidural bupivacaine and ropivacaine to compare the slopes of the curves and to compare estimates of potency.
Materials and Methods
Approval was obtained from the Clinical Research Ethics Committee of the Chinese University of Hong Kong, Shatin, Hong Kong, China. We recruited a total of 300 patients requesting epidural pain relief in labor into this randomized, double-blinded trial. Inclusion criteria were American Society of Anesthesiologists physical status 1 or 2, nulliparous, uncomplicated singleton pregnancy, ≥ 36 weeks' gestation, cephalic presentation, established labor with cervical dilatation ≤ 5 cm, baseline VAS pain score ≥ 50 mm (scale: 0–100 mm). Exclusion criteria were inability or unwillingness to give informed consent, parenteral opioid received within the preceding 2 h, any contraindication to epidural analgesia or allergy to local anesthetics. Written informed consent was obtained for all patients in a two-stage procedure. Initially, suitable patients were approached by a research nurse soon after admission to the labor ward, written and verbal information about the study was given, and preliminary consent to participate was obtained. Subsequently, if a patient requested epidural analgesia, compliance with inclusion and exclusion criteria was checked, consent was confirmed, and the patient was entered into the study. Patients were only recruited during office hours when members of the investigating team were available.
The study was conducted in two phases. First, according to the initial study design, 250 patients were recruited and randomized, by drawing of shuffled, opaque, coded envelopes, to one of the 10 groups (n  = 25 per group) to receive an epidural bolus of bupivacaine (10, 15, 20, 30, or 40 mg) or ropivacaine (15, 20, 30, 45, or 60 mg) on request for epidural analgesia. The two drugs were studied concurrently so that an enrolled patient would receive a randomized dose of either bupivacaine or ropivacaine. The doses were chosen assuming an anticipated ropivacaine:bupivacaine potency ratio of 0.61,2 and were spaced so that the logarithms of the doses for each drug would be approximately evenly spaced. Doses were rounded to convenient numbers for ease of preparation. After patient recruitment in the first phase was complete, preliminary analysis of the data showed that the dose–response curves for both drugs were incompletely defined in the lower dose range.5 Therefore, a second phase of the study was planned with approval from the local ethics committee. A further group of patients was recruited and randomized to receive either 5 mg of bupivacaine or 7 mg of ropivacaine (n = 25 per group). The consent process for the second phase of the study included specific information that small doses of local anesthetic were being investigated. All procedures and all aspects of clinical management were identical to the first stage of the study. The second phase of the study was registered in the Centre for Clinical Trials Clinical Registry of the Chinese University of Hong Kong (unique trial no. CUHK_CCT00126).
All study doses were prepared in identical syringes by an investigator not involved in patient assessment and were diluted to a volume of 20 ml with isotonic sodium chloride solution. Patients were instructed in the use of a 100-mm VAS pain ruler, and baseline measurements of pain, blood pressure, and heart rate were made. Intravenous prehydration of 500 ml of lactated Ringer's solution was given. With aseptic precautions, after local skin infiltration with lidocaine, the epidural space was located with an 18- or 16-gauge Tuohy needle at what was estimated to be the L2–3 or L3–4 interspace, using the technique chosen by the attending anesthesiologist. A multiorifice catheter was inserted 4 cm into the epidural space, and the patient was turned supine with left lateral uterine displacement. After aspirating the epidural catheter and checking for the presence of blood or cerebrospinal fluid, the study dose of local anesthetic was then injected epidurally. Initially, 5 ml of solution was injected. Five minutes later, after observing for any signs of intravenous or intrathecal injection, the remaining 15 ml was injected. “Time zero” was defined as the time of completion of injection of the first 5 ml.
After epidural injection, further VAS pain scores at the peak of a uterine contraction were measured at the nearest 5-min interval until 30 min. At the same time, we monitored maternal blood pressure and heart rate in addition to continuous cardiotocography, and we assessed sensory level with ice and motor block by using the modified Bromage scale (0 = no motor block; 1 = inability to raise the extended leg, able to move knees and feet; 2 = inability to raise the extended leg and to move knees, able to move feet; and 3 = complete motor block of the lower limbs). The primary outcome used for analysis was the decrease in VAS pain score at 30 min compared with baseline. If analgesia was not considered adequate by the patient at 30 min, a “rescue” bolus of 5 ml of bupivacaine (0.25%) was given and repeated up to two times at 15-min intervals as required. If analgesia was still inadequate 15 min after a third rescue bolus, the epidural catheter was declared nonfunctional and was resited, and the patient was withdrawn from the study. For such cases, the next patient recruited was allocated to the same study dose as a replacement. The study was terminated after 30 min when adequate analgesia was obtained and subsequent management was at the discretion of the attending team according to usual practice. Hypotension was defined as a decrease in systolic blood pressure to less than 20%, less than baseline, and less than 100 mmHg, and it was treated with intravenous fluid and vasopressors according to usual practice. Obstetric management was according to normal labor ward protocols.
Statistical Analysis
Sample size was determined empirically based on data from our previous dose–response study of epidural ropivacaine in labor.6 In that study, 15 patients were allocated to each dose, and estimates of the ED50and ED95were determined but with wide CIs (73–138% and 63–158% of the estimated values, respectively). Therefore, in this study, to achieve more narrow CIs, we arbitrarily decided to increase the number of patients allocated to each dose group to 25.
Univariate comparisons among dose groups for each drug were made using ANOVA or the Kruskal–Wallis test as appropriate using SPSS 15.0 for Windows (SPSS, Inc., Chicago, IL). Dose–response analysis was performed using GraphPad Prism 5.01 (GraphPad Software, Inc., La Jolla, CA). Data were initially entered into Microsoft Office Excel 2003 (Microsoft Corporation, Redmond, WA) and subsequently imported into GraphPad Prism. Values for dose were entered as x  values and were log transformed. Response data were entered as y  values after normalization of pain scores according to the following formula:
A variable slope E  maxmodel sigmoidal (four-parameter logistic) dose–response curve was fitted to the data for each local anesthetic, with the bottom parameter (minimum response) constrained to equal zero and the top parameter (maximum response) constrained to equal 100, using the following equation:
(where Y  is the response as a percentage and γ is the Hill coefficient or Hillslope).
GraphPad Prism uses an iterative approach to generate best-fit curves for the data. Parameters are adjusted to minimize the sum of squares (the sum of the squares of the vertical distances of data points from the curve) using the algorithm of Marquardt.7 Values for log(ED50), ED50, and Hill coefficient (Hillslope) were calculated with 95% CIs.
To obtain values for ED90, equation (2)was first rearranged:
Then, substitution into equation (3)was performed for Y  = 90%:
This equation was entered into GraphPad Prism and values for log(ED90) and ED90with 95% CIs were generated.
To compare the dose–response curves of bupivacaine and ropivacaine and to determine their relative potency, GraphPad Prism was set to compare two models. In the first model (null hypothesis), the data were fitted with the assumption that the datasets for the two local anesthetics shared the same best-fit value of log(ED50). In the second model (alternative hypothesis), the data were fitted with the assumption that the best-fit values of log(ED50) were distinct. The models were then compared with the extra sum-of-squares F  test.8 The procedure was repeated to compare values of Hill coefficient and ED90. The relative potency ratio of ropivacaine:bupivacaine at ED50with 95% CIs was calculated using the EC50Shift equation of GraphPad Prism. Values of P  < 0.05 were considered significant for all comparisons.
In addition to the above analyses, a secondary analysis was performed, which used a quantal (dichotomous) outcome. The purpose of this secondary analysis was to provide comparison with previously published studies that have used this type of analysis. For this, a positive response (“success”) was defined, according to convention for studies of drug potency, as a half-maximal effect. In our data, this equated to a decrease in VAS pain score to ≤50 of the baseline value at 30 min, which is the same endpoint as used in our previous dose–response study of epidural ropivacaine.6 For each drug, the numbers of responders at each dose level were tallied, and probit regression was used to calculate values for ED50and ED90with 95% CIs and an estimate of relative median potency was determined by comparing the values of ED50. This secondary analysis was performed using SPSS 15.0 for Windows.
Results
Data collection was completed within 34 months for the first stage of the study and within 8 months for the second stage. Recruitment of patients is summarized in figure 1. Overall, preliminary consent was obtained from a total of 805 patients of whom 334 patients were recruited with data analyzed for 300 patients. Patient characteristics were similar among dose groups for each local anesthetic (table 1). Baseline pain scores, time from injection of the study dose to the first epidural topup, sensory and motor changes, and the incidence of hypotension are summarized in table 2. There were significant trends toward a higher maximum level of sensory block (P  < 0.001) and a longer duration of initial analgesia (P  < 0.001) with increasing dose for both local anesthetics. In addition, there was a trend toward a greater incidence of hypotension with increasing dose that was significant for ropivacaine (P  = 0.001) but not for bupivacaine (P  = 0.04). The incidence of motor block was small and similar among groups.
Fig. 1.  Flow diagram showing recruitment of patients. Phase 2 of the study was commenced after completion of phase 1.
Fig. 1. 
	Flow diagram showing recruitment of patients. Phase 2 of the study was commenced after completion of phase 1.
Fig. 1.  Flow diagram showing recruitment of patients. Phase 2 of the study was commenced after completion of phase 1.
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Table 1.  Patient Characteristics
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Table 1.  Patient Characteristics
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Table 2.  Baseline Pain Scores, Time to Topup, Sensory and Motor Changes, and Incidence of Hypotension
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Table 2.  Baseline Pain Scores, Time to Topup, Sensory and Motor Changes, and Incidence of Hypotension
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The dose–response curves that were fitted to the data for both local anesthetics are shown in figure 2. Derived parameters for the curves are shown in table 3. The calculated values for ED50with 95% CIs for bupivacaine and ropivacaine were 11.3 (10.0–12.7) and 15.3 (13.7–17.1) mg, respectively, and the calculated values for ED90with 95% CIs were 33.4 (26.2–42.7) and 40.6 (32.4–51.1) mg, respectively.
Fig. 2.  Variable slope E  maxsigmoidal dose–response curves for bupivacaine and ropivacaine generated by nonlinear regression. Data points with error bars are shown as mean (SD). The horizontal axis is on a logarithmic scale. Antilog values for dose are shown below log(dose) values to aid interpretation. ED50was defined as the dose of the drug that reduces pain score to 50% of baseline at 30 min, and ED90was defined as the dose of the drug that reduces pain score to 90% of baseline at 30 min. The values for log(ED50) were different for the two local anesthetics, but the values for the Hill coefficient and log(ED90) were similar.
Fig. 2. 
	Variable slope E  maxsigmoidal dose–response curves for bupivacaine and ropivacaine generated by nonlinear regression. Data points with error bars are shown as mean (SD). The horizontal axis is on a logarithmic scale. Antilog values for dose are shown below log(dose) values to aid interpretation. ED50was defined as the dose of the drug that reduces pain score to 50% of baseline at 30 min, and ED90was defined as the dose of the drug that reduces pain score to 90% of baseline at 30 min. The values for log(ED50) were different for the two local anesthetics, but the values for the Hill coefficient and log(ED90) were similar.
Fig. 2.  Variable slope E  maxsigmoidal dose–response curves for bupivacaine and ropivacaine generated by nonlinear regression. Data points with error bars are shown as mean (SD). The horizontal axis is on a logarithmic scale. Antilog values for dose are shown below log(dose) values to aid interpretation. ED50was defined as the dose of the drug that reduces pain score to 50% of baseline at 30 min, and ED90was defined as the dose of the drug that reduces pain score to 90% of baseline at 30 min. The values for log(ED50) were different for the two local anesthetics, but the values for the Hill coefficient and log(ED90) were similar.
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Table 3.  Calculated Parameters Derived by Fitting Variable Slope Sigmoidal Emax  Dose–Response Curves to Datasets for Bupivacaine and Ropivacaine Using Nonlinear Regression
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Table 3.  Calculated Parameters Derived by Fitting Variable Slope Sigmoidal Emax  Dose–Response Curves to Datasets for Bupivacaine and Ropivacaine Using Nonlinear Regression
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The equations for the curves that were fitted to each local anesthetic were as follows:
Bupivacaine:
Ropivacaine:
Comparison of the two datasets showed that ED50was significantly different between bupivacaine and ropivacaine (P  = 0.0003) but the Hill coefficient (P  = 0.55) and ED90(P  = 0.29) were similar. The potency ratio for ropivacaine:bupivacaine obtained by comparing values for ED50was 0.75 (95% CI 0.65–0.88).
Results of the secondary analysis performed using probit regression showed that the calculated values for ED50with 95% CIs for bupivacaine and ropivacaine were 11.6 (7.8–15.8) and 16.4 (11.1–22.4) mg, respectively, and the calculated values for ED90with 95% CIs were 24.9 (18.1–41.5) and 35.0 (25.3–59.7) mg, respectively. The median potency ratio for ropivacaine:bupivacaine obtained from this analysis was 0.71 (95% CI 0.36–1.11).
Discussion
In this study, we have determined dose–response curves for bupivacaine and ropivacaine given epidurally to nulliparous patients for analgesia in the first stage of labor. Comparison of the two curves showed similar steepness, as evidenced by similar values for the Hill coefficient, but a difference in potency as evidenced by the position of the ropivacaine curve to the right of the bupivacaine curve and the significant difference in ED50. The calculated potency ratio at ED50for ropivacaine:bupivacaine of 0.75 (95% CI 0.65–0.88) was greater than the values previously derived using UDM by Polley et al.  1 (0.6 [95% CI 0.49–0.74]) and Capogna et al.  2 (0.6 [95% CI 0.47–0.75]), although there is an overlap of 95% CIs between the values in our study and those reported in the previous studies. No difference in potency was apparent at ED90values.
Use of nonsequential random allocation dose–response methodology has a number of advantages and disadvantages compared with UDM, the latter in the recent past having been used more commonly to compare epidural local anesthetics. UDM has gained popularity because it clusters data collection around a specific quantile on the dose–response curve, thereby enabling estimation of the dose or concentration associated with this quantile with a relatively small sample size and without assumptions about the shape of the dose–response curve.9,10 Usually, the parameter determined is the EC50, which is often referred to as the minimum local anesthetic concentration.3 UDM can be used to determine other quantiles using methods such as the biased coin design11 or the Narayana rule,12 but these have not been described commonly in the anesthetic literature.13 Results from UDM studies can be easily and simply displayed graphically. However, UDM has a number of important limitations. Estimation of ED50or EC50may be of limited use to clinicians who are more interested in doses at higher quantiles on the dose–response curve. UDM studies provide no information on the shape of the dose–response curve, and UDM studies that are designed to estimate ED50or EC50do not permit accurate inferences about the relative potency of different drugs at quantiles higher (e.g.  , ED90or EC90) or lower than EC50or ED50, especially if the dose–response curves differ in shape or symmetry. Blinding in UDM may be problematic and because observations are not independent, care needs to be taken to choose appropriate methods of analysis to avoid calculation of spuriously narrow CIs.14 
In comparison, random allocation studies permit estimation of the shape and position of the entire dose–response curve. The steepness of the dose–response relationship can be measured and compared, and by interpolation, dose values for any quantile response can be estimated. However, random allocation studies are inherently less efficient than UDM studies for estimating individual target doses. Simulation studies indicate that a sample size of 20–40 subjects in UDM studies will provide stable estimates of a target dose for most realistic scenarios,10 which is consistent with most UDM articles published in the anesthesia literature.2,3,15 In contrast, random allocation studies require at least 2 or 3 times more patients or greater10 and are thus substantially more demanding of time and resources. Furthermore, random allocation studies necessitate the administration of relatively small and large doses to some patients with the resultant potential for inadequate responses and adverse effects, respectively.
In our study, we quantified the response to different doses as the magnitude of change in VAS pain score, normalized to a percentage decrease from the baseline value. Thus, our ED50and other estimates were based on proportional responses averaged among subjects for each dose. In contrast, UDM studies use a binary or quantal outcome or response variable. In some random allocation designs, a binary response is also measured, followed by a linearizing transformation and regression, for example, probit and logit analyses. UDM and other techniques that use a binary outcome require the definition of an “effective” or “successful” response. Historically, such endpoints have been appropriate in toxicology studies in which the endpoint is death or survival. In anesthesia, a binary outcome has been used, for example, to determine minimum alveolar concentration of volatile anesthetics where the outcome is movement or no movement. However, in analgesia studies, the outcome is most often measured on a graded or continuous scale, for example, using a VAS to measure pain scores. In this situation, transformation to a binary outcome involves loss of information regarding the magnitude of response for individual patients and analysis by techniques such as probit or logit analysis is therefore suboptimal.16 Moreover, definitions of binary outcomes may be somewhat arbitrary and may differ among studies. In studies of labor analgesia, an effective outcome is commonly defined as a VAS pain score of 10 mm or less during a contraction.2,3,15 Although this outcome is simple and easy to measure, it takes no account of the initial pain score that may vary among subjects. With the availability of suitable computer programs, nonlinear modeling has been recommended as the preferred technique for analyzing graded dose–effect relationships.17 
For comparative purposes, we performed a secondary analysis of our data in which we converted results into binary responses and then performed probit regression. The calculated values for ED50using this method were similar to those obtained by nonlinear regression but with wider 95% CIs. The potency ratio obtained in the secondary analysis (0.71) was also similar to that obtained in the primary analysis (0.75); however, it should be noted that the 95% CI in the secondary analysis was wide (0.36–1.11), and because this spanned unity, the result was not statistically significant. Mostly likely, the decreased precision of potency estimates in the secondary analysis reflects loss of power associated with transformation of the graded pain score data to binary outcomes16; this is an example of the disadvantages of using this type of outcome.
Results of studies that use a binary outcome have a probabilistic meaning.10 Thus, ED50or EC50values derived using UDM or logit or probit regression provide an estimate of the dose or concentration at which 50% of the population is likely to respond. In comparison, in investigations such as the current study in which the response is based on a graded or continuous outcome, ED50is an estimate of the dose that is likely to elicit a response of magnitude that is 50% of the maximal response. To avoid confusion, an alternative nomenclature for parameters estimated in studies with graded outcomes is to use the terms D50and D90and so forth rather than ED50and ED90.17 
Table 4gives a summary of the results of published dose–response and dose-finding studies of epidural bupivacaine and ropivacaine for labor analgesia, converted to equivalent values for ED50. A wide range of results has been reported. In studies using UDM, the ED50values (minimum local anesthetic concentration) are estimates of the dose (concentration) required to produce a decrease in VAS pain score, most often to ≤10 mm, within 30 min in 50% of patients.1–4,18–25 In the random allocation dose–response studies using probit analysis, ED50was also calculated as the dose required to produce a decrease in VAS pain score by a predetermined amount in 50% of patients, but in these studies, the authors chose to use a proportional decrease in VAS pain score (to ≤10% of baseline26 or to ≤50% of baseline6 within 30 min) rather than an absolute score as the defined outcome. In comparison, in the current study, ED50is an estimate of the dose required to produce a decrease in VAS pain score of a magnitude of 50% and ED90is an estimate of the dose required to produce a decrease in VAS pain score of a magnitude of 90%. Because of the heterogeneity among these studies, when considering the application of the results of any study to clinical practice, it is important to consider the methodology used and to interpret the outcome determined in appropriate perspective relative to clinical objectives.
Table 4.  Results of Dose–Response and Dose-Finding Studies of Epidural Bupivacaine and Ropivacaine for Labor Analgesia
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Table 4.  Results of Dose–Response and Dose-Finding Studies of Epidural Bupivacaine and Ropivacaine for Labor Analgesia
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We administered all doses in a set volume of 20 ml and described the different groups in terms of mass rather than concentration of drug, the latter being preferred in studies that assess minimum local anesthetic concentration. Although our results are described in terms of ED50and ED90, for comparison with other studies they are easily converted to concentration by dividing values by the volume of each dose. Thus, the equivalent EC50and EC90values derived from our study for bupivacaine are 0.057 (95% CI 0.050–0.064) and 0.167 (0.131–0.214)% wt/vol, respectively, and for ropivacaine are 0.077 (0.069–0.086) and 0.203 (0.162–0.256)% wt/vol, respectively. Also, we described and analyzed doses in terms of drug mass rather than on a molar basis. Because ropivacaine has a smaller molecular weight than bupivacaine, the molar potency ratio for ropivacaine:bupivacaine is slightly less than the value calculated by drug mass.2 
Of clinical interest, although our results showed a significant difference in potency between bupivacaine and ropivacaine at ED50, the difference at ED90was not significant. This relates to the position of the ED90quantiles on the flat upper portion of the dose–response curves and may explain in part why several clinical studies that have compared single concentrations of bupivacaine and ropivacaine, particularly those that have used a relatively high concentration of 0.25%, have not shown important differences in analgesia or sensory and motor block.27 
We conducted our study in two phases. The second phase was planned and started after completion and preliminary analysis of the results of the first phase. Unfortunately, this resulted in dose allocation within the study not being fully randomized because the smallest doses of each drug were only given in the second phase. However, all other aspects of conduct of the study were identical for the two phases of the study, and we are aware of no important differences in anesthetic or obstetric management that occurred between the two periods of the study. Nonetheless, we acknowledge that this is a shortcoming of our study.
Finally, our use of nonlinear regression has a number of limitations. Our dose–response curves were derived with the assumption that an E  maxmodel was correct and appropriate. The values of the coefficients of determination (R  2) for the derived curves for bupivacaine and ropivacaine were 0.53 and 0.59, respectively, indicating only a moderate goodness of fit. It is possible that other models could also be fitted to the data equally well or better. However, use of an E  maxmodel can be justified because it is commonly used to describe drug–receptor interactions.28 Other random allocation study designs also require assumptions, for example the validity of linear transformations.
In summary, in this study, we used random allocation dose–response methodology to evaluate and compare the analgesic response to epidural bupivacaine and ropivacaine in laboring nulliparous patients. We derived variable slope sigmoidal E  maxdose–response curves using nonlinear regression and determined that ED50was greater for ropivacaine compared with bupivacaine but ED90and the slopes of the curves were similar.
The authors thank the midwives of the Labour Ward, Prince of Wales Hospital, Shatin, Hong Kong, China, for their assistance and cooperation and John L. Plummer, Ph.D., A.Stat., Chief Medical Scientist, Department of Anaesthesia and Pain Medicine, Flinders University, Bedford Park, Adelaide, South Australia, Australia, for statistical advice for the first phase of the study. Bee B. Lee, M.B.B.S., F.A.N.Z.C.A., F.H.K.A.M., Adjunct Assistant Professor, Department of Anaesthesia and Intensive Care, Chinese University of Hong Kong, Shatin, Hong Kong, China, contributed to the design of the first phase of the study and to data collection in the first phase of the study and Karman K. L. Ng, M.B., Ch.B., F.A.N.Z.C.A., F.H.K.A.M., Adjunct Assistant Professor, Department of Anaesthesia and Intensive Care, Chinese University of Hong Kong, contributed to data collection in the second phase of the study.
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Fig. 1.  Flow diagram showing recruitment of patients. Phase 2 of the study was commenced after completion of phase 1.
Fig. 1. 
	Flow diagram showing recruitment of patients. Phase 2 of the study was commenced after completion of phase 1.
Fig. 1.  Flow diagram showing recruitment of patients. Phase 2 of the study was commenced after completion of phase 1.
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Fig. 2.  Variable slope E  maxsigmoidal dose–response curves for bupivacaine and ropivacaine generated by nonlinear regression. Data points with error bars are shown as mean (SD). The horizontal axis is on a logarithmic scale. Antilog values for dose are shown below log(dose) values to aid interpretation. ED50was defined as the dose of the drug that reduces pain score to 50% of baseline at 30 min, and ED90was defined as the dose of the drug that reduces pain score to 90% of baseline at 30 min. The values for log(ED50) were different for the two local anesthetics, but the values for the Hill coefficient and log(ED90) were similar.
Fig. 2. 
	Variable slope E  maxsigmoidal dose–response curves for bupivacaine and ropivacaine generated by nonlinear regression. Data points with error bars are shown as mean (SD). The horizontal axis is on a logarithmic scale. Antilog values for dose are shown below log(dose) values to aid interpretation. ED50was defined as the dose of the drug that reduces pain score to 50% of baseline at 30 min, and ED90was defined as the dose of the drug that reduces pain score to 90% of baseline at 30 min. The values for log(ED50) were different for the two local anesthetics, but the values for the Hill coefficient and log(ED90) were similar.
Fig. 2.  Variable slope E  maxsigmoidal dose–response curves for bupivacaine and ropivacaine generated by nonlinear regression. Data points with error bars are shown as mean (SD). The horizontal axis is on a logarithmic scale. Antilog values for dose are shown below log(dose) values to aid interpretation. ED50was defined as the dose of the drug that reduces pain score to 50% of baseline at 30 min, and ED90was defined as the dose of the drug that reduces pain score to 90% of baseline at 30 min. The values for log(ED50) were different for the two local anesthetics, but the values for the Hill coefficient and log(ED90) were similar.
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Table 1.  Patient Characteristics
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Table 1.  Patient Characteristics
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Table 2.  Baseline Pain Scores, Time to Topup, Sensory and Motor Changes, and Incidence of Hypotension
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Table 2.  Baseline Pain Scores, Time to Topup, Sensory and Motor Changes, and Incidence of Hypotension
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Table 3.  Calculated Parameters Derived by Fitting Variable Slope Sigmoidal Emax  Dose–Response Curves to Datasets for Bupivacaine and Ropivacaine Using Nonlinear Regression
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Table 3.  Calculated Parameters Derived by Fitting Variable Slope Sigmoidal Emax  Dose–Response Curves to Datasets for Bupivacaine and Ropivacaine Using Nonlinear Regression
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Table 4.  Results of Dose–Response and Dose-Finding Studies of Epidural Bupivacaine and Ropivacaine for Labor Analgesia
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Table 4.  Results of Dose–Response and Dose-Finding Studies of Epidural Bupivacaine and Ropivacaine for Labor Analgesia
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