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Anesth Analg 2000;90:1191-1197
© 2000 International Anesthesia Research Society

GENERAL ARTICLES

An Alternate Method for Estimating the Dose-Response Relationships of Neuromuscular Blocking Drugs

Aaron F. Kopman, MD*, Monika M. Klewicka, BA{dagger}, and George G. Neuman, MD*

*Department of Clinical Anesthesiology, New York Medical College, Valhalla; and {dagger}Department of Anesthesiology, St. Vincent’s Hospital, New York, New York

Address correspondence and reprint requests to Aaron F. Kopman, MD, Department of Anesthesiology, Room NR 408, St. Vincent’s Hospital and Medical Center, 170 W. 12th St., New York, NY 10011. Address e-mail to AKopman{at}interport.net


   Abstract
Top
 Abstract
Introduction
 Methods
 Results
 Discussion
 Appendix 1*
 References
 
Slopes of the dose-response relationships for all available neuromuscular blocking drugs appear to be essentially parallel and to approximate a log-dose/logit value of 4.75. We tested the possibility of estimating both 50% effective dose (ED50) and 95% effective dose (ED95) values from a single dose-response data point when that slope is postulated. We compared the ED50 and ED95 values of rocuronium and succinylcholine calculated by using traditional log-dose/logit regression analysis with the same values obtained by averaging individual estimates of potency as determined by using the Hill equation. After the induction of anesthesia (propofol/alfentanil), tracheal intubation was accomplished without the administration of neuromuscular blocking drugs. Anesthesia was maintained with nitrous oxide and propofol. The evoked electromyographic response to 0.10-Hz single stimuli was continuously recorded. After baseline stabilization, a single IV bolus of succinylcholine (0.08–0.26 mg/kg, n = 50) or rocuronium (0.13–0.30 mg/kg, n = 40) was administered and the peak effect noted. By using log-dose/logit regression analysis, we calculated ED50 and ED95 values for rocuronium of 0.17 and 0.33 mg/kg and 0.14 and 0.27 mg/kg for succinylcholine. When potency was calculated from the Hill equation, the resultant ED50 and ED95 values did not differ by more than ±4% from those obtained by using regression analysis. Averaging of single-dose estimates of neuromuscular potency provides a useful adjunct and reasonable alternative to conventional regression analysis.

Implications: Averaging of single-dose estimates of neuromuscular potency provides a useful adjunct and reasonable alternative to conventional regression analysis.


   Introduction
Top
 Abstract
 Introduction
Methods
 Results
 Discussion
 Appendix 1*
 References
 
Dose-response relationships for neuromuscular blocking drugs (NMD) are customarily determined by regression analysis. Because the association between dose and effect yields a sigmoid curve, estimation of 50% effective dose (ED50) and 95% effective dose (ED95) values by linear regression analysis first requires suitable mathematical transformation of the data (1). Log dose versus probit (2), logit (3), or arc-sine (4) plots have all been used successfully. However, regression analysis does not provide dose-response information about individual subjects. A decade ago, Meretoja and Wirtavouri (5) attempted to overcome this problem by using a two-dose technique. They reasoned that the slopes of the dose-response relationships for most NMDs were essentially parallel. Because a straight line can be defined by a single point when the slope is known, once a single subparalyzing point has been determined, the additional dose required for ED95 can be estimated by extrapolation. By using log/probability graph paper and a straight edge and by assuming a log-dose/probit slope of 6.5, they were able to determine individual dose requirements for atracurium. In a more recent paper, Wright et al. (6) computerized this process by using log-dose/logit analysis. They assumed a slope of 5.0 for the dose-response relationship of atracurium and vecuronium. This is equivalent to a log-dose/probit slope of 6.43, not substantially different from the value used by Meretoja and Wirtavouri (5).

Perhaps the administration of the second incremental dose designed to achieve 90% to 95% block is unnecessary. If the slope of the dose-response relationship is assumed, then, it should be possible to estimate the ED50 and ED95 values for a person once the effect of a single dose is known. To test this hypothesis we compared the ED50 and ED95 values as calculated by traditional single-dose log-dose/logit regression analysis with the same values obtained by averaging individual estimates of potency as determined by using the modifications of the Hill equation provided by Wright et al. (6) (see Appendix 1). We used a log-dose/logit slope of 4.75 in our computations because this was the average value we calculated after a review of 62 dose-response studies of 11 different NMDs (Fig. 1).



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  		Figure 1. Slopes of clinically available neuromuscular blocking drugs do not differ significantly. This figure illustrates the average 50% and 95% effective dose (ED50 and ED95) values of 11 neuromuscular blocking drugs gathered from a review of 62 separate peer-reviewed dose-response studies. The slope of the log-dose/logit relationship was calculated from the ED50 and ED95 values and ranged from 4.0 to 5.8 with an mean value of approximately 4.75. ED50 = 0.00 logits; an ED95 = 1.28 logits.

 
Traditional methods of analysis impose an additional limitation. With long-acting NMDs, potency may be estimated by a cumulative-dose technique, minimizing the number of subjects that need to be studied (7). With NMDs of intermediate-duration this approach becomes questionable (8,9). Significant recovery may start to take place in the interval between incremental doses. For NMDs of short-duration, a cumulative dose technique is clearly not appropriate (10,11). Thus, studies of the potency of short-acting NMDs, such as rapacuronium (12) or GW 280430A (13), would appear to inevitably require recruitment of a substantial number of subjects. If the ED50 and ED95 values can both be estimated from a single dose-response point, then, it may be possible to reduce the number of subjects that need to be recruited in dose-response and dose-screening studies of NMDs of short-duration.


   Methods
Top
 Abstract
 Introduction
 Methods
Results
 Discussion
 Appendix 1*
 References
 
A total of 93 ASA physical status I and II adult patients (ages 18 to 61 yr) undergoing elective surgical procedures were included in the study. All patients were free from neuromuscular disease and had a body mass index >=17.5 and <=27.5. The protocol was approved by our human subject review committee, and informed consent was obtained. Anesthesia was induced with alfentanil 40 µg/kg plus propofol 2.0–2.5 mg/kg IV, and tracheal intubation was accomplished without the use of NMDs. Anesthesia was maintained with nitrous oxide (65% to 70% inspired), and propofol 50–75 µg · kg-1 · min-1. Ventilation was controlled, and end-tidal PCO2 was maintained between 34 and 40 mm Hg.

The indirectly evoked integrated compound action potential of the first dorsal interosseous muscle to supramaximal stimulation of the ulnar nerve at the wrist was measured and recorded by using a Datex NMT 221 monitor (Tewksbury, MA). Single stimuli at 0.10 Hz were administered during the period of observation, and twitch depression was continuously recorded. Control twitch height was established after a 15- to 20-min period of baseline stabilization. Immediately after baseline calibration, a single dose of either rocuronium or succinylcholine was administered.

The first patient received a bolus of 0.17 mg/kg of rocuronium. This dose was selected to approximate what we anticipated (from previous work in our department) to be an ED50 dose. By using the Hill equation with a postulated slope of 4.75 the ED50 was calculated for this patient (see Appendix 1). The second patient received a dose which approximated the calculated ED50 for Patient 1. Patients 3–5 were given a dose that approximated the average estimated value of ED50 from the previously studied patients in this series. In a similar manner, Patients 6–10 were administered a dose calculated to achieve 20% twitch depression. The next five patients received doses approximating the average estimated value of the ED80. In the remaining patients, doses of rocuronium were selected to provide essentially equal distribution in 0.01 mg/kg increments in the range estimated to span responses from 10% to 90% twitch depression. No attempt was made to administer ED05 or ED95 doses because we wished to avoid responses (0% or 100%) which could not be plotted on a logit scale. The protocol used with succinylcholine was identical to that used in studying rocuronium. Patient 1 received succinylcholine 0.15 mg/kg.

Method 1, Regression Analysis
After log-dose/logit transformation of the data, the best fit line of regression was determined by using the method of least squares. Complete twitch depression was plotted as an effect of 99.5%. The coefficient of determination (R2), slope (including confidence limits), and standard error of the estimate of X (log-dose) were calculated by using the data analysis tools package (Microsoft® Excel 98 for the Macintosh; Microsoft, Redmont, WA). Values of ED50 and ED95 were calculated after log/logit transformations from the previously mentioned line of regression.

Method 2, Single-dose Estimation
For each patient, the estimated ED50 and ED95 values were computed from the Hill equation (see Appendix 1, Equations 2 and 3). The arithmetic mean, standard deviation, and standard error of the mean of these individual values was then calculated.

Comparisons between ED50 and ED95 values for three different slopes (4.0, 4.75, and 5.5) were made by using an unpaired Student’s two-tailed t-test. These values were chosen because it is uncommon to find clinical studies that report log-dose/logit slopes outside of this range. The ED50 and ED95 values determined by regression analysis were also compared with the values calculated by using a postulated slope of 4.75. The Bonferroni inequality correction (for three comparisons) was applied. Observed differences were considered significant if P < 0.05.


   Results
Top
 Abstract
 Introduction
 Methods
 Results
Discussion
 Appendix 1*
 References
 
Rocuronium
A total of 41 patients were studied in the rocuronium group (see Table 1). Administered rocuronium doses ranged from 0.13 to 0.30 mg/kg. One patient was excluded from analysis for protocol violations. The range of responses in the other 40 patients ranged from 9% to 97% twitch depression.


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  		Table 1. Demographics
 
By using conventional regression analysis of the log-dose/logit plot, the calculated ED50 and ED95 values were 0.171 ± 0.038 (SD) and 0.325 ± 0.072 mg/kg, respectively (Table 2, Fig 2). The best fit line of regression had a slope of 4.55 with a R2 of 0.594 (see Figure 2). These ED50 and ED95 values were virtually identical to the estimates we obtained by assuming a slope of 4.75.


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  		Table 2. Estimates of the Potency of Rocuronium
 


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  		Figure 2. Log-dose/logit plot of the dose-effect relationship for rocuronium. Y = 4.55 x X + 3.50. R2 = 0.592.

 
By using regression analysis, the calculated values for the ED50 and ED95 did not change by more than ±2.5%, once 26 patients had been recruited. By using single-dose estimates of potency (slope = 4.75), similar stability was reached after obtaining 20 data points.

Succinylcholine
A total of 52 patients were studied in the succinylcholine group. Administered doses of succinylcholine ranged from 0.08 to 0.26 mg/kg. One extreme outlier was excluded from analysis because we suspected that this patient probably was heterozygotic for atypical plasma cholinesterase. Our estimated ED95 for this individual (0.11 mg/kg, 98% T-1 depression) was 0.09 mg/kg, the time to peak effect was 190 s, and the time to 50% return of T-1 sensation was 9.25 min. Another individual was excluded because of protocol violations.

By using conventional regression analysis of the log-dose/logit plot, the calculated ED50 and ED95 values were 0.138 ± 0.034 (SD) and 0.273 ± 0.068 mg/kg, respectively (see Table 2, Figure 3). The best fit line of regression had a slope of 4.32 with a R2 of 0.696. These ED50 and ED95 values were very similar to the estimates we obtained by assuming a slope of 4.75.



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  		Figure 3. Log-dose/logit plot of the dose-effect relationship for succinylcholine. Y = 4.35 x X + 3.75. R2 = 0.693.

 
When using regression analysis, the calculated value for ED50 did not change materially, once 19 patients had been recruited (0.142 vs 0.138 mg/kg when n = 50). However, the ED95 did not stabilize until 39 subjects had been studied (0.270 vs 0.273 mg/kg). By using single-dose estimates of potency (slope = 4.75), stability was reached after only 10 data points had been obtained (ED50 = 0.145 vs 0.143 mg/kg when n = 50, and ED95 = 0.270 vs 0.265 mg/kg).


   Discussion
Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
Appendix 1*
 References
 
The generally accepted ED95 value of rocuronium under nitrous oxide-opioid anesthesia ranges from 0.30 to 0.39 mg/kg (14–16). Our ED95 value of 0.325 mg/kg is compatible with these estimates. There is less consensus regarding the ED95 of succinylcholine. Published values range from a low of 0.22 mg/kg (17) to a high of 0.63 mg/kg (18). Our measured ED95 value of 0.273 mg/kg agrees most closely with those of Smith et al. (19,20) who report an ED95 for succinylcholine of between 0.24 and 0.31 mg/kg. In reviewing available studies that attempt to quantify the neuromuscular potency of succinylcholine, we have not been able to reconcile the differences in ED50 and ED95 values reported from various centers. Most investigators have used mechanomyography (MMG) for studying this question. Unfortunately, an isometric force transducer may not be the ideal instrument for this purpose. The initial MMG response to subparalyzing doses of succinylcholine is augmentation of single twitch response. As a consequence, investigators using MMG generally define succinylcholine-induced neuromuscular block as depression of the fourth response to train-of-four stimulation compared with control T-4 (18). This initial twitch augmentation is not observed when using electromyographic monitoring.

Even when the electromyogram is used, reported values for the ED95 range from 0.22 mg/kg (17) to 0.51 mg/kg (21). We are at a loss to explain the results of Chestnut et al. (21) who report an ED50 (0.31 mg/kg) larger than our ED95. Differences in methodology are no doubt partially responsible for this disparity. These investigators used dose/logit regression analysis rather than log-dose/logit analysis to calculate the best fit line of regression. In addition, an unknown number of their subjects responded with either zero or 100% twitch depression. The authors do not explain how these data points were handled. Finally, the test drug administered by Chestnut et al. (21) was not recently refrigerated. Ultimately, the observation of Katz et al. (22), that there are transatlantic differences in the potency of succinylcholine, may have merit.

Calculations of the dose-response relationship of NMDs have traditionally been performed (after suitable mathematic transformations) by regression analysis of pooled individual data points. However, when ED50 and ED95 values calculated by this method are reported, it is uncommon for investigators to present information regarding the expected extent of individual variability from the mean. In contrast, when potency is calculated by averaging the estimated ED50 and ED95 values from individual subjects, the SD, SEM, and range of responses are easily determined. We believe that these measures of variance should routinely be reported when dose-response studies are performed.

It may be argued that assuming a predetermined slope for the log-dose/logit plot is arbitrary and almost guarantees that some error will be introduced into the final estimates of drug potency. It was perhaps fortuitous that our preselected slope of 4.75 turned out to be very similar to the value calculated by regression analysis for rocuronium of 4.55. However, slopes of the dose response curves of all commonly used NMDs appear to be essentially parallel (Figure 1). In addition, as we demonstrate in Tables 2 and 3 , even fairly large errors in preselecting the slope will produce only very modest and clinically unimportant differences in estimates of a drug’s ED95 value and almost no error in calculating the ED50 value. Finally, it should also be recognized that the confidence limits of the calculated slope may be quite wide. Our 90% limits for the slope of rocuronium range from 3.5 to 5.6, and a single outlier can have a profound effect on the calculated slope.


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  		Table 3. Estimates of the Potency of Succinylcholine
 
We think that calculating drug potency by continuously averaging ED50 and ED95 values obtained by single-dose estimation offers the investigator practical advantages even when he also wishes to eventually process the data by regression analysis. Because assessment of drug efficacy by this method is dynamic, the incidence of eliciting data points that cannot be plotted by using logit or probit regression (0% or 100% effect) should be very low, if the investigator limits doses to those projected to produce >15% and <85% twitch depression. All 40 of the data points we obtained for rocuronium fell within the range of 9% to 97% twitch response, and only 2 of 50 patients in the succinylcholine group showed complete twitch suppression.

This approach may also be helpful when performing initial dose-ranging studies on new drugs of unknown potency. Regression analysis can be misleading or useless when sample size is very small or all of the doses administered are similar in potency. Our experience with collecting data in the succinylcholine group provides a good example. After recording 11 data points, our approximation of the succinylcholine’s ED50 and ED95 values were 0.137 ± 0.039 (SD) and 0.254 ± 0.073 mg/kg, respectively, by using single-dose estimation. Included in this sample set was an obvious outlier, a single person who developed 98% block after a dose of only 0.11 mg/kg. Inclusion of this patient produced results that were meaningless when regression analysis was applied—a slope of -0.26 and a R2 of 0.00!

Similarly, responses documented at either end of the administered dose range can produce peculiar results when using conventional regression analysis. For example, in the succinylcholine group, after 26 patients had been recruited, the calculated log-dose/logit slope was 3.93 which resulted in an estimated ED95 of 0.304 mg/kg. Patient 27 was given a dose of 0.09 mg/kg that resulted in 56% twitch depression. Because the ED50 value for this patient was, by definition <0.09 mg/kg, she was clearly sensitive to succinylcholine. Nevertheless, inclusion of this patient in the analysis resulted in a decrease in the slope, and thus, an increase in the calculated ED95 to 0.32 mg/kg! If by chance, this patient had instead received a dose of 0.20 mg/kg, >95% twitch depression would almost certainly have been the result. In this circumstance, the calculated slope would have increased and the estimated ED95 would have decreased, rather than increased.

We believe that the suggestion of Meretoja and Wirtavuori (5) and Wright et al. (6) that useful information regarding potency can be obtained from a single dose-response data point (if the slope of this relationship is assumed) has not received the attention it deserves. This approach appears to yield clinical data, which for practical purposes, differs little from that obtained by using regression analysis. In conclusion, averaging of single-dose estimates of neuromuscular potency provides a useful adjunct and a reasonable alternative to conventional log-dose/logit or probit regression analysis.


   Appendix 1*
Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 Appendix 1*
References
 
All calculations assume that the relationship between the dose of blocking drug administered and the effect produced is governed by the Hill equation: Go


where ED50 = the dose producing 50% twitch depression and {gamma} = the Hill coefficient or slope. This equation can be rewritten as follows to derive the ED50:


It can also be rewritten as follows to calculate the dose required for any desired effect:


Thus, ED95 = ED50 x [95/5](1/{gamma}) and ED90 = ED50 x [90/10] (1/{gamma}), etc.


   Footnotes
 
*Adapted from Wright et al. (6). Back


   References
Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 Appendix 1*
 References
 

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Accepted for publication January 14, 2000.




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Lippincott, Williams & Wilkins Anesthesia & Analgesia® is published for the International Anesthesia Research Society® by Lippincott Williams & Wilkins with the assistance of Stanford University Libraries' HighWire Press®. Copyright 2006 by the International Anesthesia Research Society. Online ISSN: 1526-7598   Print ISSN: 0003-2999 HighWire Press