JOURNAL HOME CME HOME THIS MONTH PAST ISSUES ETOC COLLECTIONS
AUTHORS REVIEWERS EDITORIAL BOARD FEEDBACK RSS HELP
A&A International Anesthesia Research Society
QUICK SEARCH:   [advanced]


     

This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a colleague
Right arrow Similar articles in this journal
Right arrow Similar articles in Web of Science
Right arrow Similar articles in PubMed
Right arrow Alert me to new issues of the journal
Right arrow Download to citation manager
Citing Articles
Right arrow Citing Articles via HighWire
Right arrow Citing Articles via Web of Science (7)
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Zhang, Y.
Right arrow Articles by White, P. F.
Right arrow Search for Related Content
PubMed
Right arrow PubMed Citation
Right arrow Articles by Zhang, Y.
Right arrow Articles by White, P. F.
Related Collections
Right arrow Economics and Health Care Research
Right arrow Heart
Right arrow Pharmacology

Anesth Analg 2004;98:1330-1335
© 2004 International Anesthesia Research Society
doi: 10.1213/01.ANE.0000111103.86567.F6

ANESTHETIC PHARMACOLOGY

A Model for Evaluating Droperidol’s Effect on the Median QTc Interval

Yongfeng Zhang, PhD*, Ziping Luo, PhD*, and Paul F. White, PhD MD, FANZCA{dagger}

*New Drug Center at Amphastar Pharmaceuticals Inc., Rancho Cucamonga, California; and {dagger}Department of Anesthesiology and Pain Management, University of Texas Southwestern Medical Center at Dallas, Dallas, Texas

Address correspondence and reprint requests to Paul F. White, PhD, MD, Department of Anesthesiology and Pain Management, 5323 Harry Hines Blvd., Dallas, TX 75390–9068. Address e-mail to paul.white{at}utsouthwestern.edu


   Abstract
Top
 Abstract
Introduction
 Models Used to Study...
 Discussion
 Appendix 1. Optimization of...
 References
 
Controversy surrounds the use of the antiemetic droperidol, because of the Food and Drug Administration-imposed "black box" warning alleging that even small doses of the drug can lead to serious (even fatal) arrhythmias when it is used for antiemetic prophylaxis during the perioperative period. We used mathematical modeling of electrocardiographic QT interval data published in a peer-reviewed manuscript to evaluate the relationship between the dose of droperidol (0.1–0.25 mg/kg IV) and QTc prolongation. In comparing the calculated QTc values based on the logarithm model (27–63 ms), the linear model (27–67 ms) and the square-root model (36–57 ms) to the actual measured QTc values (37–59 ms), the square-root model provided the best simulation of the experimental findings. Other models that we evaluated included the polynomial model and various exponent models (e.g., quartic-root model, cubic-root model, square model, and cubic model). The estimated median prolongation of the median QTc interval produced by droperidol 0.625–1.25 mg IV would vary from 9 ± 3 to 18 ± 3 ms. Therefore, this regression analysis suggests that small "antiemetic" doses of droperidol (<=1.25 mg) would be unlikely to produce proarrhythmogenic effects in the perioperative period.

IMPLICATIONS: Using a square-root curve fit model to evaluate the relationship between the dose of droperidol and QTc prolongation, small-dose droperidol (0.625–1.25 mg IV) would be expected to produce <30-ms prolongation of the QTc interval. Therefore, small "antiemetic" doses of droperidol would not be expected to produce proarrhythmogenic effects when used for prophylaxis in surgical patients.


   Introduction
Top
 Abstract
 Introduction
Models Used to Study...
 Discussion
 Appendix 1. Optimization of...
 References
 
Droperidol is a butyrophenone that was approved for clinical use as an antiemetic and as the primary drug during "neurolept" anesthesia in 1970 (1–3). In >30 yr of clinical use during the perioperative period, there has not been a single published report describing a cardiac arrhythmia after droperidol administration. Yet, a safety concern has been raised by the Food and Drug Administration (FDA) (www.FDA.droperidol.com) regarding QT prolongation and the possibility of serious cardiac arrhythmias after the administration of even small doses of droperidol for prophylaxis and/or treatment of postoperative nausea and vomiting (PONV). Importantly, the database that was used to support the FDA "black box" warning on droperidol has been recently challenged (4,5). After carefully evaluating all of the reports submitted to the FDA, Habib and Gan (5) concluded that "in none of the cases in which arrhythmias occurred after small doses of droperidol (<=1.25 mg) was there evidence of a cause-and-effect relationship." Curiously, the majority of the case reports in which small-dose droperidol was alleged to be the causative factor in serious cardiac arrhythmias were submitted to the FDA on the same day (Dr. Steven Shafer, FDA Advisory Committee on Anesthetic Drugs, verbal communication, June 4, 2003).

The large doses of droperidol (>1 mg/kg) occasionally used in psychiatry have been associated with significant QTc prolongation, contributing to serious cardiac arrhythmias (e.g., Torsade de Pointes), and even death in susceptible patients (6,7). However, there have been no adverse cardiovascular effects observed with the small doses of droperidol administered for antiemetic prophylaxis. In fact, a placebo-controlled, double-blind comparative study involving >2000 patients receiving droperidol, 0.625 or 1.25 mg (versus ondansetron 4 mg IV), was performed by the manufacturer of the 5-HT3 antagonist (ondansetron [Zofran®]; GlaxoSmithKline, Research Triangle Park, NC) and no differences were found between the two antiemetic drugs with respect to either their safety or efficacy (8). The overall incidences of cardiovascular side effects (e.g., arrhythmias, hypotension, hypertension) were similar to the placebo group: namely, 33% (placebo), 30% (droperidol 0.625 mg), 23% (droperidol 1.25 mg), and 28% (ondansetron 4 mg). As part of a neurolept anesthetic technique, moderately large doses of droperidol (0.5–1 mg/kg IV) have been used for many years (1) without any reports in the anesthesia literature of serious cardiac arrhythmias during the perioperative period.

Lischke et al. (9) reported that droperidol produced a dose-dependent prolongation of the QT interval. In this clinical study, patients were administered 1 of 3 different doses of droperidol, namely 0.1, 0.175, or 0.25 mg/kg IV. The droperidol-induced prolongation of the median QTc interval (PMQTI) reported by these investigators is summarized in Table 1. We have proposed a logarithm model, a linear model, and a square-root model to study the relationship between the dose of droperidol and the PMQTI. These 3 models were used to test the hypothesis that even small doses of droperidol (0.625–1.25 mg), approximately 10–20 µg/kg IV, produce PMQTI. Finally, we used the model with the smallest total deviation from the actual data to simulate the relation between the PMQTI and the dose of droperidol.


View this table:
[in this window]
[in a new window]
  		Table 1. Experimental Findings Regarding the Effect of the Droperidol Dose on the Prolongation of the Median QTc Interval (PMQTI)
 

   Models Used to Study the Dose-Dependent Effect of Droperidol on PMQTI
Top
 Abstract
 Introduction
 Models Used to Study...
Discussion
 Appendix 1. Optimization of...
 References
 
Many different mathematical models (10) can be used to study the dose-dependence effect of droperidol on PMQTI, including those shown below.

I. Polynomial model as described by Equation 1:


where Y is the PMQTI, D is the droperidol dose.

Because of the complexity of Equation 1, which results in a vague physical meaning for each term of the Equation 1 and the limited experimental data, it was impossible to optimize the multiple parameters, a, b, c. Therefore, we elected not to use the polynomial model.

II. Logarithm model as described by Equation 2


Since Y-> – {infty} when D -> 0, according to Equation 2, this model does not match with the common condition Y (0) = 0. Therefore, Equation 2 is not suitable for this analysis.

To meet Y (0) = 0, a second logarithm model was considered:


The principle of least-square approximation was used to optimize kg by minimizing the total deviation (i.e., square error) (10):


where Yj is the calculated value of PMQTI based on the second logarithm model (Equation 3) for the jth group of patients with droperidol dose Dj; yj is the clinical data of PMQTI, and j runs over all clinical groups for different doses of droperidol. Based on the principle of the least-square method, we can obtain:




Using the Dj and yj listed in Table 1, it was found that kg = 281 and Z = 117. These results were compared with the other viable models in Tables 2 and 3.


View this table:
[in this window]
[in a new window]
  		Table 2. Model Coefficients k1 and k for Prolongation of the Median QTc Interval (PMQTI) Calculated Using Data from Lischke et al. (9)
 

View this table:
[in this window]
[in a new window]
  		Table 3. Calculated Relationship Between the Prolongation of the Median QTc Interval (PMQTI) and the Droperidol Dose Using the Logarithm, Linear, and Square-Root Models Compared with Experimental Data from Lischke et al. (9)
 
III. Exponent model is described by Equation 6

Because Y (0) = 0, we have b = 0 and Equation 6 can be simplified as:


When x = 1, it is a normal linear model; when x = 1/2, it is a square-root model.

(A) The linear model suggests that PMQTI be proportional to the dose of droperidol and is described by Equation 8


where, Y is the PMQTI in milliseconds, D is the droperidol dose in milligrams/kilogram, and k1 is the coefficient of the linear model that is the value of PMQTI for a unit dose of droperidol (1 mg/kg).

(B) The square-root model for the relation between PMQTI and the droperidol dose is described by Equation 9


where k1/2 is the coefficient of the square-root model, that is the value of PMQTI for a unit dose of droperidol (1 mg/kg).

The least-square approximation can be used again to optimize k1or k1/2 by minimizing the total deviation (i.e., square errors Equation 4

where Yj is the calculated value of PMQTI based on the models (Equation 8 or Equation 9) for the jth group of patients with droperidol dose Dj; yj is the clinical data of PMQTI, and j runs over all clinical groups for different doses of droperidol. Based on the principle of the least-square method, we can obtain:




Using the equations and the original data from Table 1 (9), the calculated values for k1 and k1/2 are 253 and 113, respectively. The total deviations for the 2 models are 155 and 18, respectively.

The total deviations of the 3 models we studied (namely the logarithm, linear, and square-root models) were 117, 155, and 18, respectively. Therefore, the total deviation for the square-root model is significantly less than that for the other 2 models. Furthermore, a more general mathematical analysis of the various exponent models (Equation 7, Appendix 1, and Fig. 1), including the quartic model (x = 1/2), cubic-root model (x = 1/3), square model (x = 2), and cubic model (x = 3), demonstrated that the square-root model (x = 1/2) was the best in describing the relationship between the dose of droperidol and PMQTI. The calculated PMQTI results for the logarithm, linear, and square-root models are summarized in Table 2. Based on these data, we concluded that the square-root model:




View larger version (7K):
[in this window]
[in a new window]
  		Figure 1. The solution of x for the exponent model Y(D) = kDx.

 

was the optimal descriptor for the relationship between PMQTI and the administered dose of droperidol.

From the values for the total deviation of the 3 models (Table 2), the standard deviations for logarithm, linear, and square-root models were calculated to be 7.6, 8.8, and 3 ms, respectively. In comparing the calculated values based on the logarithm, linear, and square-root models to the actual measured values (Table 3), these data further confirm that the square-root model provided the best simulation of the actual experimental findings.

Finally, Figure 2 graphically displays the curve based on the square-root model and provides for a comparison with the mean experimental data points. The error bars in the figure are based on the standard deviation of the square-root model.



View larger version (14K):
[in this window]
[in a new window]
  		Figure 2. Stimulation of the prolongation of median QTc interval as a function of the droperidol dose based on the square-root model. The actual measured data points (mean values) from Lischke et al. (9) are superimposed on the model. The error bars represent the standard deviation of the model obtained from the total deviation of the square-root model. CPMP = Committee for Proprietary Medicinal Products.

 

   Discussion
Top
 Abstract
 Introduction
 Models Used to Study...
 Discussion
Appendix 1. Optimization of...
 References
 
In 1997, the Committee for Proprietary Medicinal Products in London, UK provided guidance on the signal value for QTc measurement, and indicated that individual changes of <30 ms are regarded as unlikely to raise significant concerns regarding the proarrhythmic potential of a drug (11). Because small-dose droperidol (0.625–1.25 mg IV) has been widely accepted as the most cost-effective therapy for the prophylaxis and/or treatment of PONV (12–15), the previously described square-root model [Equation (12)] was used to estimate the PMQTI for small doses of droperidol in patients weighing either 50 or 100 kg (Table 4). According to the square-root model, the PMQTI for the commonly used antiemetic doses of droperidol is <30 ms. The mean (and 90% confidence intervals) predicted values of the PMQTI for droperidol 0.625 and 1.25 mg would be 9–13 (4–18) and 13–18 (8–23) ms, respectively. Therefore, we would reject our null hypothesis, and conclude that droperidol, 0.625–1.25 mg, is unlikely to produce significant proarrhythmogenic effects in patients receiving routine antiemetic prophylaxis during surgery.


View this table:
[in this window]
[in a new window]
  		Table 4. Estimation of the Prolongation of the Median QTc Interval (PMQTI) for Small-Dose Droperidol, 0.625 or 1.25 mg, in Patients Weighing Either 50 or 100 kg Using the Square-Root Model
 
The lack of reliable QT data on droperidol dosages <100 µg/kg is a deficiency in this analysis of droperidol’s effect on PMQTI. Therefore, the model can be criticized for extrapolating the QT effects at doses smaller than the existing data. However, even if a "plateau effect" occurred at droperidol doses <100 µg/kg, the PMQTI would still be considered clinically insignificant. This analysis can also be criticized because we failed to use all the available methods of analyzing QT interval prolongation (e.g., Fridericia’s). It is possible that adding another exponent (or sum of terms with various exponents) as part of a polynomial regression analysis would provide an even better fit to the existing data. However, Aihoshi et al. (16) concluded that the mean-squared residual values and the Akaike information criterion were lowest for the exponential and Fridericia’s formulae. Furthermore, their data suggested that the exponential and Fridericia formulae were equally useful in screening for QT prolongation.

In a recent analysis of the relevance of prolonged QTc measurements to pediatric psychopharmacologic drugs, Labellarte et al. (17) reported that there were more "review manuscripts with clinical recommendations" than actual experimental studies examining the effects of these drugs on the QTc duration. If actual data can be generated using small antiemetic doses of droperidol to support the findings of the mathematical models described in this manuscript, it would further strengthen the argument that the FDA-imposed "black box" warning on the use of low-dose droperidol for the treatment and/or prevention of PONV should be reevaluated.

In conclusion, these model-based findings suggest that there is no significant effect of small-dose droperidol (0.625–1.25 mg) in prolonging the QTc interval, consistent with the clinical experience over the last 30 years with this popular antiemetic drug (3,18).


   Appendix 1. Optimization of the Exponent Model
Top
 Abstract
 Introduction
 Models Used to Study...
 Discussion
 Appendix 1. Optimization of...
References
 
The exponent model is given by Equation (7):

where k and x are two parameters to be optimized by minimizing the total deviation as given by Equation (7):

Substituting Equation (7) into Equation (4):, we have:


Based on the general principle of the least square,


we have:


and


From Equation (15), it is easy to obtain:


Substituting Equation (17) into Equation (16), a transcendental equation for x is obtained:


Using the experimental data listed in Table 1 and a computer program, the curve of f(x) versus x is obtained in figure 1, where


Whereas f(x) = 0, we found the optimized value of x, namely the solution of Equation (18):


This is the only meaningful solution of Equation (18): the other solution of Equation (18) is x = {infty} as demonstrated in Figure 1. This solution x ~ 0.5 is the best value of x and corresponds to the square-root model.

The values of total deviation from Equation (13) for different x (different exponent models) were calculated as follows:


View this table:
[in this window]
[in a new window]
 
 
Therefore, the square-root model (x = 0.5 = 1/2) is the best description for this work.


   Acknowledgments
 
Institutional resources from Amphastar Pharmaceuticals Inc. (Rancho Cucamonga, CA), and the Margaret Milam McDermott Distinguished Chair in Anesthesiology were used to support this analysis.


   References
Top
 Abstract
 Introduction
 Models Used to Study...
 Discussion
 Appendix 1. Optimization of...
 References
 

  1. Zsigmond EK. Neurolept and dissociative anesthesia. In: White PF, ed. Textbook of intravenous anesthesia. London: Williams & Wilkins, 1997: 393–403.
  2. Henzi I, Sonderegger J, Tramer M. Systematic review: efficacy, dose-response, and adverse effects of droperidol for prevention of postoperative nausea and vomiting. Can J Anaesth 2000; 47: 537–51.[Web of Science][Medline]
  3. White PF. Droperidol: a cost-effective antiemetic for over 30 years! Anesth Analg 2002; 95: 789–90.[Free Full Text]
  4. Bailey P, Norton R, Karan S. The FDA droperidol warning: is it justified? Anesthesiology 2002; 97: 288–9.
  5. Habib AS, Gan TJ. Food and Drug Administration black box warning on the perioperative use of droperidol: a review of the cases. Anesth Analg 2003; 96: 1377–9.[Free Full Text]
  6. Haddea P, Anderson I. Antipsychotic-related QTc prolongation, torsade de points and sudden death. Drugs 2002; 62: 1649–71.[Web of Science][Medline]
  7. Priori SG, Barhanin J, Hauer RN, et al. Genetic and molecular basis of cardiac arrhythmias: impact on clinical management parts I and II. Circulation 1999; 99: 518–28.[Abstract/Free Full Text]
  8. Fortney JT, Gan TJ, Graczyk S, et al. A comparison of the efficacy, safety, and patient satisfaction of ondansetron versus droperidol as antiemetics for elective outpatient surgical procedures: S3A-409 and S3A-410 Study Groups. Anesth Analg 1998; 86: 731–8.[Abstract]
  9. Lischke V, Behne M, Doelken P, et al. Droperidol causes a dose-dependent prolongation of the QT interval. Anesth Analg 1994; 79: 983–6.[Abstract/Free Full Text]
  10. Zwillinger D. CRC standard mathematical tables and formulae. 31st ed. New York: Chapman & Hall, 2003: 739.
  11. Committee for Proprietary Medicinal Products. The assessment of the potential for QT interval prolongation by non-cardiovascular medicinal products, CPMP/986/96. London: The European Agency for the Evaluation of Medicinal Products, 12 Dec. 1997.
  12. Watcha MF. The cost-effective management of postoperative nausea and vomiting [editorial]. Anesthesiology 2000; 92: 931–3.[Web of Science][Medline]
  13. Tang J, Watcha MF, White PF. A comparison of costs and efficacy of ondansetron and droperidol as prophylactic antiemetic therapy for elective outpatient gynecologic procedures. Anesth Analg 1996; 83: 304–13.[Abstract]
  14. Hill RP, Lubarsky DA, Phillips-Bute B, et al. Cost-effectiveness of prophylactic antiemetic therapy with ondansetron, droperidol, or placebo. Anesthesiology 1998; 68: 731–8.
  15. White PF, Watcha MF. Postoperative nausea and vomiting, prophylaxis versus treatment [editorial]. Anesth Analg 1999; 89: 1337–9.[Free Full Text]
  16. Aihoshi S, Yoshinaga M, Nakamura M, et al. Screening for QT prolongation using a new exponential formula. Jpn Circ J 1995; 59: 185–9.[Medline]
  17. Labellarte MJ, Crosson JE, Riddle MA. The relevance of prolonged QTc measurement to pediatric psychopharmacology. J Am Acad Child Adolesc Psychiatry 2003; 42: 642–50.[Medline]
  18. Bailey P, White PF. Droperidol editorial: making a mountain out of a mole hill [letter]. Anesthesiology 2003; 99: 760–1.[Web of Science][Medline]
Accepted for publication November 19, 2003.




This article has been cited by other articles:


Home page
 NEJMHome page
S. Yalcyn, B. Yalcyn, A. Buyukcelik, F. Hartig, C. Pechlaner, C. C. Apfel, and D. I. Sessler
Prevention of Postoperative Nausea and Vomiting
N. Engl. J. Med., September 30, 2004; 351(14): 1458 - 1459.
[Full Text] [PDF]

Home page
 NEJMHome page
P. F. White
Prevention of Postoperative Nausea and Vomiting -- A Multimodal Solution to a Persistent Problem
N. Engl. J. Med., June 10, 2004; 350(24): 2511 - 2512.
[Full Text] [PDF]

This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a colleague
Right arrow Similar articles in this journal
Right arrow Similar articles in Web of Science
Right arrow Similar articles in PubMed
Right arrow Alert me to new issues of the journal
Right arrow Download to citation manager
Citing Articles
Right arrow Citing Articles via HighWire
Right arrow Citing Articles via Web of Science (7)
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Zhang, Y.
Right arrow Articles by White, P. F.
Right arrow Search for Related Content
PubMed
Right arrow PubMed Citation
Right arrow Articles by Zhang, Y.
Right arrow Articles by White, P. F.
Related Collections
Right arrow Economics and Health Care Research
Right arrow Heart
Right arrow Pharmacology

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