In Reply:-We appreciate Drs Asai and Mapleson remarks because they point out two inaccuracies in our paper that we sincerely regret:(1) a typing fault in the footnote of table 1, which instead of “SEM” should say “SD,” and (2) an error in figure 3 (upper panel), on the actual values that define the ED60's of the individual agents. The ED60isobole was included to demonstrate that, at this level of effect, the 1:1 combination is antagonistic; this fact remains unaltered after correcting the data: the new isobole is included (Figure 1). Thus, the errors kindly pointed out by Drs. Asai and Mapleson do not alter the content nor the meaning of the published results.
Figure 1. Isobolographic representation of the interaction of morphine and clonidine combined in a 1:1 proportion, at 60% level of response. The axes indicate the mean doses (+/- SEM) of morphine (abscissae) and clonidine (ordinates) that individually produced 60% of maximal response. The diagonal line connects equi-effective doses of each drug alone, and the point to the right shows the doses of the combination (+/- SEM) that produced the same level of effect. The results demonstrate that the combination is antagonistic.
Figure 1. Isobolographic representation of the interaction of morphine and clonidine combined in a 1:1 proportion, at 60% level of response. The axes indicate the mean doses (+/- SEM) of morphine (abscissae) and clonidine (ordinates) that individually produced 60% of maximal response. The diagonal line connects equi-effective doses of each drug alone, and the point to the right shows the doses of the combination (+/- SEM) that produced the same level of effect. The results demonstrate that the combination is antagonistic.
However, we disagree with the calculation of the “dose ratios” and the “interpolation” of data performed by Drs. Asai and Mapleson. We could not find an “internal anomaly” in table 2 because values given in the table were experimentally obtained (observed data) and not predetermined. In these experiments, values cannot be calculated by a simple ratio or proportion (or “interpolated”) as estimated by Drs Asai and Mapleson. When analyzing interactions, only actual doses of the individual agents that (when combined) produce a given level of effect are used. Similarly, we are not sure of what Drs. Asai and Mapleson mean by “interpolation,” but in our study, responses at the different levels of effect (20%, 50%, 60%, 80%) were calculated by linear regression analysis of the dose-response relations after the equation:Equation 1.
Regarding the SEM of the MS:CL mixtures that are represented in the figures, the small magnitude of the bars (SEM) and the different scales used in ordinates and abscissae made graphic representation sometimes difficult; it is also possible that when drawing the isoboles, a few millimeters were misplaced. However, in table 3 we included the statistical evaluation of the results, which was obtained by comparing the doses that produced the expected effects (additivity) and the actual doses that produced the observed effects (experimental data). A P value < 0.05 was considered statistically significant.
We sincerely regret the errors, and appreciate the considerate comments of Drs Asai and Mapleson.
Margarita M. Puig, M.D., Ph.D
Professor and Chair; Department of Anesthesiology Hospital del Mar; Paseo Maritimo 25; Barcelona 08003; Spain
Electronic mail: 86822@IMAS.IMIM.ES
(Accepted for publication July 7, 1997.)
