To the editor:
It has been proposed that the intrathecal dose of hyperbaric bupivacaine for spinal anesthesia should be reduced in morbidly obese patients undergoing cesarean delivery.1This recommendation is consistent with the lower volume of cerebrospinal fluid observed in patients with high body mass index,2but a lack of definitive evidence has been noted.3Previously, Ginosar et al. reported the ED50of intrathecal bupivacaine obtained in a prospective, randomized, double-blind, and dose-finding study of healthy patients having elective cesarean delivery.4Using the same experimental methods, Carvalho et al. repeated this experiment about 5 yr later at the same institution in patients with a body mass index of 40 or greater.5Combining the data from the two studies on the success of the spinal block for operation, they used a quantal sigmoid Emax parametrization of the logistic model with nonlinear mixed effect model estimation using the NONMEM package (NONMEM® version V [GloboMax™, Hanover, MD]),
with dose 50representing the median effective dose (ED50) and γ representing the slope of the dose-response curve. They concluded from the similar ED50and ED95values of the two studies that obese and nonobese patients did not have significantly different dose requirements. They acknowledged their statistical methods had not compared the entire dose response of the two groups of patients. Because simultaneous analysis of families of sigmoidal curves is the preferred approach,6this letter argues that their data do allow such a contrast of the entire dose response. In fact, their data reveal that the morbidly obese require not a lower or similar dose, but possibly a higher dose, than the nonobese.
The sigmoid Emax model is equivalent to its restatement in a two-parameter logistic format.
The R software drc package (Analysis of dose-response curves) offers analysis of one or many dose-response curves in this parametrization.7An obesity/nonobesity covariate may be included in the model to specify models with separate intercepts and equivalent slopes (three-parameter model); equivalent intercepts and separate slopes (three-parameter model); and both separate intercepts and separate slopes (four-parameter model). Nested models are compared by likelihood ratio statistics; models with equal parameter counts are compared by Akaike and Bayesian Information Criterion. The binary counts were obtained from the figures of Ginosar et al. 4(1/6, 2/6, 4/6, 3/6, 6/6, 6/6, 6/6) for doses (6,7,8,9,10,11,12) and of Carvalho et al. 5(0/6, 0/6, 1/6, 1/5, 2/6, 3/6, 5/7) for doses (5,6,7,8,9,10,11). These data were reanalyzed using drc package version 2.1–2 running in R version 2.12.2 (R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria). ED50and slope are reported with standard errors and 95% CI; an adjustment for binary variable overdispersion is made.
The best model for the overall data of both studies had a common slope and separate intercepts with a right shifting of dose response for the obese patients. The slope estimate was 7.7 ± 1.7 (4.3–11.1). There were statistically different ED50doses for obese (9.8 ± 0.5 mg [8.8–10.7]) and for nonobese (7.6 ± 0.4 mg [6.9–8.4]) patients. Estimations of ED95for obese (14.3 ± 0.9 mg [12.6–16.3]) and for nonobese (11.2 ± 0.9 mg [9.5–13.2]) had overlapping CIs. The ED50estimates are very similar to those reported by Carvalho et al. However, the simultaneous comparison of the entirety of the two dose-response curves permits stronger statements about the overall dose response than pointwise comparisons.
This reanalysis of the two studies should not be interpreted as demonstrating a high degree of certainty about a larger ED95in morbidly obese parturients having cesarean delivery. First, the study sizes (totaling 84 patients) are modest; the statistical methods of nonlinear mixed-effect models assume large sample asymptotic properties in the estimation of variances. Second, there are unstated assumptions, particularly sigmoidicity, symmetry, and homoscedasticity, in using a logistic regression model; there are many other possible dose-response models.8With small samples, these assumptions are untestable. Third, the upper end of the dose response (ED95) is of greatest importance in anesthetic planning. The current data require extrapolation of the upper dose range. Fourth, the precision of the slope estimate is rather wide. And finally, there may have been temporal changes in patients and in anesthesia care between the two studies, leading to biased estimates. Carvalho et al. and this author concur in recommending that additional prospective, controlled studies are needed to more precisely identify a safe ED95.