My coauthors and I thank Drs. Sonner and Fisher for their careful reading of our manuscript. We believe it is imperative to clarify the issues they have raised. Regarding two points that are central to the article, we provide strong support for our methodology and conclusions. On a third point, we acknowledge that an error occurred. We will review our position and methodology for each issue.
First, Drs. Sonner and Fisher question the statistical analysis performed comparing the rate of coughing after tracheal stimulation in patients anesthetized with 1 minimum alveolar concentration (MAC) sevoflurane or 1 MAC desflurane. We respond on several levels, first summarizing the data. In our study, 8 of 32 subjects anesthetized with 1 MAC desflurane had a severe coughing response after tracheal stimulation. Of the 32 subjects anesthetized with 1 MAC sevoflurane, 1 had a moderate coughing response, and only 1 had a severe response to tracheal stimulation. The chi-square test comparing these rates is significant at P = 0.04. Drs. Sonner and Fisher state that this significance level is erroneous because a continuity correction (which yields P = 0.08) was not used.
We have consulted two statisticians in our institution, and we now understand that the automatic use of the continuity correction is controversial in the statistics community. A seminal collection of articles outlining the issues was published 25 yr ago, 1and the debate continues, including recent discussion articles by Haviland 2and Agresti. 3Although no one can argue against the fact that using the correction results in conservative significance tests, both the continuity-corrected chi-square statistic and Fisher exact test tend to be misleadingly conservative when applied in circumstances for which they were not designed, such as the circumstances of this study. The Fisher exact test or continuity-corrected chi-square is appropriate when all four margins of the 2 × 2 table are fixed in advance. In our study, only the number of patients who received each agent was fixed (32 and 32); the number of patients showing moderate or severe cough response was observed, not fixed in advance. Under these circumstances, even the uncorrected chi-square tends to be conservative when the samples are small. 4For these reasons, some standard statistical packages purposely do not calculate the continuity corrections (e.g. , Stata; Stata Corporation, College Station, TX). Drs. Sonner and Fisher quote a single statistical textbook stating that the Yates correction “usually should be employed” in 2 × 2 tables. At least one other reputable biostatistics book chooses not to use the correction at all, stating that it is too conservative. 5
In reviewing the statistics sections of Clinical Investigations published in issues 1–6 of volume 94 of Anesthesiology, we found that the chi-square test had been used in 15 studies other than ours. *None of these articles stated whether the continuity correction had been applied. We recognize Dr. Fisher's expertise in this area but are uncertain why this article should use different techniques than those used in similar studies and recommended by leading authorities. Given that all of the relevant data were presented in our article, the question of Drs. Sonner and Fisher regarding the continuity correction comes down to a matter of philosophy of inference rather than a matter of knowledge.
Drs. Sonner and Fisher also state that the patients anesthetized with 2.05% sevoflurane received a larger MAC dose than those anesthetized with 6.0% desflurane. The MAC values that we chose are commonly accepted. 6The package insert for sevoflurane states the MAC for 40 yr-olds is 2.1% (the average age for subjects receiving sevoflurane in our study was 43 yr). The package insert for desflurane states that the MAC for 45-yr-old patients is 6.0% (the average age for desflurane subjects was 44 yr). According to the package inserts, 7,8if any error in dosing was made, the patients randomized to sevoflurane received a relatively lower dose. The doctors then reference a study examining the MAC for tracheal extubation in children anesthetized with isoflurane 9and use statistical gymnastics to conclude, “the three experimental flaws compromise the conclusions of Klock et al. regarding differences in the effects of sevoflurane and desflurane on the response to airway stimulation.”
Drs. Sonner and Fisher correctly identify a reporting error regarding the relation between coughing and heart rate. The slopes comparing cough response and heart rate increase are not significantly different. Fortunately, this result was not central to the conclusions of the article and does not affect the principal findings of the study. We apologize for this error.
In summary, we stand by our experimental design and the statistical validity of the chi-square statistic and its P value that we report.