We wish to thank Drs. Engelman and Salengros for their comments. They correctly state that our analyses were performed on a modified intent-to-treat population, in which the patients who did not receive the treatment were excluded from analysis after randomization. The following paragraph of the International Conference on Harmonisation guidance on the use of statistics in clinical trials1makes it clear that the practice of removing patients who do not receive treatment is not without merit:
In some situations, it may be reasonable to eliminate from the set of all randomized subjects any subject who took no trial medication. The intention-to-treat principle would be preserved despite the exclusion of these patients provided, for example, that the decision of whether or not to begin treatment could not be influenced by knowledge of the assigned treatment. In other situations it may be necessary to eliminate from the set of all randomized subjects any subject without data post randomization. No analysis should be considered complete unless the potential biases arising from these specific exclusions, or any others, are addressed.
Regarding the current study,2it should be kept in mind that we are discussing only 12 patients who did not receive treatment (8 in the parecoxib–valdecoxib group and 4 in the placebo group) in a study that included more than 1,050 patients—approximately 1% of the randomized population. It is highly unlikely that the treatment responses of these few patients would have differed from the responses of the patients included in the analysis.
Drs. Engelman and Salengros also state that “this problem is further increased by the fact that the reasons for not administering the treatment are not given in the article . . . and that twice as many patients were excluded from the parecoxib–valdecoxib group as from the placebo group.” However, given that there were 12 patients, the fact that 8 were assigned to one treatment and 4 to the other is not at all unlikely; in fact, it has more than a 19% probability of occurring by chance alone. It should also be understood that the number of patients not treated could just as easily have been 8 placebo and 4 parecoxib–valdecoxib patients. If one used this distribution in the sensitivity analysis suggested by the authors, one would conclude that parecoxib is actually cardioprotective. This scenario shows that the suggested analysis is inappropriate.
Drs. Engelman and Salengros then compute the risk ratio for a cardiovascular event if those patients in the parecoxib–valdecoxib intent-to-treat group who never received the treatment (n = 8) plus the 5 patients lost to follow-up in the parecoxib–valdecoxib group had all experienced a cardiovascular event. This sensitivity analysis is based on the premise that the patients who were not treated or lost to follow-up could have had vastly greater risk than the patients included in the analysis. That is, although the percentage of patients having a cardiovascular event in both placebo and parecoxib–valdecoxib groups was actually 1%, this sensitivity analysis assumes that 100% of the excluded patients in the parecoxib–valdecoxib group could have had an event, which is not even remotely consistent with the observed data. In fact, we have gone back to look at the raw data from patients who did not receive treatment or were lost to follow-up and determined that none of these in either group experienced any cardiovascular thromboembolic events during the limited time that they were under observation.
Drs. Engelman and Salengros also state that they concentrated this analysis on the cardiovascular adverse events and could easily eliminate the possibility that placebo administration increased the frequency of cardiovascular events. This is simply not true, as shown by the confidence intervals and P values produced by these two extreme analyses. Again, the results would change dramatically with a slight change in the number of missing data points in the placebo group.
Drs. Engelman and Salengros also mention that the risk of a type I error was never stated in the article. Certainly, we agree that this information should have been included. However, the considerable breadth of the confidence interval of the risk ratio (0.3–3.5) that we reported2makes it highly unlikely that increasing the power of the study would reveal a significant difference in cardiovascular event rates between the treatment and placebo groups. In addition, we have already acknowledged this limitation in the Discussion, in which we state,
Another limitation of the study is the sample size. Although this was the largest trial of any nonsteroidal antiinflammatory drug in patients undergoing noncardiac surgery, the number of adverse events was relatively small and possibly inadequate to detect a particular safety signal. This is especially true for cardiovascular thromboembolic events, given the low level of risk in this population compared with CABG [coronary artery bypass graft] surgery patients. Nevertheless, this population was representative of the majority of patients who undergo major surgery.
In summary, we appreciate Drs. Engelman and Salengros’ thoughtful comments and speculations. Nonetheless, our interpretation of the results of our study—the largest such clinical trial yet performed worldwide—and the conclusions we draw from them remain unchanged.
*SUNY Upstate Medical University, Syracuse, New York. firstname.lastname@example.org