Letter by Diamond Regarding Article, “Bayesian Methods Affirm the Use of Percutaneous Coronary Intervention to Improve Survival in Patients With Unprotected Left Main Coronary Artery Disease”
To the Editor:
I read with interest the recent report by Bittl et al1 describing a Bayesian meta-analysis of all-cause mortality in patients with unprotected left main coronary artery disease after coronary artery bypass grafting (CABG) and percutaneous coronary intervention (PCI), which “suggested the equivalence of CABG and PCI,” and thereby justified the assignment of a Class IIa guideline recommendation in support of the latter. In my opinion, this affirmation is not supported by these analyses.
The authors begin by reporting a 95% credible interval ranging from 0.74 to 1.39 for the posterior odds ratio based on a hierarchical analysis of PCI versus CABG, and conclude that “[b]ecause the interval included 1, the results showed no significant difference between the 2 treatments.”1 Subsequently, they report an analogous 95% credible interval ranging from 0.68 to 1.45 for the posterior odds ratio based on a cross-design analysis, and conclude that “[t]he possibility that PCI is associated with different 1-year mortality than CABG is very small.”1 Both these conclusions are suspect from a Bayesian perspective.
A precise interpretation of the hierarchical interval is that (with 95% probability) the relative difference in mortality ranges from 26% in favor of PCI to 39% in favor of CABG, and an equivalently precise interpretation of the cross-design interval is that (with 95% probability) the relative difference in mortality ranges from 32% in favor of PCI to 45% in favor of CABG.
In my view, neither of these interpretations implies the “equivalence of CABG and PCI” with respect to 1-year mortality. As a matter of fact, we are not justified in believing (with 95% probability) that CABG and PCI are equivalent, unless we embrace the incredible proposition that mortality differences of such large magnitude are clinically unimportant. On the contrary, we are justified in believing (with 95% probability) the treatments are equivalent only if the mortality differences are less than those which might reasonably be considered clinically important (±5% or ±10%, for example).2 For the reported hierarchical interval, therefore, CABG and PCI are equivalent with only 27% probability (±5%) and 51% probability (±10%). For the reported cross-design interval, the treatments are equivalent with 22% probability (±5%) and 44% probability (±10%). In my opinion, these relatively low probabilities offer little support for the presumed equivalence of CABG and PCI, or for the Class IIa guideline recommendation based on that presumption (indicating that the weight of evidence is in favor of its efficacy). This is more than a little detail. The clinical and economic implications are substantial.
Nevertheless, the long-overdue application of Bayesian approaches to the analysis of clinical trial data is to be applauded.
George A. Diamond, MD
Division of Cardiology
Cedars-Sinai Medical Center and the
David Geffen School of Medicine
University of California
Los Angeles, CA
- © 2014 American Heart Association, Inc.