Because most coronary artery bypass patients receive more than one graft at surgery, it is most important to determine whether statistical analysis of graft patency should be performed on the premise that the multiple grafts within patients are dependent or independent experimental units. Veterans Administration Cooperative Study No. 207 was a multicenter clinical trial comparing four different antiplatelet regimens to placebo in the prevention of graft occlusion following coronary artery bypass grafting. Using the results from the 1-week postoperative angiograms from the Veterans Administration Cooperative Study No. 207, in which there were 3.2 distal anastomoses per patient, we have tested the hypothesis that grafts within patients tend to act dependently with respect to patency or occlusion by comparing the graft patency data to a binomial distribution (i.e., that distribution that would have been manifest if grafts were independent). Because the graft patency results in Study No. 207 significantly deviated from the binomial distribution (p = 0.0003), a more appropriate analysis for graft patency data was applied using a ratio estimate as applied to cluster sampling. The statistical methods used in 11 previous clinical trials of antithrombotic therapy after coronary artery bypass grafting were examined. Only one of the previous studies used such an analysis, and three additional reports attempted to correct for dependency of grafts within patients in their analyses using other statistical methods. In seven of the studies the investigators did not address the potential problem of a dependent relationship between multiple grafts within patients. We conclude that grafts within patients act as dependent experimental units and that the ratio estimate as applied to cluster sampling may be appropriately applied to these data.