"Within patient"-dependent outcomes in graft occlusion after coronary artery bypass. SINBA Group

In clinical trials aimed at assessing the efficacy of drugs after coronary artery grafting, statistical analysis is usually carried out on a per-patient basis and on a per-graft basis. Owing to the independence of responses among patients, the former outcome is analyzed by assuming a binomial model. However, this model cannot be directly adopted in analyzing the latter outcome because multiple vein grafts in the same patient do not act independently. It has been suggested that patients be considered as clusters of distal anastomoses, subsequently comparing the frequencies of occlusion under different treatments after adjusting the variance of each frequency for the size of the cluster. Alternatively, one can measure the intraclass (intrapatient) correlation coefficient and adopt distribution functions that include this quantity as one of the parameters. This approach has been adopted by many authors although the studies differed in the statistical model used to represent this kind of data. Two probability functions, Altham's and beta-binomial, have found wide application in different biomedical fields. Both are able to model the extrabinomial variability since their tails tend to zero more slowly than those of the binomial distribution. An alternative to adopting a specific probabilistic model consists of specifying a mixed model or a Markov-like susceptibility model. These models follow the same rationale since they assume the existence of two processes, one that causes an individual to become susceptible to occlusion, the other that determines the subsequent probability of occlusion in the individual. After presenting these models in a unified framework, this paper compares the estimates obtained by fitting the models to data gathered at coronary angiography 1 year after surgery by the SINBA group on a total of 847 saphenous vein anastomoses in 349 patients. Finally, the issue concerning the contribution of each patient to the effective sample size is discussed.