WITHIN PATIENT-DEPENDENT OUTCOMES IN GRAFT OCCLUSION AFTER CORONARY-ARTERY BYPASS

In clinical trials aimed at assessing the efficacy of drugs after coro nary 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 assumi ng 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 compari ng the frequencies of occlusion under different treatments after adjus ting the variance of each frequency for the size of the cluster 5,6,2 3!. Alternatively, one can measure the intraclass (intrapatient) corre lation coefficient and adopt distribution functions that include this quantity as one of the parameters. This approach has been adopted by m any authors 12-17! although the studies differed in the statistical m odel used to represent this kind of data. Two probability functions, A ltham's 14! and beta-binomial 11!, have found wide application in di fferent biomedical fields. Both are able to model the extrabinomial va riability since their tails tend to zero more slowly than those of the binomial distribution. An alternative to adopting a specific probabil istic model consists of specifying a mixed model or a Markov-like susc eptibility model. These models follow the same rationale since they as sume the existence of two processes, one that causes an individual to become susceptible to occlusion, the other that determines the subsequ ent probability of occlusion in the individual. After presenting these models in a unified framework, this paper compares the estimates obta ined by fitting the models to data gathered at coronary angiography 1 year after surgery by the SINBA group 26! on a total of 847 saphenous vein anastomoses in 349 patients. Finally, the issue concerning the c ontribution of each patient to the effective sample size is discussed.