Control of the immune response to the transplanted organ is fundamental to the success of transplantation. Endomyocardial biopsy to diagnose and grade rejection is the mainstay in achieving this control. As rejection tends to be a patchy process, accurate diagnosis depends on adequate sampling from the myocardium. This study estimates the error rates with which biopsy specimens are graded. The results of 459 biopsy sets, in which at least 4 fragments were graded, were analyzed. Combinations of grades observed at the same biopsy session were used to estimate error rates. An E-M algorithm was used to estimate error rates. Predictive probabilities of true grades, given a set of 4 graded fragments, were calculated using Bayes theorem. If 4 fragments at a biopsy session were negative there was a 0.02% chance of missing clinically significant rejection (moderate or severe). Similarly, if minimal rejection was the highest grade observed, the probability of missing moderate-severe rejection was negligible, between 0.06 and 0.09%. However, where mild rejection is the highest observed on the 4 fragments, there is between a 2% (1 mild fragment) and 28% (4 mild fragments) chance of moderate-severe rejection being the underlying grade. This study concludes that 4 fragments are adequate as a minimum in most cases. However, if only 4 fragments are available, and greater than or equal to 3 are graded mild, the risk of missing moderate-severe rejection is unacceptably high, and repeat biopsy or treatment may be indicated.