In most randomized clinical trials not all patients adhere to the therapy to which they were randomly assigned. Instead, they may receive the therapy assigned to another treatment group, or a therapy different from any prescribed in the protocol. When non-adherence occurs, problems occur with the analysis comparing the treatments under study. Rigorous statistical principles require attributing outcome events to the original random treatment assignment ('intent-to-treat' analysis). Using data from the Veterans Administration Cooperative Study of Coronary Artery Bypass Surgery, we report the intent-to-treat analysis and apply four other methods of analysis for analysing non-adherers: 1. exclude non-adherers from analysis; 2. transfer them to the alternative treatment group at the time of randomization; 3. censor them at the time of treatment change, and 4. transfer them to the alternative treatment group at the time of treatment change. Inherent problems and biases of these four other methods are discussed.