Large, randomized clinical trials ("megatrials") are key drivers of modern cardiovascular practice, since they are cited frequently as the authoritative foundation for evidence-based management policies. Nevertheless, fundamental limitations in the conventional approach to statistical hypothesis testing undermine the scientific basis of the conclusions drawn from these trials. This review describes the conventional approach to statistical inference, highlights its limitations, and proposes an alternative approach based on Bayes' theorem. Despite its inherent subjectivity, the Bayesian approach possesses a number of practical advantages over the conventional approach: 1). it allows the explicit integration of previous knowledge with new empirical data; 2). it avoids the inevitable misinterpretations of p values derived from megatrial populations; and 3). it replaces the misleading p value with a summary statistic having a natural, clinically relevant interpretation-the probability that the study hypothesis is true given the observations. This posterior probability thereby quantifies the likelihood of various magnitudes of therapeutic benefit rather than the single null magnitude to which the p value refers, and it lends itself to graphical sensitivity analyses with respect to its underlying assumptions. Accordingly, the Bayesian approach should be employed more widely in the design, analysis, and interpretation of clinical megatrials.