The randomized controlled clinical trial (RCT) is a prospective study using random assignment of subjects to treatment groups to compare the effect and value of a therapeutic intervention against a control. The RCT is the most definitive clinical research tool for evaluating the efficacy of a new therapy in human subjects. Often the outcome of interest in an RCT is the length of time until an event occurs after treatment or intervention. In this article we introduce statistical methods for evaluating differences in the patterns of time to response between two groups of subjects to determine whether one therapy is better than another. The collection of methods for analyzing such data, known as survival data, is called survival analysis. Using data from a hypothetical clinical trial for the prevention of the recurrence of depression, we illustrate two elementary methods for analyzing survival data. We also discuss generalizations of these methods to incorporate covariates and conclude with a general discussion of clinical trials of psychiatric therapies.