The inverse of the risk difference, commonly referred to as the number needed to treat (NNT) has been recently proposed as a useful measure for comparing two treatments. Since its introduction, the method has been used widely to establish comparative treatment benefits, and has also been the subject of extensive discussions among statisticians. In this paper, we examine the assumptions behind the original definition of NNT, and introduce a new formulation of the method based on a random walk model. Using stopping times, we develop a paradigm for NNT that avoids some of the conceptual and inferential difficulties and pitfalls associated with the previous work on NNT. Simulation results are provided to illustrate the bias introduced by using alternative formulations of NNT, and several open problems are suggested for future research.