Abstract In some clinical trials, rate of change of a physiological function is used as a surrogate for a more serious outcome. We assume an expected change linear in time for each study participant with variation in slopes and intercepts from individual to individual and repeated measures over time for each individual. We also assume that deviations of response for an individual from expected response have zero mean, constant variance, and are uncorrelated. Under these assumptions we describe ways in which stochastic curtailing as defined by Lan, Simon, and Halperin (Commun Stat Seq Anal 1: 207–219, 1982) can be implemented in a two-treatment trial for one-sided comparison of slopes in the two groups. Staggered entry is taken into account, as is the possibility that some of an individual's responses are not available; this is assumed to be random. The analysis assumes the number of participants in each group is large and that most individuals have at least two measurements (including baseline value). The possibility that rate of change is not constant and its consequences are discussed.