Confidence Statements about the Time Range Over Which Survival Curves Differ

Statistical tests can indicate that two groups have different survival experiences without the associated survival curves being stochastically ordered. Often the two survival curves are similar at early times, even though eventually one curve might dominate the other. This paper addresses the problem of making confidence statements about the range of time over which survival curves differ. In particular, the data are subjected to right censoring and we focus on estimating an upper confidence bound for the earliest time at which the survival curves diverge and remain different.