  Clinical trials involving novel immuno-oncology (IO) therapies frequently
exhibit survival profiles which violate the proportional hazards assumption due
to a delay in treatment effect, and in such settings, the survival curves in
the two treatment arms may have a crossing before the two curves eventually
separate. To flexibly model such scenarios, we describe a nonparametric
approach for estimating the treatment arm-specific survival functions which
constrains these two survival functions to cross at most once without making
any additional assumptions about how the survival curves are related. A main
advantage of our approach is that it provides an estimate of a crossing time if
such a crossing exists, and moreover, our method generates interpretable
measures of treatment benefit including crossing-conditional survival
probabilities and crossing-conditional estimates of restricted residual mean
life. We demonstrate the use and effectiveness of our approach with a large
simulation study and an analysis of reconstructed outcomes from a recent
combination-therapy trial.
