  Analyzing outcomes in long-term cancer survivor studies can be complex. The
effects of predictors on the failure process may be difficult to assess over
longer periods of time, as the commonly used assumption of proportionality of
hazards holding over an extended period is often questionable. In this
manuscript, we compare seven different survival models that estimate the hazard
rate and the effects of proportional and non-proportional covariates. In
particular, we focus on an extension of the the multi-resolution hazard (MRH)
estimator, combining a non-proportional hierarchical MRH approach with a
data-driven pruning algorithm that allows for computational efficiency and
produces robust estimates even in times of few observed failures. Using data
from a large-scale randomized prostate cancer clinical trial, we examine
patterns of biochemical failure and estimate the time-varying effects of
androgen deprivation therapy treatment and other covariates. We compare the
impact of different modeling strategies and smoothness assumptions on the
estimated treatment effect. Our results show that the benefits of treatment
diminish over time, possibly with implications for future treatment protocols.
