  Competing risk analysis considers event times due to multiple causes, or of
more than one event types. Commonly used regression models for such data
include 1) cause-specific hazards model, which focuses on modeling one type of
event while acknowledging other event types simultaneously; and 2)
subdistribution hazards model, which links the covariate effects directly to
the cumulative incidence function. Their use and in particular statistical
properties in the presence of high-dimensional predictors are largely
unexplored. Motivated by an analysis using the linked SEER-Medicare database
for the purposes of predicting cancer versus non-cancer mortality for patients
with prostate cancer, we study the accuracy of prediction and variable
selection of existing statistical learning methods under both models using
extensive simulation experiments, including different approaches to choosing
penalty parameters in each method. We then apply the optimal approaches to the
analysis of the SEER-Medicare data.
