  A two-stage procedure for simultaneously detecting multiple thresholds and
achieving model selection in the segmented accelerate failure time (AFT) model
is developed in this paper. In the first stage, we formulate the threshold
problem as a group model selection problem so that a concave 2-norm group
selection method can be applied. In the second stage, the thresholds are
finalized via a refining method. We establish the strong consistency of the
threshold estimates and regression coefficient estimates under some mild
technical conditions. The proposed procedure performs satisfactorily in our
extensive simulation studies. Its real world applicability is demonstrated via
analyzing a follicular lymphoma data.
