In this article, we consider methods of regression modeling in the competing risks setting commonly encountered in analyzing stem cell transplantation data. We clarify the distinction between modeling the cause-specific hazard rate and modeling the cumulative incidence probability or function, and we review regression techniques for both types of quantities. We apply them to 2 examples: 1 comparing engraftment and 1 examining relapse. These examples illustrate that different conclusions may result depending on the type of regression model used for comparing treatments. Finally, we show how these discrepancies occur because 2 different characteristics of the time-to-event distribution are being modeled.