Regression Models for Hazard Rates Versus Cumulative Incidence Probabilities in Hematopoietic Cell Transplantation Data

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.