In the analysis of time-to-event data, the problem of competing risks occurs when an individual may experience one, and only one, of m different types of events. The presence of competing risks complicates the analysis of time-to-event data, and standard survival analysis techniques such as Kaplan–Meier estimation, log-rank test and Cox modeling are not always appropriate and should be applied with caution. Fine and Gray developed a method for regression analysis that models the hazard that corresponds to the cumulative incidence function. This model is becoming widely used by clinical researchers and is now available in all the major software environments. Although model selection methods for Cox proportional hazards models have been developed, few methods exist for competing risks data. We have developed stepwise regression procedures, both forward and backward, based on AIC, BIC, and BICcr (a newly proposed criteria that is a modified BIC for competing risks data subject to right censoring) as selection criteria for the Fine and Gray model. We evaluated the performance of these model selection procedures in a large simulation study and found them to perform well. We also applied our procedures to assess the importance of bone mineral density in predicting the absolute risk of hip fracture in the Women's Health Initiative–Observational Study, where mortality was the competing risk. We have implemented our method as a freely available R package called crrstep. Copyright © 2013 John Wiley & Sons, Ltd.