Competing Risks: Concepts, Methods, and Software

The role of competing risks in the analysis of time-to-event data is increasingly acknowledged. Software is readily available. However, confusion remains regarding the proper analysis: When and how do I need to take the presence of competing risks into account? Which quantities are relevant for my research question? How can they be estimated and what assumptions do I need to make? The main quantities in a competing risks analysis are the cause-specific cumulative incidence, the cause-specific hazard, and the subdistribution hazard. We describe their nonparametric estimation, give an overview of regression models for each of these quantities, and explain their difference in interpretation. We discuss the proper analysis in relation to the type of study question, and we suggest software in R and Stata. Our focus is on competing risks analysis in medical research, but methods can equally be applied in other fields like social science, engineering, and economics. Expected final online publication date for the Annual Review of Statistics and Its Application, Volume 11 is March 2024. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.