Competing Risks Analysis

Luigi Santoro, Biostatistician and Staff Scientist, European Institute of Oncology

Events other than the one of interest which could precludes occurrence of the event of interest or alter the probability of experiencing the event of interest, are known as competing risk events.
In the disease/recovery process, often, more than one type of event plays a role. Usually, only one type of event can be selected as the event of interest (e.g. if relapse is the event of interest then death is a competing risk).  
The incidence of the event of interest is the probability of the event of interest given that the individuals survived BOTH the event of interest AND the competing risk event. In this terms the (cumulative) incidence (CI) is equal to 1-KM (Kaplan-Meier estimate) if removing the competing risks effect the curve will not change. In this case there would be no difference in using KM estimates or CI. On the contrary the KM estimates  would be biased and the CI should be used. When comparing CI the usual Log-Rank test has to be replaced by the Gray’s test which is a modified Log-Rank’s test. Multivariate analysis on a give event can also be adjusted for the presence of competing risks. Comparison between Cox’s model and Fine and Gray’s model will be mentioned.