Focus on an infrequently used quantity in the context of competing risks: The conditional probability function

In clinical studies of hematologic and oncologic diseases, the outcomes of interest are generally composite time to event endpoints which are usually defined by occurrence of different event types. Nonetheless, clinicians are interested in studying only one event type, which leads to a competing risks situation. In this context, Pepe and Mori presented a quantity directly derived from the cumulative incidence: the conditional probability. This function defines the probability that a given event occurs, conditionally on not having had a competing event by that time. The objective of this paper is to present this conditional cumulative incidence function and to compare its use to the cumulative incidence in different data sets. Different scenarios highlight the importance of the competing event on the interpretation of the conditional probability. Conditional probability needs to be interpreted jointly with the cumulative incidence. This quantity can be of interest especially when the risk of the competing event is large, strongly precludes the risk of the event of interest and provides useful additional information.