Modeling the hazar of the cummulative incidence function (CIF) (Fine and Gray, 1999):

Partial likelihood is given by:

The risk set is formed of those who did not experience an event by time t and of those who experienced a competing risk event by time t. Those who expererienced other types of events remain in the risk set all the time. However, individuals experiencing a competing risk envent do not participate fully in the partial likelihood.

Where the weights are defined:

The score (U) statistic has the form:

The model based estimate of the CIF is defined

and