Cumulative incidence update with tied censoring (source code)

= Cumulative incidence update with tied censoring
{title2=$\Delta\widehat F_j(t)=\widehat S(t-)d_j(t)/Y(t-)$}

For <competing risks>, a <cumulative incidence function> jumps by the displayed <Aalen–Johansen estimator> increment. A person <right-censored> at exactly the event time remains in the immediately preceding <risk set> under the usual events-before-censoring tie convention. Censoring changes the next risk set, not the current event numerator or survival jump.