Aalen–Johansen estimator
= Aalen–Johansen estimator
{c}
{title2=$\widehat P(0,t)=\prod_{u\le t}(I+d\widehat A(u))$}
The Aalen–Johansen estimator is a product of empirical state-transition matrices over event times. In <competing risks>, the estimated <cumulative incidence function> for cause $j$ jumps by $\widehat S(t-)d_j(t)/Y(t)$, while overall survival is updated using all event causes. <Right censoring> changes subsequent <risk sets> but does not itself create a <probability> jump.