Δ F_{B} (t) = S (t -) \frac{d _{B} ( t )}{Y ( t )}, S (t) = S (t -) [1 - \frac{d _{A} ( t ) + d _{B} ( t )}{Y ( t )}] .

Right censoring changes subsequent risk sets, not the survival function by itself. Starting with the given estimates at

a_{k}

, the complete calculation is

event time a_{k + 1} a_{k + 2} a_{k + 3} Y (t) 1098 S (t -) 0.40 0.36 0.32 Δ F_{B} (t) 0.40/10 = 0.04 0 0.32/8 = 0.04 F_{B} (t) 0.34 0.34 0.38 S (t) 0.36 0.32 0.28

(2)

The middle event is of the competing type: it decreases overall survival while leaving the disease cumulative incidence function unchanged at that instant. The event-free intervals leave every estimate and risk set unchanged.

At the final time, both the event subject and the subject censored at that time are in the just-before risk set, so its denominator is eight. This is the usual event-before-censoring convention for recorded ties. After the event and right censoring, six subjects remain at risk. Consequently