A cohort of 100 newborns is observed from birth. During the first year, 10 drop out of the study and one dies at time 1. Eight more drop out during the next six months, then, at time 1.5, three deaths occur.

Calculate [math]\hat{S}(1.5)[/math], the Nelson-Aalen estimator of the survival function, [math]S(1.5)[/math].

• 0.950
• 0.951
• 0.952
• 0.953
• 0.954

Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Answer: D

[math]\hat{H}(1.5)=\frac{1}{90}+\frac{3}{81}=0.048148[/math]

[math]\hat{S}(1.5)=e^{-\hat{H}(1.5)}=0.9530[/math]

Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.