Initially, 50 lives are included in an observation of survival times following a specific medical treatment. You are given excerpted information from the study data in the table below.

[math]j[/math]	[math]t_{(j)}[/math]	Deaths at [math]t_{(j)}[/math]	Exits (Other than deaths) in [math](t_{(j)},t_{(j+1)}][/math]	Entrants in [math](t_{(j)},t_{(j+1)}][/math]
0			4	0
1	0.2	1	2	3
2	1.8	1	5	0
3	1.9	1	0	0
4	2.1	1	7	0

Calculate the Nelson-Aalen estimate of [math]S(2)[/math].

• 0.910
• 0.916
• 0.922
• 0.928
• 0.934

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

Answer: E

[math]r_{1}=50-4=46 ; \quad r_{2}=45-2+3=46 ; \quad r_{3}=45-5=40[/math]

[math]\hat{H}(2)=\frac{1}{46}+\frac{1}{46}+\frac{1}{40}=0.06848[/math]

[math]\hat{S}(2)=e^{-\hat{H}(2)}=0.9338[/math]

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