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].
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.