Homework SoursehttpfacultybusinessutsaedumandersoSTA1403PROBLEM20SETSExerci
http://faculty.business.utsa.edu/manderso/STA1403/PROBLEM%20SETS/Exercise_Kaplan-MeierEstimates.pdf
Part 3 and Part 4
Solution
Part 3
Part 4
At 95% confidence interval the survival probability for S(21) lies between 0.586647-1.96*sqrt(0.016948) and 0.586647+1.96*sqrt(0.016948), i,e (0.3315, 0.8418)
| time | #failed | #censored | at risk | 1-dt/nt | S(t) | Variance | CI(Lower limit) | CI(Upper limit) |
| 0 | 15 | 1 | 1 | |||||
| 14 | 1 | 0 | 15 | 0.933333 | 0.933333 | 0.004148 | 0.80709734 | 1.059569326 |
| 15 | 2 | 0 | 14 | 0.857143 | 0.8 | 0.010667 | 0.59757207 | 1.00242793 |
| 17 | 1 | 1 | 12 | 0.916667 | 0.733333 | 0.013037 | 0.509540837 | 0.95712583 |
| 20 | 1 | 0 | 10 | 0.9 | 0.66 | 0.0154 | 0.416770397 | 0.903229603 |
| 21 | 1 | 0 | 9 | 0.888889 | 0.586667 | 0.016948 | 0.331503962 | 0.841829371 |
| 23 | 1 | 0 | 8 | 0.875 | 0.513333 | 0.017681 | 0.252708739 | 0.773957928 |
| 30 | 0 | 1 | 7 | 1 | 0.513333 | 0.017681 | 0.252708739 | 0.773957928 |
| 32 | 1 | 0 | 6 | 0.833333 | 0.427778 | 0.018379 | 0.162065089 | 0.693490466 |
| 38 | 1 | 0 | 5 | 0.8 | 0.342222 | 0.017618 | 0.082065116 | 0.602379328 |
| 42 | 1 | 0 | 4 | 0.75 | 0.256667 | 0.0154 | 0.013437063 | 0.49989627 |
| 58 | 1 | 0 | 3 | 0.666667 | 0.171111 | 0.011724 | -0.041115168 | 0.38333739 |
| 60 | 0 | 2 | 2 | 1 | 0.171111 | 0.011724 | -0.041115168 | 0.38333739 |
