Survival Analysis Notes

For large samples survival times are near each other

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Unformatted text preview: Life table estimator is k S ∗ (t ) = j =1 nj − dj nj ; tk ≤ t < tk +1 Kaplan-Meier estimator follows same idea as the life table estimator, except Each time interval (except initial) has 1 death. Death time at start of interval. No actuarial correction (use nj in formulas). For large samples, survival times are near each other with few censored cases. k ˆ S (t ) = j =1 nj − dj nj ; tk ≤ t < tk +1 UNM Example: Survival times of women with tumors that were negatively stained (Collett Ex. 1.2 pg. 7): 23, 47, 69, 70∗ , 71∗ , 100∗ , 101∗ , 148, 181, 198∗ , 208∗ , 212∗ , 224∗ ∗ means censored observation. Interval nj dj cj nj [0, 50) [50, 100) [100, 150) [150, 200) [200, 250) 13 11 8 5 3 2 1 1 1 0 0 2 2 1 3 13 10 7 4.5 1.5 nj −dj nj 0.846 0.900 0.857 0.778 1 S ∗ (t ) 0.846 0.761...
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