2 Right Censoring and Kaplan-Meier Estimator - NCSU Statistics

CHAPTER 2 ST 745, Daowen Zhang
> summary(fit)
Call: survfit(formula = Surv(obstime, status), conf.type = c("plain"))
time n.risk n.event survival std.err lower 95% CI upper 95% CI
0.0747 50 1 0.980 0.0198 0.9412 1.000
0.0908 49 1 0.960 0.0277 0.9057 1.000
0.4332 46 1 0.939 0.0341 0.8723 1.000
0.4420 45 1 0.918 0.0392 0.8414 0.995
0.5454 44 1 0.897 0.0435 0.8121 0.983
0.6126 43 1 0.877 0.0472 0.7839 0.969
0.7238 42 1 0.856 0.0505 0.7567 0.955
1.1662 40 1 0.834 0.0536 0.7292 0.939
1.2901 39 1 0.813 0.0563 0.7025 0.923
1.3516 38 1 0.791 0.0588 0.6763 0.907
1.4490 37 1 0.770 0.0609 0.6506 0.890
1.6287 35 1 0.748 0.0630 0.6245 0.872
1.8344 34 1 0.726 0.0649 0.5988 0.853
1.9828 33 1 0.704 0.0666 0.5736 0.835
2.1467 32 1 0.682 0.0680 0.5487 0.815
2.3481 31 1 0.660 0.0693 0.5242 0.796
2.4668 30 1 0.638 0.0704 0.5001 0.776
2.5135 29 1 0.616 0.0713 0.4763 0.756
2.5999 28 1 0.594 0.0721 0.4528 0.735
2.9147 27 1 0.572 0.0727 0.4296 0.715
2.9351 25 1 0.549 0.0733 0.4055 0.693
3.2168 24 1 0.526 0.0737 0.3818 0.671
3.4501 22 1 0.502 0.0742 0.3570 0.648
3.5620 21 1 0.478 0.0744 0.3326 0.624
3.6795 20 1 0.455 0.0744 0.3087 0.600
3.8475 18 1 0.429 0.0744 0.2834 0.575
4.8888 16 1 0.402 0.0745 0.2565 0.548
5.3910 15 1 0.376 0.0742 0.2302 0.521
6.1186 14 1 0.349 0.0736 0.2046 0.493
6.1812 13 1 0.322 0.0726 0.1796 0.464
6.1957 12 1 0.295 0.0714 0.1552 0.435
6.2686 10 1 0.266 0.0701 0.1283 0.403
6.3252 9 1 0.236 0.0682 0.1024 0.370
6.5206 7 1 0.202 0.0663 0.0724 0.332
7.1127 6 1 0.169 0.0632 0.0447 0.293
9.3017 3 1 0.112 0.0623 0.0000 0.235
11.1589 1 1 0.000 NA NA NA
The Kaplan estimate (solid line) and its symmetric 95% confidence intervals (dotted lines) are
shown in Figure 2.6. Note that the Kaplan estimate is the same as before. From this figure, the
median survival time is estimated to be 3.56 years, with its 95% confidence interval [2.51, 6.12].
Note: If we treat the censored data obstime as uncensored and fit an exponential model
to it, then the “best” estimate of the median survival time is 2.5, with 95% confidence interval
[1.8, 3.2] (using the methodology to be presented in next chapter). These estimates severely
underestimate the true median survival time 3.5 years.
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