# If there is no censoring, can be the naive 3rd quantile different from the one calculated with from the Kaplan-Meier?

I know, that the median survival time calculated from the Kaplan-Meier estimator is equal to the "naive" descriptive median of the survival time when no censoring in data occurs.

Does it apply also to the other quantiles, like the 3rd quantile? Is this possible that they differ, if no censoring occurs and all subjects experience the event?

> quantile(d$time) 0% 25% 50% 75% 100% 2.5000 3.1375 4.3050 11.3700 71.4200 > km <- survfit( Surv(time, event) ~ 1, data = d, conf.type = "log-log") > > quantile(km)$quantile
25     50     75
3.120  4.305 12.140


No censoring:

> d %>% count(event)
event  n
1     1 86


EDIT: OK, got it, thanks to @Frank Harrell

I should use the empirical CDF with averaging at discontinuities:

> quantile(km)$quantile 25 50 75 3.120 4.305 12.140 > quantile(d$time, type=2)
0%    25%    50%    75%   100%
2.500  3.120  4.305 12.140 71.420