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
```

## Best Answer

There are multiple definitions of sample (and population, in case of discreteness) quantiles. If you use the empirical cumulative distribution function definition (which is

nota weighted average of two estimates) this agrees fully with Kaplan-Meier under no censoring, because K-M is precisely one minus the empirical cumulative distribution function. Note that sample quantiles are noisy estimates --- even more so with censoring which lowers the effective sample size.