Kaplan-Meier estimate

Survival Analysis in R

Heidi Seibold

Statistician at LMU Munich

Survival function

$S(t) = 1 - F(t) = P(T > t)$

$\hat{S}(t) = \prod\limits_{i: ~ t_i \leq t} \frac{n_i-d_i}{n_i}$

$\hat{S}(t) = \prod\limits_{i: ~ t_i \leq t} \frac{n_i-d_i}{n_i}$

$\hat{S}(t) = \prod\limits_{i: ~ t_i \leq t} \frac{n_i-d_i}{n_i}$

$\hat{S}(2) = \frac{5 - 0}{5} = \frac{5}{5} = 1$

$\hat{S}(3) = \frac{4 - 0}{4} = \frac{4}{4} = 1$

$\hat{S}(4) = \frac{4 - 2}{4} = \frac{2}{4} = \frac{1}{2} = 0.5$

$\hat{S}(5) = \frac{1}{2} \cdot \frac{2 - 1}{2} = \frac{1}{4} = 0.25$

$\hat{S}(6) = \frac{1}{4} \cdot \frac{1 - 0}{1} = \frac{1}{4} = 0.25$

km <- survfit(Surv(time, event) ~ 1)

ggsurvplot(km, conf.int = FALSE, 
  risk.table = "nrisk_cumevents",
  legend = "none")

Survival Analysis in R