The KM estimator is estimated by: $$ S(t_i) = \prod_{t\le t_i} \left(1 - \frac{d_i}{n_i}\right) $$ where $d_i$ is the number of deaths at time $t$ and $n_i$ is the number of individuals alive just before $t$.

Given a large enough observation time, the last number of deaths will be equal to $n_i$. At this time point and into the future, the survival function is zero as $\left(1 - \frac{d_i}{n_i}\right)=0$.

class KaplanMeier[source]

KaplanMeier()

data:

df.head()

	ctryname	cowcode2	politycode	un_region_name	un_continent_name	ehead	leaderspellreg	democracy	regime	start_year	duration	observed
0	Afghanistan	700	700.0	Southern Asia	Asia	Mohammad Zahir Shah	Mohammad Zahir Shah.Afghanistan.1946.1952.Mona...	Non-democracy	Monarchy	1946	7	1
1	Afghanistan	700	700.0	Southern Asia	Asia	Sardar Mohammad Daoud	Sardar Mohammad Daoud.Afghanistan.1953.1962.Ci...	Non-democracy	Civilian Dict	1953	10	1
2	Afghanistan	700	700.0	Southern Asia	Asia	Mohammad Zahir Shah	Mohammad Zahir Shah.Afghanistan.1963.1972.Mona...	Non-democracy	Monarchy	1963	10	1
3	Afghanistan	700	700.0	Southern Asia	Asia	Sardar Mohammad Daoud	Sardar Mohammad Daoud.Afghanistan.1973.1977.Ci...	Non-democracy	Civilian Dict	1973	5	0
4	Afghanistan	700	700.0	Southern Asia	Asia	Nur Mohammad Taraki	Nur Mohammad Taraki.Afghanistan.1978.1978.Civi...	Non-democracy	Civilian Dict	1978	1	0

km = KaplanMeier()
km.fit(df.rename(columns={'duration': 't', 'observed': 'e'}))
km.plot_survival_function();

km.predict(np.array([5, 20, 30, 100]))

array([0.33400794, 0.09099421, 0.05275089, 0.        ])