`kaplan.meier(obs, nco, breaks)`

obs

vector of $n$ integers giving the histogram of
all observations (censored or uncensored survival times)

nco

vector of $n$ integers giving the histogram of
uncensored observations (those survival times that are less than or
equal to the censoring time)

breaks

Vector of $n+1$ breakpoints which were used to form
both histograms.

- A list with two elements:
km Kaplan-Meier estimate of the survival time c.d.f. $F(t)$ lambda corresponding Nelson-Aalen estimate of the hazard rate $\lambda(t)$ - These are numeric vectors of length $n$.

`spatstat`

,
but may be useful in other applications where you want to form the
Kaplan-Meier estimator from a huge dataset.Suppose $T_i$ are the survival times of individuals $i=1,\ldots,M$ with unknown distribution function $F(t)$ which we wish to estimate. Suppose these times are right-censored by random censoring times $C_i$. Thus the observations consist of right-censored survival times $\tilde T_i = \min(T_i,C_i)$ and non-censoring indicators $D_i = 1{T_i \le C_i}$ for each $i$.

If the number of observations $M$ is large, it is efficient to
use histograms.
Form the histogram `obs`

of all observed times $\tilde T_i$.
That is, `obs[k]`

counts the number of values
$\tilde T_i$ in the interval
`(breaks[k],breaks[k+1]]`

for $k > 1$
and `[breaks[1],breaks[2]]`

for $k = 1$.
Also form the histogram `nco`

of all uncensored times,
i.e. those $\tilde T_i$ such that $D_i=1$.
These two histograms are the arguments passed to `kaplan.meier`

.
The vectors `km`

and `lambda`

returned by `kaplan.meier`

are (histogram approximations to) the Kaplan-Meier estimator
of $F(t)$ and its hazard rate $\lambda(t)$.
Specifically, `km[k]`

is an estimate of
`F(breaks[k+1])`

, and `lambda[k]`

is an estimate of
the average of $\lambda(t)$ over the interval
`(breaks[k],breaks[k+1])`

.

`reduced.sample`

,
`kmrs`