`reduced.sample(nco, cen, ncc, show=FALSE)`

nco

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

cen

vector of counts giving the histogram of
censoring times

ncc

vector of counts giving the histogram of
censoring times for the uncensored observations only

show

Logical value controlling the amount of detail
returned by the function value (see below)

- If
`show = FALSE`

, a numeric vector giving the values of the reduced sample estimator. If`show=TRUE`

, a list with three components which are vectors of equal length, rs Reduced sample estimate of the survival time c.d.f. $F(t)$ numerator numerator of the reduced sample estimator denominator denominator of the reduced sample estimator

`spatstat`

,
but may be useful in other applications where you want to form the
reduced sample 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 `cen`

of all censoring times $C_i$.
That is, `obs[k]`

counts the number of values
$C_i$ 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 $D_i=1$,
and the histogram of all censoring times for which the survival time
is uncensored,
i.e. those $C_i$ such that $D_i=1$.
These three histograms are the arguments passed to `kaplan.meier`

.

The return value `rs`

is the reduced-sample estimator
of the distribution function $F(t)$. Specifically,
`rs[k]`

is the reduced sample estimate of `F(breaks[k+1])`

.
The value is exact, i.e. the use of histograms does not introduce any
approximation error.

`kaplan.meier`

,
`kmrs`