# reduced.sample

##### Reduced Sample Estimator using Histogram Data

Compute the Reduced Sample estimator of a survival time distribution function, from histogram data

- Keywords
- spatial

##### Usage

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

##### Arguments

- 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)

##### Details

This function is needed mainly for internal use in `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.

##### Value

- 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

##### See Also

*Documentation reproduced from package spatstat, version 1.3-4, License: GPL version 2 or newer*