reduced.sample {spatstat} | R Documentation |
Compute the Reduced Sample estimator of a survival time distribution function, from histogram data
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) |
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,...,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 T*[i] = min(T[i],C[i]) and non-censoring indicators D[i] = 1(T[i] <= 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 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.
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 |
Adrian Baddeley adrian@maths.uwa.edu.au http://www.maths.uwa.edu.au/~adrian/ and Rolf Turner rolf@math.unb.ca http://www.math.unb.ca/~rolf