| km.rs {spatstat.univar} | R Documentation |
Kaplan-Meier and Reduced Sample Estimator using Histograms
Description
Compute the Kaplan-Meier and Reduced Sample estimators of a survival time distribution function, using histogram techniques
Usage
km.rs(o, cc, d, breaks)
Arguments
o |
vector of observed survival times |
cc |
vector of censoring times |
d |
vector of non-censoring indicators |
breaks |
Vector of breakpoints to be used to form histograms. |
Details
This function is needed mainly for internal use in 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.
The arguments to this function are
vectors o, cc, d
of observed values of \tilde T_i, C_i
and D_i respectively.
The function computes histograms and forms the reduced-sample
and Kaplan-Meier estimates of F(t) by
invoking the functions kaplan.meier
and reduced.sample.
This is efficient if the lengths of o, cc, d
(i.e. the number of observations) is large.
The vectors km and hazard 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]). This approximation is exact only if the
survival times are discrete and the
histogram breaks are fine enough to ensure that each interval
(breaks[k],breaks[k+1]) contains only one possible value of
the survival time.
The vector rs is the reduced-sample estimator,
rs[k] being the reduced sample estimate of F(breaks[k+1]).
This value is exact, i.e. the use of histograms does not introduce any
approximation error in the reduced-sample estimator.
Value
A list with five elements
rs |
Reduced-sample estimate of the survival time c.d.f. |
km |
Kaplan-Meier estimate of the survival time c.d.f. |
hazard |
corresponding Nelson-Aalen estimate of the
hazard rate |
r |
values of |
breaks |
the breakpoints vector |
Author(s)
Adrian Baddeley Adrian.Baddeley@curtin.edu.au
and Rolf Turner rolfturner@posteo.net