Kaplan-Meier and Reduced Sample Estimator using Histograms

Compute the Kaplan-Meier and Reduced Sample estimators of a survival time distribution function, using histogram techniques

spatial, nonparametric
Usage, cc, d, breaks)
vector of observed survival times
vector of censoring times
vector of non-censoring indicators
Vector of breakpoints to be used to form histograms.

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.


  • A list with five elements
  • rsReduced-sample estimate of the survival time c.d.f. $F(t)$
  • kmKaplan-Meier estimate of the survival time c.d.f. $F(t)$
  • hazardcorresponding Nelson-Aalen estimate of the hazard rate $\lambda(t)$
  • rvalues of $t$ for which $F(t)$ is estimated
  • breaksthe breakpoints vector

See Also

reduced.sample, kaplan.meier

Documentation reproduced from package spatstat, version 1.16-3, License: GPL (>= 2)

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