R: Kaplan-Meier Estimator using Histogram Data

kaplan.meier {spatstat.core} | R Documentation

## Kaplan-Meier Estimator using Histogram Data

### Description

Compute the Kaplan-Meier estimator of a survival time distribution function, from histogram data

### Usage

      kaplan.meier(obs, nco, breaks, upperobs=0)

### Arguments

`obs` | vector of n integers giving the histogram of all observations (censored or uncensored survival times)
`nco` | vector of n integers giving the histogram of uncensored observations (those survival times that are less than or equal to the censoring time)
`breaks` | Vector of n+1 breakpoints which were used to form both histograms.
`upperobs` | Number of observations beyond the rightmost breakpoint, if any.

### 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,…,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 `obs` of all observed times T*[i]. That is, `obs[k]` counts the number of values T*[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. These two histograms are the arguments passed to `kaplan.meier`.

The vectors `km` and `lambda` 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])`.

The histogram breaks must include 0. If the histogram breaks do not span the range of the observations, it is important to count how many survival times T*[i] exceed the rightmost breakpoint, and give this as the value `upperobs`.

### Value

A list with two elements:

`km` | Kaplan-Meier estimate of the survival time c.d.f. F(t)
`lambda` | corresponding Nelson-Aalen estimate of the hazard rate lambda(t)

These are numeric vectors of length n.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

and Rolf Turner r.turner@auckland.ac.nz

### See Also

`reduced.sample`, `km.rs`

[Package spatstat.core version 2.3-0 Index]