icfit {interval}R Documentation

calculate non-parametric MLE for interval censored survival function

Description

This function calculates the the non-parametric maximum likelihood estimate for the distribution from interval censored data using the self-consistent estimator, so the associated survival distribution generalizes the Kaplan-Meier estimate to interval censored data. Formulas using Surv are allowed similar to survfit.

Usage


## S3 method for class 'formula':
icfit(formula, data, ...)

## Default S3 method:
icfit(L, R,initfit = NULL, control=icfitControl(), Lin=NULL, Rin=NULL, ...)

Arguments

L numeric vector of left endpoints of censoring interval
R numeric vector of right endpoints of censoring interval
initfit an object of class icfit or icsurv, used for the initial estimate (see details)
control list of arguments for controling algorithm (see icfitControl)
Lin logical vector, should L be included in the interval? (see details)
Rin logical vector, should R be included in the interval? (see details)
formula a formula with response a numeric vector (which assumes no censoring) or Surv object the right side of the formula may be 1 or a factor (which produces separate fits for each level).
data an optional matrix or data frame containing the variables in the formula formula. By default the variables are taken from environment(formula).
... values passed to other functions

Details

The icfit function fits the nonparametric maximum likelihood estimate (NPMLE) of the distribution function for interval censored data. In the default case (when Lin=Rin=NULL) we assume there are n (n=length(L)) failure times, and the ith one is in the interval between L[i] and R[i]. The default is not to include L[i] in the interval unless L[i]=R[i], and to include R[i] in the interval unless R[i]=Inf. When Lin and Rin are not NULL they describe whether to include L and R in the associated interval. If either Lin or Rin is length 1 then it is repeated n times, otherwise they should be logicals of length n.

The algorithm is basically an EM-algorithm applied to interval censored data (see Turnbull, 1976); however first there is a primary reduction (see Aragon and Eberly, 1992). Convergence is defined when the maximum reduced gradient is less than epsilon (see icfitControl), and the Kuhn-Tucker conditions are approximately met, otherwise a warning will result. (see Gentleman and Geyer, 1994). There are other faster algorithms (for example see EMICM in the package Icens.

The output is of class icfit which is identical to the icsurv class of the Icens package when there is only one group for which a distribution is needed. Following that class, there is an intmap element which gives the bounds about which each drop in the NPMLE survival function can occur.

Since the classes icfit and icsurv are so closely related, one can directly use of initial (and faster) fits from the Icens package as input in initfit. Note that when using a non-null initfit, the Lin and Rin values of the initial fit are ignored. The advantage of the icfit function is that it allows a call similar to that used in survfit of the survival package so that different groups may be plotted at the same time with similar calls.

An icfit object prints as a list (see value below). A print function prints output as a list except suppresses printing of A matrix. A summary function prints the distribution (i.e., probabilities and the intervals where those probability masses are known to reside) for each group in the icfit object. There is also a plot method, see plot.icfit.

Value

An object of class icfit (same as icsurv class, see details). A list with elements:

A this is the n by k matrix of indicator functions, NULL if more than one strata, not printed by default
strata a named numeric vector of numbers of observations in each strata, if one strata observation named NPMLE
error this is max(d + u - n), see Gentleman and Geyer, 1994
numit number of iterations
pf vector of estimated probabilities of the distribution
intmap 2 by k matrix, where the ith column defines an interval corresponding to the probability, pf[i]
converge a logical, TRUE if normal convergence
message character text message on about convergence

Author(s)

Michael P. Fay

References

Aragon, J and Eberly, D (1992). On convergence of convex minorant algorithms for distribution estimation with interval-censored data. J. of Computational and Graphical Statistics. 1: 129-140.

Gentleman, R. and Geyer, C.J. (1994). Maximum likelihood for interval censored data:consistency and computation. Biometrika, 81, 618-623.

Turnbull, B.W. (1976) The empirical distribution function with arbitrarily grouped, censored and truncated data. J. R. Statist. Soc. B 38, 290-295.

See Also

ictest

Examples

data(bcos)
icout<-icfit(Surv(left,right,type="interval2")~treatment, data=bcos)
plot(icout)
## can pick out just one group
plot(icout[1])

[Package interval version 0.7-5.5 Index]