glrt (version 2.0)

ModifiedEMICM: Estimate the distribution function using the hybrid EM-ICM approach

Description

A modified version of function EMICM in package Icens by incorporating function Aintmap in package interval. By defult, the function provides an NPMLE for the distribution function of the survival time.

Usage

ModifiedEMICM(A, EMstep = TRUE, ICMstep = TRUE, keepiter = FALSE, 
tol = 1e-06, maxiter = 1000)

Arguments

A

an $n$ by 2 matrix with containing the end points of censoring intervals of the format (Li, Ri].

EMstep

a boolean variable indicating whether to take an EM step in the iteration when estimating the common distribution function. The default is TRUE.

ICMstep

a boolean variable indicating whether to take an ICM step in the iteration when estimating the common distribution function. The default is TRUE.

keepiter

TRUE/FALSE determining whether to keep the iteration states.

tol

the maximal L1 distance between successive estimates before stopping iteration when estimating the common distribution function. The default is 1.0e-6.

maxiter

the maximal number of iterations to perform before stopping when estimating the common distribution function. The default is 1000.

Value

An object containing the following components:

pf

Estimated probabilities

sigma

NPMLE/self-consistant estimate of the distribution function

weights

the diagonal of the likelihood functions's second derivative

lastchange

a vector of differences between the last two iterations

numiter

number of iterations performed

iter

only present if keepiter is true; state of sigma during the iteration

intmap

the real representation associated with the probabilities reported in pf

startend

the indices for $L_i$ and $R_i$ identifying the end points in intmap where a subject is at risk.

Details

After incorporating function Aintmap, function ModifiedEMICM often produces intmap with smaller size than function EMICM, especially when exact observations ($L_i = R_i$) exist. In addition, object ppairs is returned for later use in computing the test statistics in functions gLRT1, gLRT2, gLRT3, gLRT4, and ScoreTest. Also, a bug was identified in using EMICM when ICMstep=F is specified. The problem is fixed by calling ModifiedEMICMmac, a modified version of function EMICMmac from package Icens.

Either EM, ICM, or both steps can be taken in the estimation. When ICMstep = FALSE, the function computes a self-consistent estimate, the same results as obtained from function icfit in package interval.

References

Function EMICM by Alain Vandal and Robert Gentleman .

J. A. Wellner and Y. Zhan (1997), "A hybrid algorithm for computation of the nonparametric maximum likelihood estimator from censored data", JASA.

See Also

Aintmap, ModifiedEMICMmac

Examples

data(diabetes)
ModifiedEMICM(diabetes[,1:2])

data(cosmesis)
ModifiedEMICM(cosmesis[,1:2])