EMICM: Compute the NPMLE for censored data using the EMICM.

In Icens: NPMLE for Censored and Truncated Data

Description

An implementation of the hybrid EM ICM (Iterative convex minorant) estimator of the distribution function proposed by Wellner and Zahn (1997).

Usage

EMICM(A, EMstep=TRUE, ICMstep=TRUE, keepiter=FALSE, tol=1e-07,
maxiter=1000) 

Arguments

A	Either the m by n clique matrix or the n by 2 matrix containing the event time intervals.
EMstep	Boolean, indicating whether to take an EM step in the iteration.
ICMstep	Boolean, indicating whether to take an ICM step.
keepiter	Boolean determining whether to keep the iteration states.
tol	The maximal L1 distance between successive estimates before stopping iteration.
maxiter	The maximal number of iterations to perform before stopping.

Details

Lots, and they're complicated too!

Value

An object of class icsurv containing the following components:

pf	The estimated probabilities.
sigma	The NPMLE of the survival function on the maximal antichains.
weights	The diagonal of the likelihood function's second derivative.
lastchange	A vector of differences between the last two iterations.
numiter	The total number of iterations performed.
iter	Is only present if keepiter is true; states of sigma during the iteration.
intmap	The real representation associated with the probabilities reported in pf.

Author(s)

Alain Vandal and Robert Gentleman

References

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

See Also

EM,VEM, PGM

Examples

  data(cosmesis)
  csub1 <- subset(cosmesis, subset=Trt==0, select=c(L,R))
  EMICM(csub1)
  data(pruitt)
  EMICM(pruitt)

Example output

Loading required package: survival
$sigma
 [1] 0.04634677 0.07971014 0.16837751 0.23913044 0.23913044 0.23913044
 [7] 0.33177627 0.33177627 0.41356204 0.41356204 0.41356204 0.53444187
[13] 0.53444187 1.00000000

$pf
 [1] 0.04634677 0.03336337 0.08866737 0.07075292 0.00000000 0.00000000
 [7] 0.09264584 0.00000000 0.08178577 0.00000000 0.00000000 0.12087983
[13] 0.00000000 0.46555813

$llk
[1] -58.06002

$weights
 [1] 626.75573 236.08264 604.37156 267.74235 274.08638 356.04281 382.51309
 [8] 294.83287 152.40891 110.02664 229.56934  28.96042 178.39798  84.24237

$lastchange
 [1]  2.176308e-09  2.622902e-15  9.322564e-10  1.199292e-09  1.199292e-09
 [6]  1.199292e-09 -1.521946e-08 -1.521946e-08 -7.066271e-09 -7.066271e-09
[11] -7.066271e-09 -2.250525e-08 -2.250525e-08  0.000000e+00

$numiter
[1] 10

$eps
[1] 1e-07

$intmap
     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
[1,]    4    6    7   11   15   17   24   25   33    34    36    38    40    46
[2,]    5    7    8   12   16   18   25   26   34    35    37    40    44    48

attr(,"class")
[1] "icsurv"
$sigma
[1] 0.1250000 0.2666349 0.4860189 0.6389807 0.6885481 0.7345821 1.0000000

$pf
[1] 0.12499999 0.14163492 0.21938398 0.15296184 0.04956740 0.04603393 0.26541795

$llk
[1] -10.68207

$weights
[1] 99.02612 43.68736 64.60762 79.90472 43.68736 28.39026 24.00636

$lastchange
[1] -1.325223e-08  9.560889e-08  8.196677e-08  7.318327e-08  8.754193e-08
[6] -4.528669e-08  0.000000e+00

$numiter
[1] 27

$eps
[1] 1e-07

attr(,"class")
[1] "icsurv"

Icens documentation built on Nov. 8, 2020, 8:12 p.m.