# 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

1 2 | ```
ModifiedEMICM(A, EMstep = TRUE, ICMstep = TRUE, keepiter = FALSE,
tol = 1e-06, maxiter = 1000)
``` |

### Arguments

`A` |
an |

`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. |

### 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`

.

### 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 |

`intmap` |
the real representation associated with the probabilities reported in |

`startend` |
the indices for |

### Author(s)

Qiang Zhao and Jianguo Sun

### 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

1 2 3 4 5 | ```
data(diabetes)
ModifiedEMICM(diabetes[,1:2])
data(cosmesis)
ModifiedEMICM(cosmesis[,1:2])
``` |

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