# Conduct a generalized logrank test for interval-censored data

### Description

Function `gLRT3`

conducts a *k*(>=2)-sample test for interval-censored survival data. The test is based on Zhao, Zhao, Sun, and Kim (2008). The null hypothesis is that all *k*hel survival functions of the failure time are the same, and the alternative hypothesis is that not all functions are the same.

### Usage

1 2 |

### Arguments

`A` |
an |

`k` |
number of treatments. The default is 2. |

`rho` |
non-negative parameter of the link function used for calculating the test statistics. The default is 0. |

`gamma` |
non-negative parameter of the link function used for calculating the test statistics. The default is 0. |

`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. |

`tol` |
the maximal |

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

`inf` |
value used in data for infinity. The default is Inf. |

### Details

Under the null hypothesis, the NPMLE of the common distribution function is computed by function `ModifiedEMICM`

.

Censoring interval for each observation take the form *(L_i, R_i]*. For exact observations, *L_i = R_i*.

The chi-square test in `gLRT3`

has either *k* or *k - 1* degrees of freedom depending on the existence and proportion of exact observations in each treatment. See Zhao, Zhao, Sun, and Kim (2008) for more details.

The link function used in `gLRT3`

is *ξ(x) = x log(x) x^ρ (1 - x)^γ. *

### Value

The function returns an object containing the following components:

`method` |
test procedure used |

`u` |
the test statistic |

`v` |
the estimated covariance of the test statistic |

`chisq` |
the chisquare test statistic |

`df` |
the degrees of freedom of the test |

`p` |
p-value of the test |

### Author(s)

Qiang Zhao and Jianguo Sun

### References

X. Zhao, Q. Zhao, J. Sun, Q. and J. S. Kim (2008), "Generalized Log-rank Tests for Partly Interval-Censored Failure Time Data", Biometrical Journal, 50 (3): 375-385.

Q. Zhao (2012), "gLRT - A New R Package for Analyzing Interval-censored Survival Data", Interval-Censored Time-to-Event Data: Methods and Applications, CRC Press, 377-396.

### See Also

`gLRT`

, `gLRT1`

, `gLRT2`

, `gLRT4`

, `ScoreTest`

### Examples

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