CG.test {compound.Cox} | R Documentation |

## Testing survival difference of two groups via the CG estimators

### Description

Testing survival difference of two prognostic groups separated by a prognostic index (PI). Survival probabilities are computed by the CG estimators (Yeh, et al. 2023).

### Usage

```
CG.test(t.vec,d.vec,PI,cutoff=median(PI),alpha=2,
copula=CG.Clayton,S.plot=TRUE,N=10000,mark.time=TRUE)
```

### Arguments

`t.vec` |
Vector of survival times (time to either death or censoring) |

`d.vec` |
Vector of censoring indicators, 1=death, 0=censoring |

`PI` |
Vector of real numbers (the values of a prognostic index) |

`cutoff` |
A number determining the cut-off value of a prognostic index |

`alpha` |
Copula parameter |

`copula` |
Copula function: "CG.Clayton","CG.Gumbel" or "CG.Frank" |

`S.plot` |
If TRUE, the survival curve is displayed |

`N` |
The number of permutations |

`mark.time` |
If TRUE, then curves are marked at each censoring time |

### Details

Two-sample comparison based on estimated survival functions via copula-graphic estimators under dependent censoring. The D statistic (the mean vertical difference betewen two estimated survival functions) is used for testing the null hypothesis of no difference in survival. See Yeh et al.(2023) for details.

### Value

`test` |
Testing the difference of two survival functions |

`Good` |
Good prognostic group defined by PI<=c |

`Poor` |
Poor prognostic group defined by PI>c |

### Author(s)

Takeshi Emura, Pauline Baur

### References

Emura T, Chen YH (2018). Analysis of Survival Data with Dependent Censoring, Copula-Based Approaches, JSS Research Series in Statistics, Springer, Singapore.

Rivest LP, Wells MT (2001). A Martingale Approach to the Copula-graphic Estimator for the Survival Function under Dependent Censoring, J Multivar Anal; 79: 138-55.

Yeh CT, Liao GY, Emura T (2023). Sensitivity analysis for survival prognostic prediction with gene selection: a copula method for dependent censoring, Biomedicines 11(3):797.

### Examples

```
t.vec=c(1,3,5,4,7,8,10,13)
d.vec=c(1,0,0,1,1,0,1,0)
PI=c(8,7,6,5,4,3,2,1)
CG.test(t.vec,d.vec,PI,copula=CG.Clayton,alpha=18,N=100)
CG.test(t.vec,d.vec,PI,copula=CG.Gumbel,alpha=2,N=100)
```

*compound.Cox*version 3.30 Index]