# Function to compare two IAUCs through time-dependent ROC curves

### Description

This function compares two integrated areas under the curves (IAUC) through the results of time-dependent ROC curves at some points in time. The statistical test is a Wilcoxon rank sum test for dependent samples.

### Usage

1 |

### Arguments

`auc1` |
vector of AUCs computed from the first time-dependent ROC curves for some points in time |

`auc2` |
vector of AUCs computed from the second time-dependent ROC curves for some points in time |

`time` |
vector of points in time for which the AUCs are computed |

### Details

The two vectors of AUCs must be computed from the same samples (and corresponding survival data) and for the same points in time. The function uses a Wilcoxon rank sum test for dependent samples.

### Value

`p.value ` |
p-value from the Wilcoxon rank sum test for the comparison iauc1 > iauc2 |

`iauc1 ` |
value of the IAUC for the first set of time-depdent ROC curves |

`iauc2 ` |
value of the IAUC for the second set of time-depdent ROC curves |

### Author(s)

Benjamin Haibe-Kains

### References

Wilcoxon, F. (1945) "Individual comparisons by ranking methods", *Biometrics Bulletin*, **1**, pages 80–83.

Haibe-Kains, B. and Desmedt, C. and Sotiriou, C. and Bontempi, G. (2008) "A comparative study of survival models for breast cancer prognostication based on microarray data: does a single gene beat them all?", *Bioinformatics*, **24**, 19, pages 2200–2208.

### See Also

`tdrocc`

, `wilcox.test`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | ```
set.seed(12345)
age <- rnorm(30, 50, 10)
size <- rexp(30,1)
stime <- rexp(30)
cens <- runif(30,.5,2)
sevent <- as.numeric(stime <= cens)
stime <- pmin(stime, cens)
##time-dependent ROC curves
tt <- unique(sort(stime[sevent == 1]))
##size
mytdroc1 <- NULL
for(i in 1:length(tt)) {
rr <- tdrocc(x=size, surv.time=stime, surv.event=sevent, time=tt[i],
na.rm=TRUE, verbose=FALSE)
mytdroc1 <- c(mytdroc1, list(rr))
}
auc1 <- unlist(lapply(mytdroc1, function(x) { return(x$AUC) }))
##age
mytdroc2 <- NULL
for(i in 1:length(tt)) {
rr <- tdrocc(x=age, surv.time=stime, surv.event=sevent, time=tt[i],
na.rm=TRUE, verbose=FALSE)
mytdroc2 <- c(mytdroc2, list(rr))
}
auc2 <- unlist(lapply(mytdroc2, function(x) { return(x$AUC) }))
iauc.comp(auc1=auc1, auc2=auc2, time=tt)
``` |