# Function to statistically compare two hazard ratios (alternative interface)

### Description

This function compares two hazard ratios from their betas and standard errors as computed by a Cox model for instance. The statistical test is a Student t test for dependent samples. The two hazard ratios must be computed from the same survival data.

### Usage

1 | ```
hr.comp2(x1, beta1, se1, x2, beta2, se2, n)
``` |

### Arguments

`x1` |
risk score used to estimate the first hazard ratio. |

`beta1` |
beta estimate for the first hazard ratio. |

`se1` |
standard error of beta estimate for the first hazard ratio. |

`x2` |
risk score used to estimate the second hazard ratio. |

`beta2` |
beta estimate for the second hazard ratio. |

`se2` |
standard error of beta estimate for the first hazard ratio. |

`n` |
number of samples from which the hazard ratios were estimated. |

### Details

The two hazard ratios must be computed from the same samples (and corresponding survival data). The function uses a Student t test for dependent samples.

### Value

`p.value ` |
p-value from the Student t test for the comparison beta1 > beta2 (equivalently hr1 > hr2) |

`hr1 ` |
value of the first hazard ratio |

`hr2 ` |
value of the second hazard ratio |

### Author(s)

Benjamin Haibe-Kains

### References

Student 1908) "The Probable Error of a Mean", *Biometrika*, **6**, 1, pages 1–25.

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

`coxph`

, `t.test`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 | ```
require(survival)
set.seed(12345)
age <- as.numeric(rnorm(100, 50, 10) >= 50)
size <- as.numeric(rexp(100,1) > 1)
stime <- rexp(100)
cens <- runif(100,.5,2)
sevent <- as.numeric(stime <= cens)
stime <- pmin(stime, cens)
coxm1 <- coxph(Surv(stime, sevent) ~ age)
coxm2 <- coxph(Surv(stime, sevent) ~ size)
hr.comp2(x1=age, beta1=coxm1$coefficients, se1=drop(sqrt(coxm1$var)),
x2=size, beta2=coxm2$coefficients, se2=drop(sqrt(coxm2$var)), n=100)
``` |