### Abstract

We propose two test statistics based on the covariance process of the martingale residuals for testing independence of bivariate survival data. The first test statistic takes the supremum over time of the absolute value of the covariance process, and the second test statistic is a time-weighted summary of the process. We derive asymptotic properties of the two test statistics under the null hypothesis of independence. In addition, we derive the asymptotic distribution of the weighted test and construct optimal weights for contiguous alternatives to independence. Through simulations, we compare the performance of the proposed tests and the inner product of the Savage scores statistics of Clayton and Cuzick (1985, Journal of the Royal Statistical Society, Series A 148, 82 108). These demonstrate that the supremum test is generally more powerful with comparatively little power loss relative to their test when Clayton's family alternative holds, and the weighted test is more powerful when the weight is appropriately chosen.

Original language | English (US) |
---|---|

Pages (from-to) | 1440-1449 |

Number of pages | 10 |

Journal | Biometrics |

Volume | 52 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1996 |

Externally published | Yes |

### Fingerprint

### Keywords

- Bivariate failure times
- Covariance
- Cross ratio
- Martingale residuals

### ASJC Scopus subject areas

- Agricultural and Biological Sciences(all)
- Public Health, Environmental and Occupational Health
- Agricultural and Biological Sciences (miscellaneous)
- Applied Mathematics
- Statistics and Probability

### Cite this

*Biometrics*,

*52*(4), 1440-1449. https://doi.org/10.2307/2532857

**Tests of independence for bivariate survival data.** / Shih, Joanna H.; Louis, Thomas.

Research output: Contribution to journal › Article

*Biometrics*, vol. 52, no. 4, pp. 1440-1449. https://doi.org/10.2307/2532857

}

TY - JOUR

T1 - Tests of independence for bivariate survival data

AU - Shih, Joanna H.

AU - Louis, Thomas

PY - 1996/12

Y1 - 1996/12

N2 - We propose two test statistics based on the covariance process of the martingale residuals for testing independence of bivariate survival data. The first test statistic takes the supremum over time of the absolute value of the covariance process, and the second test statistic is a time-weighted summary of the process. We derive asymptotic properties of the two test statistics under the null hypothesis of independence. In addition, we derive the asymptotic distribution of the weighted test and construct optimal weights for contiguous alternatives to independence. Through simulations, we compare the performance of the proposed tests and the inner product of the Savage scores statistics of Clayton and Cuzick (1985, Journal of the Royal Statistical Society, Series A 148, 82 108). These demonstrate that the supremum test is generally more powerful with comparatively little power loss relative to their test when Clayton's family alternative holds, and the weighted test is more powerful when the weight is appropriately chosen.

AB - We propose two test statistics based on the covariance process of the martingale residuals for testing independence of bivariate survival data. The first test statistic takes the supremum over time of the absolute value of the covariance process, and the second test statistic is a time-weighted summary of the process. We derive asymptotic properties of the two test statistics under the null hypothesis of independence. In addition, we derive the asymptotic distribution of the weighted test and construct optimal weights for contiguous alternatives to independence. Through simulations, we compare the performance of the proposed tests and the inner product of the Savage scores statistics of Clayton and Cuzick (1985, Journal of the Royal Statistical Society, Series A 148, 82 108). These demonstrate that the supremum test is generally more powerful with comparatively little power loss relative to their test when Clayton's family alternative holds, and the weighted test is more powerful when the weight is appropriately chosen.

KW - Bivariate failure times

KW - Covariance

KW - Cross ratio

KW - Martingale residuals

UR - http://www.scopus.com/inward/record.url?scp=0030472598&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030472598&partnerID=8YFLogxK

U2 - 10.2307/2532857

DO - 10.2307/2532857

M3 - Article

VL - 52

SP - 1440

EP - 1449

JO - Biometrics

JF - Biometrics

SN - 0006-341X

IS - 4

ER -