Description Usage Arguments Details Value Author(s) References See Also

The function `covariance`

calculates the covariance between two survival probabilty
obtained with a Cox proportional hazard model. Follow-up times and covariates
may differ for the two survival probabilties. This is mostly an internal function, meant to be used by the function `var.expDeath`

.

1 | ```
covariance(t_i, delta_i, beta, time1, z1, time2, z2, S0_i, S1_i, S02_i, Omega_1)
``` |

`t_i` |
All the follow up times. |

`delta_i` |
Indicator that the individual was censored: 1 if the individual was censored, 0 otherwise. |

`beta` |
The coefficients of the Cox model. |

`time1` |
First survival time. |

`z1` |
Covariates for first survival. |

`time2` |
Second survival time. |

`z2` |
Covariates for second survival. |

`S0_i` |
Object described in Lin, Flemming and Wei (1994), slightly modified for computationnal efficiency. It is obtained with |

`S1_i` |
Object described in Lin et al. (1994), slightly modified for computationnal efficiency. It is obtained with |

`S02_i` |
Object described in Lin et al. (1994), slightly modified for computationnal efficiency. It is obtained with |

`Omega_1` |
Inverse of the asymptotic variance-covariance matrix of the estimated parameters of the Cox model. It is obtained with |

This function was built to be an internal function, only used by the function `var.expDeath`

.

The covariance between the two estimated survival probability.

Denis Talbot, Thierry Duchesne, Jacques Brisson, Nathalie Vandal.

Lin D.Y., Fleming T.R., Wei L.J. (1994) *Confidence bands for survival curves under the proportional hazards model*, Biometrika, 81 (1): 73-81.

Talbot, D., Duchesne, T., Brisson, J., Vandal, N. (2011) *Variance estimation and confidence intervals for the standardized mortality ratio with application to the assessment of a cancer screening program*, Statistics in Medicine, 30, 3024-3037.

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