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

This is a utility function to calculate the overall variance accouting for staggered entry, delayed treatment effect, treatment crossover and loss to follow-up.

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`tfix` |
The upper point where the integral is computed. |

`t` |
A vector of lower bounds where the integral is computed. |

`taur` |
Recruitment time |

`u` |
Piecewise constant recuitment rate |

`ut` |
Recruitment intervals |

`rate1` |
Hazard before crossover |

`rate2` |
Hazard after crossover |

`rate3` |
Hazard for time to crossover |

`rate4` |
Hazard after crossover for complex case |

`rate5` |
Hazard after crossover for complex case |

`ratec` |
Hazard for time to censoring |

`tchange` |
A strictly increasing sequence of time points at which the event rates changes. The first element of tchange must be zero. It must have the same length as |

`type` |
Type of crossover |

`rp2` |
re-randomization prob |

`eps` |
A small number representing the error tolerance when calculating the utility function
with |

This is to calculate the function

*B_l(t,s)=\int_0^s x^l G_E(t-x)\widetilde{f}(x)S_C(x)dx,*

where *G_E* is the accrual function defined by `taur`

, `u`

and `ut`

, *S_C* is the piecewise exponential survival function of the censoring time, defined by `tchange`

and `ratec`

, and *\widetilde{f}* is the density for the event distribution subject to crossover defined by `tchange`

, `rate1`

to `rate5`

and `type`

. This function is useful when calculating the overall varaince and covariance.

`f0` |
the integral when |

`f1` |
the integral when |

Version 1.0 (7/19/2016)

Xiaodong Luo

Luo, et al. (2017)

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