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

This will calculate the functions according to the piecewise exponential distribution with crossover

1 2 3 |

`t` |
a vector of time points |

`rate1` |
piecewise constant event rate before crossover |

`rate2` |
piecewise constant event rate after crossover |

`rate3` |
piecewise constant event rate for crossover |

`rate4` |
additional piecewise constant event rate for more complex crossover |

`rate5` |
additional piecewise constant event rate for more complex crossover |

`ratec` |
censoring piecewise constant event rate |

`tchange` |
a strictly increasing sequence of time points starting from zero at which event rate changes. The first element of tchange must be zero. The above rates |

`type` |
type of crossover, i.e. markov, semi-markov and hybrid |

`rp2` |
re-randomization prob |

`eps` |
tolerance |

This is to calculate the function (and its derivative)

*ΞΎ(t)=\int_0^t \widetilde{f}(s)S_C(s)ds,*

where *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`

.

`du` |
the function |

`duprime` |
its derivative |

`s` |
the survival function of |

`sc` |
the survival function |

Xiaodong Luo

Luo, et al. (2017)

1 2 3 4 5 6 7 8 9 10 |

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