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

View source: R/powerNbinomTest.R

Compute sample size or power for comparing two negative binomial rates.

1 2 3 | ```
power.nb.test(n = NULL, mu0, mu1, RR, duration = 1, theta, ssize.ratio = 1,
sig.level = 0.05, power = NULL, alternative = c("two.sided", "one.sided"),
approach = 3)
``` |

`n` |
Sample size for group 0 (control group). |

`mu0` |
expected rate of events per time unit for group 0 |

`mu1` |
expected rate of events per time unit for group 1 |

`RR` |
ratio of expected event rates: mu1/mu0 |

`duration` |
(average) treatment duration |

`theta` |
theta parameter of negative binomial distribution; see |

`ssize.ratio` |
ratio of sample sizes: n/n1 where n1 is sample size of group 1 |

`sig.level` |
Significance level (Type I error probability) |

`power` |
Power of test (1 minus Type II error probability) |

`alternative` |
one- or two-sided test |

`approach` |
1, 2, or 3; see Zhu and Lakkis (2014). |

Exactly one of the parameters `n`

and `power`

must be passed as
`NULL`

, and that parameter is determined from the other.

The computations are based on the formulas given in Zhu and Lakkis (2014).
Please be careful, as we are using a slightly different parametrization
(`theta`

= 1/k).

Zhu and Lakkis (2014) based on their simulation studies recommend to use their approach 2 or 3.

Object of class `"power.htest"`

, a list of the arguments
(including the computed one) augmented with a `note`

element.

Matthias Kohl [email protected]

H. Zhu and H. Lakkis (2014). Sample size calculation for comparing two negative
binomial rates. *Statistics in Medicine*, **33**:376-387.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 | ```
## examples from Table I in Zhu and Lakkis (2014)
## theta = 1/k, RR = rr, mu0 = r0, duration = mu_t
power.nb.test(mu0 = 0.8, RR = 0.85, theta = 1/0.4, duration = 0.75, power = 0.8, approach = 1)
power.nb.test(mu0 = 0.8, RR = 0.85, theta = 1/0.4, duration = 0.75, power = 0.8, approach = 2)
power.nb.test(mu0 = 0.8, RR = 0.85, theta = 1/0.4, duration = 0.75, power = 0.8, approach = 3)
power.nb.test(mu0 = 1.4, RR = 1.15, theta = 1/1.5, duration = 0.75, power = 0.8, approach = 1)
power.nb.test(mu0 = 1.4, RR = 1.15, theta = 1/1.5, duration = 0.75, power = 0.8, approach = 2)
power.nb.test(mu0 = 1.4, RR = 1.15, theta = 1/1.5, duration = 0.75, power = 0.8, approach = 3)
## examples from Table II in Zhu and Lakkis (2014) - seem to be total sample sizes
## can reproduce the results with mu_t = 1.0 (not 0.7!)
power.nb.test(mu0 = 2.0, RR = 0.5, theta = 1, duration = 1.0, ssize.ratio = 1,
power = 0.8, approach = 1)
power.nb.test(mu0 = 2.0, RR = 0.5, theta = 1, duration = 1.0, ssize.ratio = 1,
power = 0.8, approach = 2)
power.nb.test(mu0 = 2.0, RR = 0.5, theta = 1, duration = 1.0, ssize.ratio = 1,
power = 0.8, approach = 3)
power.nb.test(mu0 = 10.0, RR = 1.5, theta = 1/5, duration = 1.0, ssize.ratio = 3/2,
power = 0.8, approach = 1)
power.nb.test(mu0 = 10.0, RR = 1.5, theta = 1/5, duration = 1.0, ssize.ratio = 3/2,
power = 0.8, approach = 2)
power.nb.test(mu0 = 10.0, RR = 1.5, theta = 1/5, duration = 1.0, ssize.ratio = 3/2,
power = 0.8, approach = 3)
## examples from Table III in Zhu and Lakkis (2014)
power.nb.test(mu0 = 5.0, RR = 2.0, theta = 1/0.5, duration = 1, power = 0.8, approach = 1)
power.nb.test(mu0 = 5.0, RR = 2.0, theta = 1/0.5, duration = 1, power = 0.8, approach = 2)
power.nb.test(mu0 = 5.0, RR = 2.0, theta = 1/0.5, duration = 1, power = 0.8, approach = 3)
## examples from Table IV in Zhu and Lakkis (2014)
power.nb.test(mu0 = 5.9/3, RR = 0.4, theta = 0.49, duration = 3, power = 0.9, approach = 1)
power.nb.test(mu0 = 5.9/3, RR = 0.4, theta = 0.49, duration = 3, power = 0.9, approach = 2)
power.nb.test(mu0 = 5.9/3, RR = 0.4, theta = 0.49, duration = 3, power = 0.9, approach = 3)
power.nb.test(mu0 = 13/6, RR = 0.2, theta = 0.52, duration = 6, power = 0.9, approach = 1)
power.nb.test(mu0 = 13/6, RR = 0.2, theta = 0.52, duration = 6, power = 0.9, approach = 2)
power.nb.test(mu0 = 13/6, RR = 0.2, theta = 0.52, duration = 6, power = 0.9, approach = 3)
## see Section 5 of Zhu and Lakkis (2014)
power.nb.test(mu0 = 0.66, RR = 0.8, theta = 1/0.8, duration = 0.9, power = 0.9)
``` |

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