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

Computes the Proportional Allocation 2 procedure's power to detect the overall A effect or the simple AB effect, respectively.

1 | ```
powerPA2(n, hrA, hrB, hrAB, avgprob, probAB_C, critPA2A, critPA2ab, dig)
``` |

`n` |
total subjects with n/4 subjects in each of the C, A, B, and AB groups |

`hrA` |
group A to group C hazard ratio; |

`hrB` |
group B to group C hazard ratio; |

`hrAB` |
group AB to group C hazard ratio; |

`avgprob` |
event probability averaged across the C, A, B, and AB groups |

`probAB_C` |
event probability averaged across the AB and C groups |

`critPA2A` |
rejection critical value for the overall A stratified logrank statistic |

`critPA2ab` |
rejection critical value for the simple AB ordinary logrank statistic |

`dig` |
number of decimal places to which we |

The Proportional Allocation 2 procedure uses a two-sided
2/3 * alpha significance level to test the overall A effect and the
remaining Dunnett-corrected type 1 error to thest the simple AB effect.
When the familywise error is alpha = 0.05, this corresponds to a
critical value `critPA2A`

= -2.13.
Then `crit2x2`

is used to compute a critical value
`critPA2ab`

= -2.24 to test the simple AB effect. This corresponds to
a two-sided 0.0251 significance level. This controls the
asymptotic familywise type I error for the two hypothesis tests at the
two-sided 0.05 level. This is because of the `1/sqrt(2)`

asymptotic
correlation between the logrank test statistics for the overall A
and simple AB effects (Slud, 1994). The overall A effect's significance
level 2/3 * 0.05 is prespecified and the simple AB effect's significance
level 0.0251 is computed using `crit2x2`

.

`powerPA2overallA ` |
power to detect the overall A effect |

`powerPA2simpleAB ` |
power to detect the simple AB effect |

Eric Leifer, James Troendle

Leifer, E.S., Troendle, J.F., Kolecki, A., Follmann, D. Joint testing of overall and simple effect for the two-by-two factorial design. (2020). Submitted.

Lin, D-Y., Gong, J., Gallo, P., et al. Simultaneous inference on treatment effects in survival studies with factorial designs. Biometrics. 2016; 72: 1078-1085.

Slud, E.V. Analysis of factorial survival experiments. Biometrics. 1994; 50: 25-38.

`crit2x2`

, `eventProb`

, `lgrkPower`

, `strLgrkPower`

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 | ```
# Corresponds to scenario 4 in Table 2 from Leifer, Troendle, et al. (2020).
rateC <- 0.0445 # one-year C group event rate
hrA <- 0.80
hrB <- 0.80
hrAB <- 0.72
mincens <- 4.0
maxcens <- 8.4
evtprob <- eventProb(rateC, hrA, hrB, hrAB, mincens, maxcens)
avgprob <- evtprob$avgprob
probAB_C <- evtprob$probAB_C
dig <- 2
alpha <- 0.05
corAa <- 1/sqrt(2)
corAab <- 1/sqrt(2)
coraab <- 1/2
critvals <- crit2x2(corAa, corAab, coraab, dig, alpha)
critPA2A <- critvals$critPA2A
critPA2ab <- critvals$critPA2ab
n <- 4600
powerPA2(n, hrA, hrB, hrAB, avgprob, probAB_C,
critPA2A, critPA2ab, dig)
# $powerPA2overallA
# [1] 0.6582819
# $powerPA2simpleAB
# [1] 0.9197286
``` |

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