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

A variable margin difference in proportion test for non-inferiority. The test is based on Barnard's test.

1 | ```
brkTest(x1, n1, x2, n2, threshold = 0.2, delta = 0.1, control = brkControl())
``` |

`x1` |
number of events in the control group |

`n1` |
number of individuals in the control group |

`x2` |
number of events in the test group |

`n2` |
number of events in the test group |

`threshold` |
proportion in the control group associated with the threshold, above that threshold use a constant difference margin, below the threshold use a difference margin with a constant odds ratio. We use only continuous variable margins that meet at the threshold. |

`delta` |
difference in proportions at the threshold |

`control` |
list of parameters for algorithm control, see |

This test is labeled T4 in Rohmel and Keiser (2013).

a list of class `brk`

, with elements:

`statistic` |
the threshold, delta (difference margin at threshold), and odds ratio at threshold |

`data.name` |
gives x1,x2,n1,n2 as a character string |

`method` |
description of test |

`p.value` |
one-sided p-value |

`FullResults` |
a list with 4 matrices, each n1+1 by n2+1 representing the total sample space. R=a matrix with logical values with TRUE elements representing the rejection region, its 'sig.level' attribute gives the significance level of the test; PVALbounds=a matrix of p-value bounds, pb; PVALsymbols=a matrix of symbols that describe the pb, '<=' means 'p<=pb', '=' means 'p=pb' and '>' means 'p>pb'; PVALUES=a matrix giving the p-value expression, e.g., 'p<=.00321' or 'p>0.025'. |

Michael P. Fay

Rohmel, J, and Kieser, M (2013). "Investigations on non-inferiority - - the Food and Drug Administration draft guidance on treatments for nosocomial pneumonia as a case for exact tests for binomial proportions" Statistics in Medicine 32:2335-2348.

See Also `nicqTest`

, ~~~

1 2 3 | ```
x<-brkTest(3,8,0,6)
x
x$FullResults$PVALUES
``` |

```
Loading required package: bpcp
Loading required package: ssanv
Barnard-Rohmel-Kieser Test
data: x1=3 n1=8 x2=0 n2=6
threshold = 0.2000, difference = 0.1000, odds ratio = 1.7143
One-sided p-value:
p>0.025
Note: to save computational time, only bound on p-value calculated.
For rejection region and p-values for any possible
result with these sample sizes, save output as x,
and see the list x$FullResults
x2=0 x2=1 x2=2 x2=3 x2=4
x1=0 "p>0.025" "p>0.025" "p>0.025" "p>0.025" "p>0.025"
x1=1 "p>0.025" "p>0.025" "p>0.025" "p>0.025" "p>0.025"
x1=2 "p>0.025" "p>0.025" "p>0.025" "p>0.025" "p>0.025"
x1=3 "p>0.025" "p>0.025" "p>0.025" "p>0.025" "p>0.025"
x1=4 "p=0.011699" "p>0.025" "p>0.025" "p>0.025" "p>0.025"
x1=5 "p=0.003668" "p>0.025" "p>0.025" "p>0.025" "p>0.025"
x1=6 "p=0.000852" "p=0.008467" "p>0.025" "p>0.025" "p>0.025"
x1=7 "p<=0.000293" "p=0.002501" "p=0.013915" "p>0.025" "p>0.025"
x1=8 "p<=0.000293" "p<=0.000293" "p=0.001404" "p=0.006229" "p=0.024348"
x2=5 x2=6
x1=0 "p>0.025" "p>0.025"
x1=1 "p>0.025" "p>0.025"
x1=2 "p>0.025" "p>0.025"
x1=3 "p>0.025" "p>0.025"
x1=4 "p>0.025" "p>0.025"
x1=5 "p>0.025" "p>0.025"
x1=6 "p>0.025" "p>0.025"
x1=7 "p>0.025" "p>0.025"
x1=8 "p>0.025" "p>0.025"
```

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