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

Rohmel and Keier (2013) developed these non-inferioirty tests with variable margins. One margin function, NiM3, has the variable margin measuring a constant difference in proportions (0.10 in paper) after a threshold (0.20 proportion in the control group), or tests for differences defined in terms of a constant odds ratio (1.71 in paper) at values less than the threshold. The `fmecTest`

with type='max' gives the maximum of two p-values, either a difference in proportions test (one-sided asymptotic method of Farrington and Manning, 1990) or an odds ratio test (one-sided Fisher's exact). This test is NiM3/T2 in Rohmel and Keier (2013). We also provide an exact version of this test with `fmecExact`

, denoted NiM3/T3 in Rohmel and Keier (2013). When type='switch' the tests are like T1 of Rohmel and Keier (2013).

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`x1` |
number of failures in control group |

`n1` |
number of individuals in control group |

`x2` |
number of failures in test group |

`n2` |
number of individuals in test group |

`threshold` |
threshold on proportion in control group: above it use constant difference margin, below it use difference margin with constant odds ratio |

`delta` |
difference margin at threshold |

`alternative` |
must be 'less'. the value 'greater' is not supported at this time. |

`type` |
either 'max' (maximum of Fisher's exact p-value or Farrington and Manning p-value) or 'switch' (Fisher's exact p-value below threhold and Farington and Manning p-value above threhold). |

`ngrid` |
grid size for the search for the maximum p-value. Search over the control proportion values 0:ngrid/ngrid. |

For details see Rohmel and Keier (2013, Section 3). These functions only use NiM3.

a list of class 'htest':

`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 |

`null.value` |
delta, the difference margin at threshold |

`alternative` |
direction of alternative hypothesis |

Michael P. Fay

Farrington, CP and Manning G (1990). "Test statistics and sample size formulae for comparative binomial trials with null hypothesis of non-zero risk difference or non-unit relative risk" Statistics in Medicine 9:1447-1454.

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.

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```
Loading required package: bpcp
Loading required package: ssanv
Odds Ratio/Difference Test type=max
data: x1=6 n1=10 x2=2 n2=12
threshold = 0.2000, difference = 0.1000, odds ratio = 1.7143, p-value =
0.01064
alternative hypothesis: true difference in proportions is less than 0.1
Exact Odds Ratio/Difference Test type=max
data: x1=6 n1=10 x2=2 n2=12
threshold = 0.2000, difference = 0.1000, odds ratio = 1.7143, p-value =
0.008839
alternative hypothesis: true difference in proportions is less than 0.1
```

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