FarringtonManning-class {blindrecalc} | R Documentation |

## Farrington Manning test

### Description

This class implements a Farrington-Manning test for non-inferiority
trials. A trial with binary outcomes in two groups `E`

and
`C`

is assumed. The null and alternative hypotheses for the
non-inferiority of response probabilities are:

`H_0: p_E - p_C \leq -\delta \textrm{ vs. } H_1: p_E - p_C > -\delta,`

where `\delta`

denotes the non-inferiority margin.

The function `setupFarringtonManning`

creates an object of
`FarringtonManning`

.

### Usage

```
setupFarringtonManning(alpha, beta, r = 1, delta, delta_NI, n_max = Inf, ...)
```

### Arguments

`alpha` |
One-sided type I error rate. |

`beta` |
Type II error rate. |

`r` |
Allocation ratio between experimental and control group. |

`delta` |
Difference of effect size between alternative and null hypothesis. |

`delta_NI` |
Non-inferiority margin. |

`n_max` |
Maximal overall sample size. If the recalculated sample size
is greater than |

`...` |
Further optional arguments. |

### Details

The nuisance parameter is the overall response probability `p_0`

.
In the blinded sample size recalculation procedure it is blindly estimated
by:

`\hat{p}_0 := (X_{1,E} + X_{1,C}) / (n_{1,E} + n_{1,C}),`

where
`X_{1,E}`

and `X_{1,C}`

are the numbers of responses and `n_{1,E}`

and `n_{1,C}`

are the sample sizes of the respective group after the first stage.
The event rates in both groups under the alternative hypothesis can then be
blindly estimated as:

```
\hat{p}_{C,A} := \hat{p}_0 - \Delta \cdot r / (1 + r) \textrm{, }
\hat{p}_{E,A} := \hat{p}_0 + \Delta / (1 + r),
```

where `\Delta`

is the difference in
response probabilities under the alternative hypothesis and r is the
allocation ratio of the sample sizes in the two groups.
These blinded estimates can then be used to re-estimate the sample
size.

### Value

An object of class `FarringtonManning`

.

### References

Friede, T., Mitchell, C., & Mueller-Velten, G. (2007). Blinded sample size
reestimation in non-inferiority trials with binary endpoints.
Biometrical Journal, 49(6), 903-916.

Kieser, M. (2020). Methods and applications of sample size calculation and
recalculation in clinical trials. Springer.

### Examples

```
design <- setupFarringtonManning(alpha = .025, beta = .2, r = 1, delta = 0,
delta_NI = .15)
```

*blindrecalc*version 1.0.1 Index]