FarringtonManning: Farrington Manning test

FarringtonManning-classR Documentation

Farrington Manning test


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.


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



One-sided type I error rate.


Type II error rate.


Allocation ratio between experimental and control group.


Difference of effect size between alternative and null hypothesis.


Non-inferiority margin.


Maximal overall sample size. If the recalculated sample size is greater than n_max it is set to n_max.


Further optional arguments.


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.


An object of class FarringtonManning.


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.


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

blindrecalc documentation built on Oct. 4, 2023, 5:06 p.m.