| 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)