| ChiSquare-class {blindrecalc} | R Documentation |
Chi-squared test
Description
This class implements a chi-squared test for superiority trials. A trial
with binary outcomes in two groups E and C is assumed. If
alternative == "greater" the null and alternative hypotheses for the
difference in response probabilities are
H_0: p_E \leq p_C \textrm{ vs. } H_1: p_E > p_C.
If alternative == "smaller", the direction of the effect is changed.
The function setupChiSquare creates an object of class
ChiSquare.
Usage
setupChiSquare(
alpha,
beta,
r = 1,
delta,
alternative = c("greater", "smaller"),
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. |
alternative |
Does the alternative hypothesis contain greater
( |
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.
The following methods are available for this class:
toer, pow, n_dist,
adjusted_alpha, and n_fix.
Check the design specific documentation for details.
For non-inferiority trials use the function setupFarringtonManning.
Value
An object of class ChiSquare.
References
Friede, T., & Kieser, M. (2004). Sample size recalculation for binary data
in internal pilot study designs. Pharmaceutical Statistics:
The Journal of Applied Statistics in the Pharmaceutical Industry,
3(4), 269-279.
Kieser, M. (2020). Methods and applications of sample size calculation and
recalculation in clinical trials. Springer.
Examples
design <- setupChiSquare(alpha = .025, beta = .2, r = 1, delta = 0.2,
alternative = "greater")