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 (greater) or smaller (smaller) values than the null hypothesis. n_max Maximal overall sample size. If the recalculated sample size is greater than n_max it is set to n_max. ... 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")



[Package blindrecalc version 1.0.1 Index]