ChiSquare-class: 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,
  ...
)

Value

An object of class ChiSquare.

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.

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

Run this code

design <- setupChiSquare(alpha = .025, beta = .2, r = 1, delta = 0.2,
alternative = "greater")

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