ChiSquare-class | R Documentation |

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`

.

```
setupChiSquare(
alpha,
beta,
r = 1,
delta,
alternative = c("greater", "smaller"),
n_max = Inf,
...
)
```

`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. |

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`

.

An object of class `ChiSquare`

.

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.

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

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