Student-class | R Documentation |

This class implements Student's t-test for superiority and non-inferiority
tests.
A trial with continuous outcomes of the two groups `E`

and `C`

is assumed.
If `alternative == "greater"`

the null hypothesis for the
mean difference *Δ = μ_E - μ_C* is

*H_0: Δ ≤q -δ_{NI} \textrm{ vs. } H_1: Δ > -δ_{NI}.*

Here, *δ_{NI} ≥q 0* denotes the non-inferiority margin.
For superiority trials,*δ_{NI}* can be set to zero (default).
If `alternative=="smaller"`

, the direction of the effect is changed.

The function `setupStudent`

creates an object of class
`Student`

that can be used for sample size recalculation.

setupStudent( alpha, beta, r = 1, delta, delta_NI = 0, 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. |

`delta_NI` |
Non-inferiority margin. |

`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 variance *σ^2*.
Within the blinded sample size recalculation procedure, it is re-estimated by
the one-sample variance estimator that is defined by

*\widehat{σ}^2
:= \frac{1}{n_1-1} ∑_{j \in \{T, C \}}
∑_{k=1}^{n_{1,j}}(x_{j,k} - \bar{x} )^2,*

where *x_{j,k}* is the outcome of patient *k* in group *j*,
*n_{1,j}* denotes the first-stage sample size in group *j* and
*\bar{x}* equals the mean over all *n_1* observations.
The following methods are available for this class:
`toer`

, `pow`

, `n_dist`

,
`adjusted_alpha`

, and `n_fix`

.
Check the design specific documentation for details.

An object of class `Student`

.

Lu, K. (2019). Distribution of the two-sample t-test statistic following blinded sample size re-estimation. Pharmaceutical Statistics 15(3): 208-215.

d <- setupStudent(alpha = .025, beta = .2, r = 1, delta = 3.5, delta_NI = 0, alternative = "greater", n_max = 156)

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