Student-class {blindrecalc} | R Documentation |

## Student's t test

### Description

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 `\Delta = \mu_E - \mu_C`

is

`H_0: \Delta \leq -\delta_{NI} \textrm{ vs. } H_1: \Delta > -\delta_{NI}.`

Here, `\delta_{NI} \geq 0`

denotes the non-inferiority margin.
For superiority trials,`\delta_{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.

### Usage

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

`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. |

### Details

The nuisance parameter is the variance `\sigma^2`

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

```
\widehat{\sigma}^2
:= \frac{1}{n_1-1} \sum_{j \in \{T, C \}}
\sum_{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.

### Value

An object of class `Student`

.

### References

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

### Examples

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

*blindrecalc*version 1.0.1 Index]