# Student: Student's t test In blindrecalc: Blinded Sample Size Recalculation

## 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 Δ = μE - μC is

H0: Δ ≤ -δNI vs. H1: Δ > -δNI.

Here, δNI ≥ 0 denotes the non-inferiority margin. For superiority trials, δNI 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

 ``` 1 2 3 4 5 6 7 8 9 10``` ```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 (`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 variance σ2. Within the blinded sample size recalculation procedure, it is re-estimated by the one-sample variance estimator that is defined by

σ2est := 1/(n1-1) ∑j=T,Ck=1,...,n1,j (xj,k - x)2,

where xj,k is the outcome of patient k in group j, n1,j denotes the first-stage sample size in group j and x equals the mean over all n1 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

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

### Example output

```
```

blindrecalc documentation built on July 6, 2021, 5:06 p.m.