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

 Student-class 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 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.

### 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 (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 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.

### 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 documentation built on Nov. 18, 2022, 5:06 p.m.