Student-class: 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,
  ...
)

Value

An object of class Student.

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 $\sigma^2$. 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.

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

Run this code

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

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