| 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)