Type:	Package
Title:	Blinded Sample Size Recalculation
Version:	1.1.0
Description:	Computation of key characteristics and plots for blinded sample size recalculation. Continuous as well as binary endpoints are supported in superiority and non-inferiority trials. See Baumann, Pilz, Kieser (2022) <doi:10.32614/RJ-2022-001> for a detailed description. The implemented methods include the approaches by Lu, K. (2019) <doi:10.1002/pst.1737>, Kieser, M. and Friede, T. (2000) <doi:10.1002/(SICI)1097-0258(20000415)19:7%3C901::AID-SIM405%3E3.0.CO;2-L>, Friede, T. and Kieser, M. (2004) <doi:10.1002/pst.140>, Friede, T., Mitchell, C., Mueller-Veltern, G. (2007) <doi:10.1002/bimj.200610373>, and Friede, T. and Kieser, M. (2011) <doi:10.3414/ME09-01-0063>.
License:	MIT + file LICENSE
URL:	https://github.com/imbi-heidelberg/blindrecalc
Encoding:	UTF-8
Suggests:	testthat, covr, knitr, rmarkdown, bookdown
Imports:	methods, Rcpp
Collate:	test_statistics.R methods.R Student.R blindrecalc.R ChiSquare.R ChiSquare_helper.R FarringtonManning.R FarringtonManning_helper.R RcppExports.R
RoxygenNote:	7.3.2
LinkingTo:	Rcpp
VignetteBuilder:	knitr
NeedsCompilation:	yes
Packaged:	2025-06-17 07:44:52 UTC; uy240
Author:	Lukas Baumann [aut, cre], Maximilian Pilz [aut], Institute of Medical Biometry - University of Heidelberg [cph]
Maintainer:	Lukas Baumann <baumann@imbi.uni-heidelberg.de>
Repository:	CRAN
Date/Publication:	2025-06-17 08:00:02 UTC

Blinded Sample Size Recalculation

Description

The package blindrecalc provides characteristics and plots of trial designs with blinded sample size recalculation where a nuisance parameter is estimated at an blinded interim analysis.

Details

Currently, for continuous outcomes, a t-test is implemented for superiority and non-inferiority trials. For superiority trials with binary endpoint, the chi^2-test is implemented. The Farrington Manning test covers non-inferiority trials with binary endpoint.

Author(s)

Maintainer: Lukas Baumann baumann@imbi.uni-heidelberg.de (ORCID)

Authors:

• Maximilian Pilz maximilian.pilz@itwm.fraunhofer.de (ORCID)

Other contributors:

• Institute of Medical Biometry - University of Heidelberg [copyright holder]

See Also

Useful links:

• https://github.com/imbi-heidelberg/blindrecalc

Chi-squared test

Description

This class implements a chi-squared test for superiority trials. A trial with binary outcomes in two groups E and C is assumed. If alternative == "greater" the null and alternative hypotheses for the difference in response probabilities are

H_0: p_E \leq p_C \textrm{ vs. } H_1: p_E > p_C.

If alternative == "smaller", the direction of the effect is changed.

The function setupChiSquare creates an object of class ChiSquare.

Usage

setupChiSquare(
  alpha,
  beta,
  r = 1,
  delta,
  alternative = c("greater", "smaller"),
  n_max = Inf,
  ...
)

Arguments

Details

The nuisance parameter is the overall response probability p_0. In the blinded sample size #' recalculation procedure it is blindly estimated by:

\hat{p}_0 := (X_{1,E} + X_{1,C}) / (n_{1,E} + n_{1,C}),

where X_{1,E} and X_{1,C} are the numbers of responses and n_{1,E} and n_{1,C} are the sample sizes of the respective group after the first stage. The event rates in both groups under the alternative hypothesis can then be blindly estimated as:

\hat{p}_{C,A} := \hat{p}_0 - \Delta \cdot r / (1 + r) \textrm{, } \hat{p}_{E,A} := \hat{p}_0 + \Delta / (1 + r),

where \Delta is the difference in response probabilities under the alternative hypothesis and r is the allocation ratio of the sample sizes in the two groups. These blinded estimates can then be used to re-estimate the sample size.

The following methods are available for this class: toer, pow, n_dist, adjusted_alpha, and n_fix. Check the design specific documentation for details.

For non-inferiority trials use the function setupFarringtonManning.

Value

An object of class ChiSquare.

References

Friede, T., & Kieser, M. (2004). Sample size recalculation for binary data in internal pilot study designs. Pharmaceutical Statistics: The Journal of Applied Statistics in the Pharmaceutical Industry, 3(4), 269-279.
Kieser, M. (2020). Methods and applications of sample size calculation and recalculation in clinical trials. Springer.

Examples

design <- setupChiSquare(alpha = .025, beta = .2, r = 1, delta = 0.2,
alternative = "greater")

Farrington Manning test

Description

This class implements a Farrington-Manning test for non-inferiority trials. A trial with binary outcomes in two groups E and C is assumed. The null and alternative hypotheses for the non-inferiority of response probabilities are:

H_0: p_E - p_C \leq -\delta \textrm{ vs. } H_1: p_E - p_C > -\delta,

where \delta denotes the non-inferiority margin.

The function setupFarringtonManning creates an object of FarringtonManning.

Usage

setupFarringtonManning(alpha, beta, r = 1, delta, delta_NI, n_max = Inf, ...)

Arguments

Details

The nuisance parameter is the overall response probability p_0. In the blinded sample size recalculation procedure it is blindly estimated by:

\hat{p}_0 := (X_{1,E} + X_{1,C}) / (n_{1,E} + n_{1,C}),

where X_{1,E} and X_{1,C} are the numbers of responses and n_{1,E} and n_{1,C} are the sample sizes of the respective group after the first stage. The event rates in both groups under the alternative hypothesis can then be blindly estimated as:

\hat{p}_{C,A} := \hat{p}_0 - \Delta \cdot r / (1 + r) \textrm{, } \hat{p}_{E,A} := \hat{p}_0 + \Delta / (1 + r),

where \Delta is the difference in response probabilities under the alternative hypothesis and r is the allocation ratio of the sample sizes in the two groups. These blinded estimates can then be used to re-estimate the sample size.

Value

An object of class FarringtonManning.

References

Friede, T., Mitchell, C., & Mueller-Velten, G. (2007). Blinded sample size reestimation in non-inferiority trials with binary endpoints. Biometrical Journal, 49(6), 903-916.
Kieser, M. (2020). Methods and applications of sample size calculation and recalculation in clinical trials. Springer.

Examples

design <- setupFarringtonManning(alpha = .025, beta = .2, r = 1, delta = 0,
delta_NI = .15)

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

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)

Adjusted level of significance

Description

This method returns an adjusted significance level that can be used such that the actual type I error rate is preserved.

Usage

adjusted_alpha(design, n1, nuisance, recalculation, ...)

Arguments

Details

The method is only vectorized in either nuisance or n1.

The method is implemented for the classes Student, ChiSquare, and FarringtonManning. Check the class-specific documentation for further parameters that have to be specified.

Value

Value of the adjusted significance level for every nuisance parameter and every value of n1.

Examples

d <- setupStudent(alpha = .025, beta = .2, r = 1, delta = 0, delta_NI = 1.5, n_max = 848)
sigma <- c(2, 5.5, 9)
adjusted_alpha(design = d, n1 = 20, nuisance = sigma, recalculation = TRUE,
               tol = 1e-4, iters = 1e3)

Adjusted level of significance

Description

This method returns an adjusted significance level that can be used such that the actual type I error rate is preserved.

Usage

## S4 method for signature 'ChiSquare'
adjusted_alpha(
  design,
  n1,
  nuisance,
  recalculation,
  nuis_ass,
  precision = 0.001,
  gamma = 0,
  allocation = c("exact", "approximate"),
  ...
)

Arguments

Details

The method is only vectorized in either nuisance or n1.

Value

Value of the adjusted significance level for every nuisance parameter and every value of n1.

Examples

  d <- setupChiSquare(alpha = 0.025, beta = 0.2, r = 1, delta = 0.2)
  adjusted_alpha(d, n1 = 10, nuisance = 0.3, gamma = 0.001,
     nuis_ass = 0.3, precision = 0.001, recalculation = TRUE)

Adjusted level of significance

Description

This method returns an adjusted significance level that can be used such that the actual type I error rate is preserved.

Usage

## S4 method for signature 'FarringtonManning'
adjusted_alpha(
  design,
  n1,
  nuisance,
  recalculation,
  nuis_ass,
  precision = 0.001,
  gamma = 0,
  allocation = c("exact", "approximate"),
  ...
)

Arguments

Details

The method is only vectorized in either nuisance or n1.

Value

Value of the adjusted significance level for every nuisance parameter and every value of n1.

Examples

d <- setupFarringtonManning(alpha = 0.025, beta = 0.2, r = 1,
                            delta = 0, delta_NI = 0.25)
adjusted_alpha(d, n1 = 20, nuisance = 0.5, recalculation = TRUE)

Adjusted level of significance

Description

This method returns an adjusted significance level that can be used such that the actual type I error rate is preserved.

Usage

## S4 method for signature 'Student'
adjusted_alpha(
  design,
  n1,
  nuisance,
  recalculation,
  tol,
  iters = 10000,
  seed = NULL,
  ...
)

Arguments

Details

The method is only vectorized in either nuisance or n1.

In the case of the Student's t-test, the adjusted alpha is calculated using the algorithm by Kieser and Friede (2000): "Re-calculating the sample size in internal pilot study designs with control of the type I error rate". Statistics in Medicine 19: 901-911.

Value

Value of the adjusted significance level for every nuisance parameter and every value of n1.

Examples

d <- setupStudent(alpha = .025, beta = .2, r = 1, delta = 0, delta_NI = 1.5,
                  n_max = 848)
sigma <- c(2, 5.5, 9)
adjusted_alpha(design = d, n1 = 20, nuisance = sigma, recalculation = TRUE,
               tol = 1e-4, iters = 1e3)

Distribution of the Sample Size

Description

Calculates the distribution of the total sample sizes of designs with blinded sample size recalculation for different values of the nuisance parameter or of n1.

Usage

n_dist(design, n1, nuisance, summary = TRUE, plot = FALSE, ...)

Arguments

Details

The method is only vectorized in either nuisance or n1.

The method is implemented for the classes Student, ChiSquare, and FarringtonManning.

Value

Summary and/or plot of the sample size distribution for every nuisance parameter and every value of n1.

Examples

d <- setupStudent(alpha = .025, beta = .2, r = 1, delta = 3.5, delta_NI = 0,
                  alternative = "greater", n_max = 156)
n_dist(d, n1 = 20, nuisance = 5.5, summary = TRUE, plot = FALSE, seed = 2020)

Distribution of the Sample Size

Description

Calculates the distribution of the total sample sizes of designs with blinded sample size recalculation for different values of the nuisance parameter or of n1.

Usage

## S4 method for signature 'ChiSquare'
n_dist(
  design,
  n1,
  nuisance,
  summary = TRUE,
  plot = FALSE,
  allocation = c("exact", "approximate"),
  ...
)

Arguments

Details

Only sample sizes that occur with a probability of at least 0.01 are considered.

The method is only vectorized in either nuisance or n1.

Value

Summary and/or plot of the sample size distribution for every nuisance parameter and every value of n1.

Examples

  d <- setupChiSquare(alpha = 0.025, beta = 0.2, r = 1, delta = 0.2)
  n_dist(d, n1 = 20, nuisance = 0.25, summary = TRUE, plot = FALSE)

Distribution of the Sample Size

Description

Calculates the distribution of the total sample sizes of designs with blinded sample size recalculation for different values of the nuisance parameter or of n1.

Usage

## S4 method for signature 'FarringtonManning'
n_dist(
  design,
  n1,
  nuisance,
  summary,
  plot,
  allocation = c("exact", "approximate"),
  ...
)

Arguments

Details

Only sample sizes that occur with a probability of at least 0.01 are considered.

The method is only vectorized in either nuisance or n1.

Value

Summary and/or plot of the sample size distribution for each nuisance parameter and every value of n1.

Examples

d <- setupFarringtonManning(alpha = 0.025, beta = 0.2, r = 1,
                            delta = 0, delta_NI = 0.25)
n_dist(d, n1 = 30, nuisance = 0.2, summary = TRUE, plot = FALSE)

Distribution of the Sample Size

Description

Calculates the distribution of the total sample sizes of designs with blinded sample size recalculation for different values of the nuisance parameter or of n1.

Usage

## S4 method for signature 'Student'
n_dist(
  design,
  n1,
  nuisance,
  summary = TRUE,
  plot = FALSE,
  iters = 10000,
  seed = NULL,
  range = 0,
  allocation = c("approximate", "exact"),
  ...
)

Arguments

Details

The method is only vectorized in either nuisance or n1.

Value

Summary and/or plot of the sample size distribution for every nuisance parameter and every value of n1.

Examples

d <- setupStudent(alpha = .025, beta = .2, r = 1, delta = 3.5, delta_NI = 0,
                  alternative = "greater", n_max = 156)
n_dist(d, n1 = 20, nuisance = 5.5, summary = TRUE, plot = FALSE, seed = 2020)

Fixed Sample Size

Description

Returns the total sample size of a fixed design without sample size recalculation.

Usage

n_fix(design, nuisance, ...)

Arguments

Details

The method is only vectorized in either nuisance or n1.

The method is implemented for the classes Student, ChiSquare, and FarringtonManning.

Value

One value of the fixed sample size for every nuisance parameter and every value of n1.

Examples

d <- setupStudent(alpha = .025, beta = .2, r = 1, delta = 3.5, delta_NI = 0,
                  alternative = "greater", n_max = 156)
n_fix(design = d, nuisance = 5.5)

Fixed Sample Size

Description

Returns the sample size of a fixed design without sample size recalculation.

Usage

## S4 method for signature 'ChiSquare'
n_fix(
  design,
  nuisance,
  variance = c("heterogeneous", "homogeneous"),
  rounded = TRUE,
  ...
)

Arguments

Details

The method is only vectorized in either nuisance or n1.

Value

One value of the fixed sample size for every nuisance parameter and every value of n1.

Examples

  design1 <- setupChiSquare(alpha = 0.025, beta = 0.2, r = 1, delta = 0.2)
  n_fix(design1, nuisance = c(0.2, 0.3))

Fixed Sample Size

Description

Returns the sample size of a fixed design without sample size recalculation.

Usage

## S4 method for signature 'FarringtonManning'
n_fix(design, nuisance, rounded = TRUE, ...)

Arguments

Details

The method is only vectorized in either nuisance or n1.

Value

One value of the fixed sample size for every nuisance parameter and every value of n1.

Examples

d <- setupFarringtonManning(alpha = 0.025, beta = 0.2, r = 1,
                            delta = 0, delta_NI = 0.25)
n_fix(d, nuisance = 0.3)

Fixed Sample Size

Description

Returns the sample size of a fixed design without sample size recalculation.

Usage

## S4 method for signature 'Student'
n_fix(design, nuisance, ...)

Arguments

Details

The method is only vectorized in either nuisance or n1.

Value

One value of the fixed sample size for every nuisance parameter and every value of n1.

Examples

d <- setupStudent(alpha = .025, beta = .2, r = 1, delta = 3.5, delta_NI = 0,
                  alternative = "greater", n_max = 156)
n_fix(design = d, nuisance = 5.5)

Power

Description

Calculates the power of designs with blinded sample size recalculation or of fixed designs for one or several values of the nuisance parameter.

Usage

pow(design, n1, nuisance, recalculation, ...)

Arguments

Details

The method is only vectorized in either nuisance or n1.

The method is implemented for the classes Student, ChiSquare, and FarringtonManning.

Value

One power value for every nuisance parameter and every value of n1.

Examples

d <- setupStudent(alpha = .025, beta = .2, r = 1, delta = 3.5, delta_NI = 0,
                  alternative = "greater", n_max = 156)
pow(d, n1 = 20, nuisance = 5.5, recalculation = TRUE)

Power

Description

Calculates the power of designs with blinded sample size recalculation or of fixed designs for one or several values of the nuisance parameter.

Usage

## S4 method for signature 'ChiSquare'
pow(
  design,
  n1,
  nuisance,
  recalculation,
  allocation = c("exact", "approximate", "kf_approx"),
  ...
)

Arguments

Details

The method is only vectorized in either nuisance or n1.

Value

One power value for every nuisance parameter and every value of n1.

Examples

  d <- setupChiSquare(alpha = 0.025, beta = 0.2, r = 1, delta = 0.2)
  pow(d, n1 = 20, nuisance = c(0.2, 0.4), recalculation = TRUE)

Power

Description

Calculates the power of designs with blinded sample size recalculation or of fixed designs for one or several values of the nuisance parameter.

Usage

## S4 method for signature 'FarringtonManning'
pow(
  design,
  n1,
  nuisance,
  recalculation,
  allocation = c("exact", "approximate"),
  ...
)

Arguments

Details

The method is only vectorized in either nuisance or n1.

Value

One power value for every nuisance parameter and every value of n1.

Examples

d <- setupFarringtonManning(alpha = 0.025, beta = 0.2, r = 1,
                            delta = 0, delta_NI = 0.25)
pow(d, n1 = 30, nuisance = 0.4, allocation = "approximate",
    recalculation = TRUE)

Power

Description

Calculates the power of designs with blinded sample size recalculation or of fixed designs for one or several values of the nuisance parameter.

Usage

## S4 method for signature 'Student'
pow(
  design,
  n1,
  nuisance,
  recalculation = TRUE,
  iters = 10000,
  seed = NULL,
  allocation = c("approximate", "exact"),
  ...
)

Arguments

Details

The method is only vectorized in either nuisance or n1.

Value

One power value for every nuisance parameter and every value of n1.

Examples

d <- setupStudent(alpha = .025, beta = .2, r = 1, delta = 3.5, delta_NI = 0,
                  alternative = "greater", n_max = 156)
pow(d, n1 = 20, nuisance = 5.5, recalculation = TRUE)

Simulate Rejection Probability and Sample Size for Student's t-Test

Description

This function simulates the probability that a test defined by setupStudent rejects the null hypothesis. Note that here the nuisance parameter nuisance is the variance of the outcome variable sigma^2.

Usage

simulation(
  design,
  n1,
  nuisance,
  recalculation = TRUE,
  delta_true,
  iters = 1000,
  seed = NULL,
  allocation = c("approximate", "exact"),
  ...
)

Arguments

Details

The implementation follows the algorithm in Lu (2019): Distribution of the two-sample t-test statistic following blinded sample size re-estimation. Pharmaceutical Statistics 15: 208-215. Since Lu (2019) assumes negative non-inferiority margins, the non-inferiority margin of design is multiplied with -1 internally.

Value

Simulated rejection probabilities and sample sizes for each nuisance parameter.

Examples

d <- setupStudent(alpha = .025, beta = .2, r = 1, delta = 3.5, delta_NI = 0,
                  alternative = "greater", n_max = 156)
simulation(d, n1 = 20, nuisance = 5.5, recalculation = TRUE, delta_true = 3.5)

Type I Error Rate

Description

Computes the type I error rate of designs with blinded sample size recalculation or of fixed designs for one or several values of the nuisance parameter.

Usage

toer(design, n1, nuisance, recalculation, ...)

Arguments

Details

The method is only vectorized in either nuisance or n1.

The method is implemented for the classes Student, ChiSquare, and FarringtonManning.

Value

One type I error rate value for every nuisance parameter and every value of n1.

Examples

d <- setupStudent(alpha = .025, beta = .2, r = 1, delta = 3.5, delta_NI = 0,
                  alternative = "greater", n_max = 156)
toer(d, n1 = 20, nuisance = 5.5, recalculation = TRUE)

Type I Error Rate

Description

Computes the type I error rate of designs with blinded sample size recalculation or of fixed designs for one or several values of the nuisance parameter.

Usage

## S4 method for signature 'ChiSquare'
toer(
  design,
  n1,
  nuisance,
  recalculation,
  allocation = c("exact", "approximate", "kf_approx"),
  ...
)

Arguments

Details

The method is only vectorized in either nuisance or n1.

Value

One type I error rate value for every nuisance parameter and every value of n1.

Examples

  d <- setupChiSquare(alpha = 0.025, beta = 0.2, r = 1, delta = 0.2)
  toer(d, n1 = c(10, 20), nuisance = 0.25, recalculation = TRUE)

Type I Error Rate

Description

Computes the type I error rate of designs with blinded sample size recalculation or of fixed designs for one or several values of the nuisance parameter.

Usage

## S4 method for signature 'FarringtonManning'
toer(
  design,
  n1,
  nuisance,
  recalculation,
  allocation = c("exact", "approximate"),
  ...
)

Arguments

Details

The method is only vectorized in either nuisance or n1.

Value

One type I error rate value for every nuisance parameter and every value of n1.

Examples

d <- setupFarringtonManning(alpha = 0.025, beta = 0.2, r = 1,
                            delta = 0, delta_NI = 0.2)
toer(d, n1 = 20, nuisance = 0.25, recalculation = TRUE, allocation = "approximate")

Type I Error Rate

Description

Computes the type I error rate of designs with blinded sample size recalculation or of fixed designs for one or several values of the nuisance parameter.

Usage

## S4 method for signature 'Student'
toer(
  design,
  n1,
  nuisance,
  recalculation = TRUE,
  iters = 10000,
  seed = NULL,
  allocation = c("approximate", "exact"),
  ...
)

Arguments

Details

The method is only vectorized in either nuisance or n1.

Value

One type I error rate value for every nuisance parameter and every value of n1.

Examples

d <- setupStudent(alpha = .025, beta = .2, r = 1, delta = 3.5, delta_NI = 0,
                  alternative = "greater", n_max = 156)
toer(d, n1 = 20, nuisance = 5.5, recalculation = TRUE)