Package 'blindrecalc' reference manual

Title:	Blinded Sample Size Recalculation
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>.
Authors:	Lukas Baumann [aut, cre] , Maximilian Pilz [aut] , Institute of Medical Biometry - University of Heidelberg [cph]
Maintainer:	Lukas Baumann <[email protected]>
License:	MIT + file LICENSE
Version:	1.0.1
Built:	2025-03-07 04:04:05 UTC
Source:	https://github.com/imbi-heidelberg/blindrecalc

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

Arguments

`design`	object of class `TestStatistic` created by `setup`
`n1`	total number of patients that are recruited before the sample size is recalculated
`nuisance`	nuisance parameter that is estimated at the interim analysis
`...`	Further optional 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, tol = 1e-4, iters = 1e3)

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

Arguments

`design`	Object of class `ChiSquare` created by `setupChiSquare`.
`n1`	Either the sample size of the first stage (if `recalculation = TRUE` or the total sample size (if `recalculation = FALSE`).
`nuisance`	Value of the nuisance parameter in (0,1). For the Chi-Squared test this is the overall response rate.
`nuis_ass`	If `recalculation = FALSE` this is the value for the overall response rate that is used to calculate the sample size for the adjusted significance level.
`precision`	Value by which the nominal type 1 error rate is reduced in each iteration until the nominal type 1 error rate is preserved.
`gamma`	If `gamma > 0` then the significance level is adjusted such that the actual level is at most `alpha - gamma`. This is necessary to maintain the nomininal significance level if a confidence interval approach proposed by Friede & Kieser (2011) is used.
`recalculation`	Should the sample size be recalculated after n1 n1 patients are recruited?
`allocation`	Whether the allocation ratio should be preserved exactly (`exact`) or approximately (`approximate` or `kf_approx`). `appproximate` uses the unrounded calculated sample size in the sample size recalculation, `kf_approx` rounds the sample size to the next integer.
`...`	Further optional 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)

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

Arguments

`design`	Object of class `FarringtonManning` created by `setupFarringtonManning`.
`n1`	Either the sample size of the first stage (if `recalculation = TRUE` or the total sample size (if `recalculation = FALSE`).
`nuisance`	Value of the nuisance parameter in (0,1). For the Farrington-Manning test this is the overall response rate.
`nuis_ass`	If `recalculation = FALSE` this is the value for the overall response rate that is used to calculate the sample size for the adjusted significance level.
`precision`	Value by which the nominal type 1 error rate is reduced in each iteration until the nominal type 1 error rate is preserved.
`gamma`	If `gamma > 0` then the significance level is adjusted such that the actual level is at most `alpha - gamma`. This is necessary to maintain the nomininal significance level if a confidence interval approach proposed by Friede & Kieser (2011) is used.
`recalculation`	Should the sample size be recalculated after n1 n1 patients are recruited?
`allocation`	Whether the allocation ratio should be preserved exactly (`exact`) or approximately (`approximate`).
`...`	Further optional 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)

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

Arguments

`design`	Object of class `Student` created by `setupStudent`.
`n1`	Either the sample size of the first stage (if `recalculation = TRUE` or the toal sample size (if `recalculation = FALSE`).
`nuisance`	Value of the nuisance parameter. For the Student's t-test this is the variance.
`tol`	desired absolute tolerance
`iters`	Number of simulation iterations.
`seed`	Random seed for simulation.
`...`	Further optional 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, tol = 1e-4, iters = 1e3)

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, tol = 1e-4, iters = 1e3)

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.

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,
  ...
)
setupChiSquare(
  alpha,
  beta,
  r = 1,
  delta,
  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.
`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 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")

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, ...)
setupFarringtonManning(alpha, beta, r = 1, delta, delta_NI, 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.
`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 overall response probability $p_0$ . In the blinded sample size recalculation procedure it is blindly estimated by:

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

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

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)

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

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

Arguments

`design`	object of class `TestStatistic` created by `setup`
`n1`	total number of patients that are recruited before the sample size is recalculated
`nuisance`	nuisance parameter that is estimated at the interim analysis
`summary`	logical - is a summary of the sample size distribution desired? Otherwise, a vector with sample sizes is returned.
`plot`	Should a plot of the sample size distribution be drawn?
`...`	Further optional 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)


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

Arguments

`design`	Object of class `ChiSquare` created by `setupChiSquare`.
`n1`	Either the sample size of the first stage (if `recalculation = TRUE` or the total sample size (if `recalculation = FALSE`).
`nuisance`	Value of the nuisance parameter in (0,1). For the Chi-Squared test this is the overall response rate.
`summary`	Is a summary of the sample size distribution desired? Otherwise, a vector with sample sizes is returned.
`plot`	Should a plot of the sample size distribution be drawn?
`allocation`	Whether the allocation ratio should be preserved exactly (`exact`) or approximately (`approximate` or `kf_approx`). `appproximate` uses the unrounded calculated sample size in the sample size recalculation, `kf_approx` rounds the sample size to the next integer.
`...`	Further optional 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)

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

Arguments

`design`	Object of class `FarringtonManning` created by `setupFarringtonManning`.
`n1`	Either the sample size of the first stage (if `recalculation = TRUE` or the total sample size (if `recalculation = FALSE`).
`nuisance`	Value of the nuisance parameter in (0,1). For the Farrington-Manning test this is the overall response rate.
`summary`	Is a summary of the sample size distribution desired? Otherwise, a vector with sample sizes is returned.
`plot`	Should a plot of the sample size distribution be drawn?
`allocation`	Whether the allocation ratio should be preserved exactly (`exact`) or approximately (`approximate`).
`...`	Further optional 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)

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"),
  ...
)
## 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

`design`	Object of class `Student` created by `setupStudent`.
`n1`	Either the sample size of the first stage (if `recalculation = TRUE` or the toal sample size (if `recalculation = FALSE`).
`nuisance`	Value of the nuisance parameter. For the Student's t-test this is the variance.
`summary`	Is a summary of the sample size distribution desired? Otherwise, a vector with sample sizes is returned.
`plot`	Should a plot of the sample size distribution be drawn?
`iters`	Number of simulation iterations.
`seed`	Random seed for simulation.
`range`	determines how far the plot whiskers extend out from the box. If range is positive, the whiskers extend to the most extreme data point which is no more than range times the interquartile range from the box. A value of zero causes the whiskers to extend to the data extremes.
`allocation`	Whether the allocation ratio should be preserved exactly (`exact`) or approximately (`approximate`).
`...`	Further optional 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)

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, ...)
n_fix(design, nuisance, ...)

Arguments

`design`	test statistic object created by `setup`
`nuisance`	nuisance parameter for the respective test problem
`...`	Further optional 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)

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

Arguments

`design`	Object of class `ChiSquare` created by `setupChiSquare`.
`nuisance`	Value of the nuisance parameter. For the Chi-Squared test this is the overall response rate.
`variance`	A character string indicating whether the "`heterogenous`" (default) or the "`homogeneous`" variance formula should be used.
`rounded`	Whether the calculated sample size should be rounded up such that the allocation ratio is preserved.
`...`	Further optional 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))

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

Arguments

`design`	Object of class `FarringtonManning` created by `setupFarringtonManning`.
`nuisance`	Value of the nuisance parameter. For the Farrington-Manning test this is the overall response rate.
`rounded`	Whether the calculated sample size should be rounded up such that the allocation ratio is preserved.
`...`	Further optional 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)

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

Arguments

`design`	test statistic object
`nuisance`	nuisance parameter
`...`	Further optional 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)

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

Arguments

`design`	object of class `TestStatistic` created by `setup`
`n1`	total number of patients that are recruited before the sample size is recalculated
`nuisance`	nuisance parameter that is estimated at the interim analysis
`recalculation`	Should the sample size be recalculated after n1 n1 patients are recruited?
`...`	Further optional 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)


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

Arguments

`design`	Object of class `ChiSquare` created by `setupChiSquare`.
`n1`	Either the sample size of the first stage (if `recalculation = TRUE` or the total sample size (if `recalculation = FALSE`).
`nuisance`	Value of the nuisance parameter in (0,1). For the Chi-Squared test this is the overall response rate.
`recalculation`	Should the sample size be recalculated after n1 n1 patients are recruited?
`allocation`	Whether the allocation ratio should be preserved exactly (`exact`) or approximately (`approximate` or `kf_approx`). `appproximate` uses the unrounded calculated sample size in the sample size recalculation, `kf_approx` rounds the sample size to the next integer.
`...`	Further optional 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)

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

Arguments

`design`	Object of class `FarringtonManning` created by `setupFarringtonManning`.
`n1`	Either the sample size of the first stage (if `recalculation = TRUE` or the total sample size (if `recalculation = FALSE`).
`nuisance`	Value of the nuisance parameter in (0,1). For the Farrington-Manning test this is the overall response rate.
`recalculation`	Should the sample size be recalculated after n1 n1 patients are recruited?
`allocation`	Whether the allocation ratio should be preserved exactly (`exact`) or approximately (`approximate`).
`...`	Further optional 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)

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

Arguments

`design`	Object of class `Student` created by `setupStudent`.
`n1`	Either the sample size of the first stage (if `recalculation = TRUE` or the toal sample size (if `recalculation = FALSE`).
`nuisance`	Value of the nuisance parameter. For the Student's t-test this is the variance.
`recalculation`	Should the sample size be recalculated after n1 n1 patients are recruited?
`iters`	Number of simulation iterations.
`seed`	Random seed for simulation.
`allocation`	Whether the allocation ratio should be preserved exactly (`exact`) or approximately (`approximate`).
`...`	Further optional 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)

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

Arguments

`design`	Object of class `Student` created by `setupStudent`.
`n1`	Either the sample size of the first stage (if `recalculation = TRUE` or the toal sample size (if `recalculation = FALSE`).
`nuisance`	Value of the nuisance parameter. For the Student's t-test this is the variance.
`recalculation`	Should the sample size be recalculated after n1 n1 patients are recruited?
`delta_true`	effect measure under which the rejection probabilities are computed
`iters`	Number of simulation iterations.
`seed`	Random seed for simulation.
`allocation`	Whether the allocation ratio should be preserved exactly (`exact`) or approximately (`approximate`).
`...`	Further optional 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)

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)

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

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

Arguments

`design`	object of class `TestStatistic` created by `setup`
`n1`	total number of patients that are recruited before the sample size is recalculated
`nuisance`	nuisance parameter that is estimated at the interim analysis
`recalculation`	Should the sample size be recalculated after n1 n1 patients are recruited?
`...`	Further optional 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)

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

Arguments

`design`	Object of class `ChiSquare` created by `setupChiSquare`.
`n1`	Either the sample size of the first stage (if `recalculation = TRUE` or the total sample size (if `recalculation = FALSE`).
`nuisance`	Value of the nuisance parameter in (0,1). For the Chi-Squared test this is the overall response rate.
`recalculation`	Should the sample size be recalculated after n1 n1 patients are recruited?
`allocation`	Whether the allocation ratio should be preserved exactly (`exact`) or approximately (`approximate` or `kf_approx`). `appproximate` uses the unrounded calculated sample size in the sample size recalculation, `kf_approx` rounds the sample size to the next integer.
`...`	Further optional 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)

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

Arguments

`design`	Object of class `FarringtonManning` created by `setupFarringtonManning`.
`n1`	Either the sample size of the first stage (if `recalculation = TRUE` or the total sample size (if `recalculation = FALSE`).
`nuisance`	Value of the nuisance parameter in (0,1). For the Farrington-Manning test this is the overall response rate.
`recalculation`	Should the sample size be recalculated after n1 n1 patients are recruited?
`allocation`	Whether the allocation ratio should be preserved exactly (`exact`) or approximately (`approximate`).
`...`	Further optional 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")

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

Arguments

`design`	Object of class `Student` created by `setupStudent`.
`n1`	Either the sample size of the first stage (if `recalculation = TRUE` or the toal sample size (if `recalculation = FALSE`).
`nuisance`	Value of the nuisance parameter. For the Student's t-test this is the variance.
`recalculation`	Should the sample size be recalculated after n1 n1 patients are recruited?
`iters`	Number of simulation iterations.
`seed`	Random seed for simulation.
`allocation`	Whether the allocation ratio should be preserved exactly (`exact`) or approximately (`approximate`).
`...`	Further optional 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)

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)

Package 'blindrecalc'

Help Index

Adjusted level of significance

Description

Usage

Arguments

Details

Value

Examples

Adjusted level of significance

Description

Usage

Arguments

Details

Value

Examples

Adjusted level of significance

Description

Usage

Arguments

Details

Value

Examples

Adjusted level of significance

Description

Usage

Arguments

Details

Value

Examples

Blinded Sample Size Recalculation

Description

Details

Chi-squared test

Description

Usage

Arguments

Details

Value

References

Examples

Farrington Manning test

Description

Usage

Arguments

Details

Value

References

Examples

Distribution of the Sample Size

Description

Usage

Arguments

Details

Value

Examples

Distribution of the Sample Size

Description

Usage

Arguments

Details

Value

Examples

Distribution of the Sample Size

Description

Usage

Arguments

Details

Value

Examples

Distribution of the Sample Size

Description

Usage

Arguments

Details

Value

Examples

Fixed Sample Size

Description

Usage