Title:	Adaptive Clinical Trial Designs with Endpoint Selection and Sample Size Reassessment
Version:	1.1
Maintainer:	Marta Bofill Roig <marta.bofillroig@meduniwien.ac.at>
Description:	Endpoint selection and sample size reassessment for multiple binary endpoints based on blinded and/or unblinded data. Trial design that allows an adaptive modification of the primary endpoint based on blinded information obtained at an interim analysis. The decision rule chooses the endpoint with the lower estimated required sample size. Additionally, the sample size is reassessed using the estimated event probabilities and correlation between endpoints. The implemented design is proposed in Bofill Roig, M., Gómez Melis, G., Posch, M., and Koenig, F. (2022). <doi:10.48550/arXiv.2206.09639>.
License:	MIT + file LICENSE
Encoding:	UTF-8
Imports:	stats, CompAREdesign
RoxygenNote:	7.2.1
NeedsCompilation:	no
Packaged:	2023-02-02 13:22:06 UTC; marta.bofill
Author:	Marta Bofill Roig [aut, cre], Guadalupe Gomez Melis [ctb], Franz Koenig [ctb], Martin Posch [ctb]
Repository:	CRAN
Date/Publication:	2023-02-03 10:22:32 UTC

OR_function

Description

computes the odds ratio

Usage

OR_function(p0, p1)

Value

Odds ratio calculation based on marginal probabilities

corr_rest

Description

computes the correlation restrictions phat0_e1,phat0_e2: estimated probabilities p0_e1,p0_e2,p1_e1,p1_e2: assumed probabilities (design) OR1,OR2: expected effect sizes

Usage

corr_rest_b(phat0_e1, phat0_e2, p0_e1, p0_e2, p1_e1, p1_e2, OR1, OR2)

Value

Correlation bounds based on estimated and assumed probabilities

corr_rest_ub: computes the correlation restrictions unblinded case

Description

computes the correlation restrictions with unblinded data phat0_e1,phat0_e2,phat1_e1,phat1_e2: estimated probabilities p0_e1,p0_e2,p1_e1,p1_e2: assumed probabilities (design) OR1,OR2: expected effect sizes

Usage

corr_rest_ub(
  phat0_e1,
  phat0_e2,
  phat1_e1,
  phat1_e2,
  p0_e1,
  p0_e2,
  p1_e1,
  p1_e2,
  OR1,
  OR2
)

Value

Correlation bounds based on estimated and assumed probabilities (unblinded case)

Endpoint selection and sample size reassessment for composite endpoints based on blinded data

Description

Endpoint selection and sample size reassessment for composite endpoints based on blinded data. The composite endpoint is assumed to be a binary endpoint formed by a combination of two events (E1 and E2). We assume that the endpoint 1 is more relevant for the clinical question than endpoint 2. This function selects between the composite endpoint or the relevant endpoint as the primary endpoint of the study and recalculate the sample size accordingly. The decision criteria to decide between the composite endpoint or the relevant endpoint might be the ratio of the corresponding sample sizes ("SS") or the Asymptotic Relative Efficiency ("ARE"). The algorithm of the function is the following: First, the probabilities of the composite components in the control group and the correlation between them are estimated based on blinded data. Second, using the estimated probabilities and the estimated correlation, the decision criteria is computed and the primary endpoint is selected. Finally, the sample size is recalculated according to the decision.

Usage

eselect(db, p0_e1, OR1, p0_e2, OR2, criteria = "SS", alpha = 0.05, beta = 0.2)

Arguments

Value

This function returns the decision (Decision = 1, meaning the chosen endpoint is the composite endpoint; and Decision = 0, meaning the chosen endpoint is the relevant endpoint) and the sample size according to the decision.

References

Bofill Roig, M., Gómez Melis, G., Posch, M., & Koenig, F. (2022). Adaptive clinical trial designs with blinded selection of binary composite endpoints and sample size reassessment. Biostatistics (in press). arXiv e-prints, arXiv-2206 (https://doi.org/10.48550/arXiv.2206.09639). Bofill Roig, M., & Gómez Melis, G. "Selection of composite binary endpoints in clinical trials." Biometrical Journal 60.2 (2018): 246-261.

Examples

# Based on Bofill Roig, M., et al.
# (See supplementary material in https://doi.org/10.48550/arXiv.2206.09639)
p0_e1 = 0.173
p0_e2 = 0.055
p1_e1 = 0.121;
p1_e2 = 0.057;
n1 = 569
n0 = 576
n = n0+n1
p1 = (p0_e1*n0 + p1_e1*n1)/n
p2 = (p0_e2*n0 + p1_e2*n1)/n
p_ce = (0.203*n0 + 0.146*n1)/n
OR1 = 0.7
OR2 = 0.9
x11 = round((p1+p2-p_ce)*n)
x12 = round((p1)*n-x11)
x21 = round((p2)*n- x11)
x22 = round((1-p_ce)*n)
data = matrix(c(x11,x12,x21,x22), nrow = 2 , ncol = 2, byrow = FALSE)
eselect(db=data,p0_e1=0.18,OR1=0.70,p0_e2=0.05,OR2=0.9,criteria="SS",alpha=0.05,beta=0.2)

Endpoint selection and sample size reassessment for composite endpoints based on unblinded data

Description

Endpoint selection and sample size reassessment for composite endpoints based on unblinded data. The composite endpoint is assumed to be a binary endpoint formed by a combination of two events (E1 and E2). We assume that the endpoint 1 is more relevant for the clinical question than endpoint 2. This function selects between the composite endpoint or the relevant endpoint as the primary endpoint of the study and recalculate the sample size accordingly. The decision criteria to decide between the composite endpoint or the relevant endpoint might be the ratio of the corresponding sample sizes ("SS") or the Asymptotic Relative Efficiency ("ARE"). The algorithm of the function is the following: First, the probabilities of the composite components in the control group and the correlation between them are estimated based on unblinded data. Second, using the estimated probabilities and the estimated correlation, the decision criteria is computed and the primary endpoint is selected. Finally, the sample size is recalculated according to the decision.

Usage

eselect_ub(
  db0,
  db1,
  p0_e1,
  OR1,
  p0_e2,
  OR2,
  criteria = "SS",
  alpha = 0.05,
  beta = 0.2
)

Arguments

Value

This function returns the decision (Decision = 1, meaning the chosen endpoint is the composite endpoint; and Decision = 0, meaning the chosen endpoint is the relevant endpoint) and the sample size according to the decision.

Simulation trials with endpoint selection and sample size reassessment for composite endpoints based on blinded data

Description

This function simulates trials with endpoint selection and sample size reassessment for composite binary endpoints based on blinded data. The composite endpoint is assumed to be a binary endpoint formed by a combination of two events (E1 and E2). We assume that the endpoint 1 is more relevant for the clinical question than endpoint 2. This function simulates a trial based on the design parameters and use the algorithm implemented in eselect() to select the primary endpoint and recalculate the sample size accordingly.

Usage

eselectsim(
  ss_arm,
  p0_e1,
  OR1,
  p0_e2,
  OR2,
  p0_ce,
  p_init = 1,
  criteria = "SS",
  H0_e1 = FALSE,
  H0_e2 = FALSE,
  SS_r = TRUE,
  alpha = 0.05,
  beta = 0.2
)

Arguments

Value

This function returns the decision (Decision = 1, meaning the chosen endpoint is the composite endpoint; and Decision = 0, meaning the chosen endpoint is the relevant endpoint) and the statistic to test the primary hypothesis according to the decision.

References

Bofill Roig, M., Gómez Melis, G., Posch, M., & Koenig, F. (2022). Adaptive clinical trial designs with blinded selection of binary composite endpoints and sample size reassessment. Biostatistics (in press). arXiv e-prints, arXiv-2206 (https://doi.org/10.48550/arXiv.2206.09639).

Simulation trials with endpoint selection and sample size reassessment for composite endpoints based on unblinded data

Description

This function simulates trials with endpoint selection and sample size reassessment for composite binary endpoints based on unblinded data. The composite endpoint is assumed to be a binary endpoint formed by a combination of two events (E1 and E2). We assume that the endpoint 1 is more relevant for the clinical question than endpoint 2. This function simulates a trial based on the design parameters and use the algorithm implemented in eselect() to select the primary endpoint and recalculate the sample size accordingly.

Usage

eselectsim_ub(
  ss_arm,
  p0_e1,
  OR1,
  p0_e2,
  OR2,
  p0_ce,
  p_init = 1,
  criteria = "SS",
  H0_e1 = FALSE,
  H0_e2 = FALSE,
  SS_r = TRUE,
  alpha = 0.05,
  beta = 0.2
)

Arguments

Value

This function returns the decision (Decision = 1, meaning the chosen endpoint is the composite endpoint; and Decision = 0, meaning the chosen endpoint is the relevant endpoint) and the statistic to test the primary hypothesis according to the decision.

Blinded estimation of the correlation

Description

This function estimates the correlation between two binary endpoints based on blinded data.

Usage

estimation_b(samplesize, p0_e1, p1_e1, OR1, p0_e2, p1_e2, OR2, p0_ce, p1_ce)

Arguments

Value

This function returns the estimated correlation and the truncated correlation within the possible margins.

Unblinded estimation of the correlation

Description

This function estimates the correlation between two binary endpoints based on unblinded data.

Usage

estimation_ub(samplesize, p0_e1, p1_e1, OR1, p0_e2, p1_e2, OR2, p0_ce, p1_ce)

Arguments

Value

This function returns the estimated correlation based on unblinded data and the truncated correlation within the possible margins.

f_OR

Description

simulates binary outcomes and computes the statistic

Usage

f_OR(samplesize, p0, p1)

Value

Two-sample test statistics using unpooled variance estimator

Simulation 2x2 table binary endpoints

Description

simulation binary data two outcomes

Usage

f_sim(samplesize, p_e1, p_e2, p_ce)

Arguments

Value

Simlated data

the function returns 2x2 table s1+s2: num X1 s1+s3: num X2

fun_p0

Description

computes the probability under the control group based on the pooled probability and the odds ratio p: pooled probability l: odds ratio

Usage

fun_p0(p, l)

Value

Probability under the control group based on OR and pooled probability

samplesize_OR

Description

Sample size calculations in terms of odds ratio

Usage

samplesize_OR(p0, OR, alpha = 0.05, beta = 0.2, Unpooled = "Unpooled Variance")

Value

Sample size for odds ratios

test_f

Description

computes the statistical test (OR)

Usage

test_f(OR, p0, n)

Value

Two-sample test statistics for a single endpoint

test_me

Description

computes the statistical tests (OR) for two endpoints

Usage

test_me(OR1, p0_e1, OR2, p0_e2, n)

Value

Two-sample test statistics for endpoint 1 and 2