Type: Package
Title: Group Sequential Testing of a Treatment Effect Using a Surrogate Marker
Version: 1.0
Description: Provides functions to implement group sequential procedures that allow for early stopping to declare efficacy using a surrogate marker and the possibility of futility stopping. More details are available in: Parast, L. and Bartroff, J (2024) <doi:10.1093/biomtc/ujae108>. A tutorial for this package can be found at https://laylaparast.com/home/SurrogateSeq.html.
License: GPL-2 | GPL-3 [expanded from: GPL]
Imports: stats, MASS, ggplot2
NeedsCompilation: no
Packaged: 2025-01-22 17:23:16 UTC; parastlm
Author: Layla Parast [aut, cre], Jay Bartroff [aut]
Maintainer: Layla Parast <parast@austin.utexas.edu>
Depends: R (≥ 3.5.0)
Repository: CRAN
Date/Publication: 2025-01-24 12:50:02 UTC

Calculates kernel matrix

Description

Helper function; this calculates the kernel matrix

Usage

Kern.FUN(zz, zi, bw)

Arguments

zz

zz

zi

zi

bw

bandwidth

Value

the kernel matrix

Author(s)

Layla Parast

ACTG 320 clinical trial data

Description

Primary outcome and surrogate marker measurements over time from the ACTG 320 clinical trial data

Usage

data("StudyA.aids")

Format

A list with 4 elements:

y1

the primary outcome in the treatment group in Study A; the primary outcome is defined as -1 times (log of RNA at 40 weeks - log of RNA at baseline) because a DECREASE in RNA is better

y0

the primary outcome in the control group in Study A

s1

a dataframe of the surrogate markers at different time points in the treatment group in Study A; the surrogate marker is change in CD4 cell count from baseline to 4 weeks (CD4_4weeks), 8 weeks (CD4_8weeks), 24 weeks (CD4_24weeks), and 40 weeks (CD4_40weeks). Note that higher values indicate increasing CD4 cell count which is "better".

s0

a dataframe of the surrogate markers at different time points in the control group in Study A

Examples

data(StudyA.aids)

ACTG 193A clinical trial data

Description

Surrogate marker measurements over time from the ACTG 193A clinical trial data. Note that the time points do not exactly match up to ACTG 320. In the paper, we use Study A surrogate data at 24 weeks to construct the conditional mean function applied to Study B at 16 weeks. Also note that some subjects are missing values of the surrogate at one or more time points. The naive estimate of the treatment effect using the surrogates uses all non-missing data available at each time point.

Usage

data("StudyB.aids")

Format

A list with 2 elements:

s1

a dataframe of the surrogate markers at different time points in the treatment group in Study B; the surrogate marker is change in CD4 cell count from baseline to 8 weeks (CD4_8weeks), 16 weeks (CD4_16weeks), 24 weeks (CD4_24weeks), and 40 weeks (CD4_40weeks). Note that higher values indicate increasing CD4 cell count which is "better".

s0

a dataframe of the surrogate markers at different time points in the control group in Study B

Examples

data(StudyB.aids)

Repeats a row.

Description

Helper function; this function creates a matrix that repeats vc, dm times where each row is equal to the vc vector.

Usage

VTM(vc, dm)

Arguments

vc

the vector to repeat.

dm

number of rows.

Value

a matrix that repeats vc, dm times where each row is equal to the vc vector

Calculates the boundaries for the group sequential tests with futility stopping

Description

Returns the boundaries for any group sequential test of the null vs. 2-sided alternative whose boundaries take the form of a single constant times a known weight vector, which is w.vec; allows for futility stopping. These include Pocock (w.vec=(1,1,..)), O'Brien-Fleming (w.vec=(sqrt(n.stg/1), sqrt(n.stg/2), ..., 1)), etc. It does this by returning quantiles of the sample paths of the (null) test statistic paths in mc.paths.

Usage

bdr.gs.mc.fut(c1 = NULL, c2 = NULL, pp = 0.4, n.stg, j.star = 1, alpha = 0.05, 
alpha0 = (j.star/n.stg) * alpha, mc.paths, inf.fraction = (1:n.stg)/n.stg, 
N.iter.max = 100, alpha.tol = 0.02 * alpha)

Arguments

c1

c1 and c2 are the constants determining the outer boundary b[j] = c1 * (j/J)^{pp-1/2} and futility boundaries a[j] = (c1+c2) * (j/J)^{1/2} - c2 * (j/J)^{pp-1/2} for j >= j.star, where J is the max no of stages (AKA n.stg). If c1 is null, it is found as the upper alpha0 quantile of the max over the first j.star stages.

c2

see description in c1

pp

power parameter for Wang-Tsiatis boundaries; default is 0.4

n.stg

maximum number of analyses

j.star

earliest stage at which futility stopping is allowed. Should be <= n.stg-1 (there is already "futility stopping" at the n.stg-th stage anyway). Default is 1.

alpha

desired rejection probability of the test; default is 0.05

alpha0

the part of alpha that c1 is chosen to spend in first j.star stages; default is (j.star/n.stg) * alpha

mc.paths

matrix of sample paths, each row being a sample path, no. of columns is number of stages

inf.fraction

information fraction vector of the same length as n.stg which reflects the fraction of information at each analysis, should be positive, non-decreasing, and the last entry should be 1; default is (1:n.stg)/n.stg, user may want to specify a different vector for unequal time points

N.iter.max

max no. of iterations for finding c2

alpha.tol

the tolerance for stopping search for c2

Value

Returns a list:

a

the futility boundary vectors

b

the null-rejection boundary vectors

prej

prob. of rejecting the null (at any stage)

EM

expected stopping stage number

se.M

standard error of stopping time

c1

constants used in boundaries a, b

c2

constants used in boundaries a, b

Author(s)

Jay Bartroff

Calculates the boundaries for the group sequential tests

Description

Returns the boundaries for any group sequential test of the null vs. 2-sided alternative whose boundaries take the form of a single constant times a known weight vector, which is w.vec. These include Pocock (w.vec=(1,1,..)), O'Brien-Fleming (w.vec=(sqrt(n.stg/1), sqrt(n.stg/2), ..., 1)), etc. It does this by returning quantiles of the sample paths of the (null) test statistic paths in mc.paths.

Usage

bdr.gs.mc.gen(alpha = 0.05, mc.paths, w.vec)

Arguments

alpha

desired rejection probability of the test; default is 0.05

mc.paths

matrix of sample paths, each row being a sample path, no. of columns is number of stages

w.vec

weight vector corresponding to desired test

Value

Returns a list:

cons

the constant in the boundary vector cons*w.vec

bndry.vec

the boundary vector cons*w.vec

Author(s)

Jay Bartroff

Computes variances and standardized covariance matrix for the group sequential statistic

Description

Computes variances and standardized covariance matrix for the group sequential statistic

Usage

cov.surr.gs(s0.4.est, s1.4.est, sa.0, ya.0, nb.0, nb.1, full.matrix = TRUE, 
naive = FALSE)

Arguments

s0.4.est

surrogate marker in the control group which is used for estimating means and covariances of S0, S1 in the Study B data. For designing tests (e.g., finding boundaries) these may come from Study A data, but for analyzing tests these may come from Study B data. Number of columns is the number of stages, number of rows may differ from rows in sa.0

s1.4.est

surrogate marker in the treated group which is used for estimating means and covariances of S0, S1 in the Study B data. For designing tests (e.g., finding boundaries) these may come from Study A data, but for analyzing tests these may come from Study B data. Number of columns is the number of stages, number of rows may differ from rows in sa.0

sa.0

surrogate marker in the control group in Study A

ya.0

primary outcome in the control group in Study A

nb.0

sample size for the control group in Study B

nb.1

sample size for the treated group in Study B

full.matrix

if TRUE, the standardized covariance matrix is provided; default is TRUE

naive

user should set to TRUE to compute covariance for "cumulative" test statistic, FALSE for naive statistic that only uses study B data from timepoint J at the J-th analysis; default is FALSE

Value

Returns a list:

var.vec.del

variance vector computed by the delta method

cov.stand.del

if full.matrix = TRUE, covariance matrix of the standardized test statistic computed by the delta method

var.vec.samp

variance vector computed by the sample mean and covariance of s0.4.est and s1.4.est

cov.stand.samp

if full.matrix = TRUE, covariance matrix of the standardized test statistic computed by the sample mean and covariance of s0.4.est and s1.4.est

Author(s)

Jay Bartroff

Tests for a treatment effect on the primary outcome using surrogate marker information

Description

Nonparametric test for a treatment effect on the primary outcome using surrogate marker information. This test borrows information from a prior study (Study A) about the relationship between the surrogate and the primary outcome to test for a treatment effect in the current study (Study B).

Usage

delta.e.estimate(sone = NULL, szero = NULL, szerop, yzerop, extrapolate = TRUE, 
mat = NULL, n1 = NULL, n0 = NULL)

Arguments

sone

surrogate marker in the treated group in Study B

szero

surrogate marker in the control group in Study B

szerop

surrogate marker in the control group in Study A

yzerop

primary outcome in the control group in Study A

extrapolate

TRUE or FALSE; extrapolate for values outside of the support in Study A

mat

for Study B, the user can either provide sone and szero or can provide a vector, mat, where the first n1 values are the surrogate marker in the treated group in the Study B, and the remaining values are the surrogate marker in the control group in Study B

n1

sample size of treated group in Study B; only needed if mat is provided instead of sone and szero

n0

sample size of control group in Study B; only needed if mat is provided instead of sone and szero

Value

delta.e

estimated treatment effect using surrogate marker information

sd.closed

estimated standard error of treatment effect estimate

delta.e.z

test statistic

delta.e.p

p-value of test statistic

Author(s)

Layla Parast

References

Parast, Cai, and Tian (2023). Using a Surrogate with Heterogeneous Utility to Test for a Treatment Effect. Statistics in Medicine, 42(1): 68-88.

Parast and Bartroff (2024). Group sequential testing of a treatment effect using a surrogate marker. Biometrics, 80(4), ujae108.

Examples

data(example.data)
delta.e.estimate(sone = example.data$s1, szero = example.data$s0, szerop = example.data$s0.p, 
yzerop = example.data$y0.p)

data(StudyA.aids)
data(StudyB.aids)
s1.studyb = StudyB.aids$s1
s0.studyb = StudyB.aids$s0
s0.studya = StudyA.aids$s0

#24 weeks

delta.e.vec = delta.e.estimate(sone=s1.studyb$CD4_24weeks[!is.na(s1.studyb$CD4_24weeks)],
szero=s0.studyb$CD4_24weeks[!is.na(s0.studyb$CD4_24weeks)], szerop = s0.studya$CD4_24weeks, 
yzerop = StudyA.aids$y0, extrapolate = TRUE)
delta.e.vec

Example data

Description

Example data

Usage

data("example.data")

Format

A list with 9 elements:

w0.p

the baseline covariate in the control group in the prior study (Study A)

s0.p

the surrogate marker in the control group in the prior study (Study A

y0.p

the primary outcome in the control group in the prior study (Study A

w1

a baseline covariate in the treatment group in the current study (Study B)

w0

a baseline covariate in the control group in the current study (Study B)

s1

the surrogate marker in the treatment group in the current study (Study B)

s0

the surrogate marker in the control group in the current study (Study B)

y1

the primary outcome in the treatment group in the current study (Study B)

y0

the primary outcome in the control group in the current study (Study B)

Examples

data(example.data)
names(example.data)

Computes group sequential boundaries

Description

Computes group sequential (and naive) boundaries for the nonparametric test for a treatment effect on the primary outcome using surrogate marker information. The boundaries and test statistic borrow information from a prior study (Study A) about the relationship between the surrogate and the primary outcome to test for a treatment effect in the current study (Study B).

Usage

gs.boundaries(szerop, sonep, yzerop, nzero, none, n.stg, B.norm = 1e+06, 
alpha = 0.05, pp = 0.4, inf.fraction = (1:n.stg)/n.stg, plot=FALSE)

Arguments

szerop

surrogate marker in the control group in Study A

sonep

surrogate marker in the treated group in Study A

yzerop

primary outcome in the control group in Study A

nzero

sample size of control group in Study B

none

sample size of treated group in Study B

n.stg

maximum number of analyses

B.norm

number of multivariate normal vectors to use in simulation for boundaries; default is 1e+06

alpha

desired rejection probability of the test; default is 0.05

pp

power parameter for Wang-Tsiatis boundaries; default is 0.4

inf.fraction

information fraction vector of the same length as n.stg which reflects the fraction of information at each analysis, should be positive, non-decreasing, and the last entry should be 1; default is (1:n.stg)/n.stg, user may want to specify a different vector for unequal time points

plot

TRUE or FALSE if a plot of the boundaries is desired; default is FALSE

Value

Returns a list of boundaries:

Naive

Naive boundaries

Bonf

Bonferroni boundaries

Pocock

Pocock boundaries

OBrien_Fleming

O'Brien-Fleming boundaries

Wang_Tsiatis

Wang-Tsiatis boundaries

Author(s)

Layla Parast and Jay Bartroff

References

Parast and Bartroff (2024). Group sequential testing of a treatment effect using a surrogate marker. Biometrics, 80(4), ujae108.

Examples

data(example.data)
data(StudyA.aids)
data(StudyB.aids)
s0.studya = StudyA.aids$s0
s1.studya = StudyA.aids$s1


bound = gs.boundaries(szerop = s0.studya, sonep = s1.studya, yzerop=StudyA.aids$y0, 
nzero = nrow(StudyB.aids$s0),none = nrow(StudyB.aids$s1), n.stg=4, B.norm=1e6, 
alpha=0.05)

bound

Computes group sequential boundaries with futility stopping

Description

Computes group sequential (and naive) boundaries for the nonparametric test for a treatment effect on the primary outcome using surrogate marker information. The boundaries and test statistic borrow information from a prior study (Study A) about the relationship between the surrogate and the primary outcome to test for a treatment effect in the current study (Study B). The group sequential boundaries allow for futility stopping (bounds given).

Usage

gs.boundaries.fut(szerop, sonep, yzerop, nzero, none, n.stg, B.norm = 1e+06, 
alpha = 0.05, pp = 0.4, inf.fraction = (1:n.stg)/n.stg, j.star=1, 
alpha0=(j.star/n.stg)*alpha, 
plot = FALSE)

Arguments

szerop

surrogate marker in the control group in Study A

sonep

surrogate marker in the treated group in Study A

yzerop

primary outcome in the control group in Study A

nzero

sample size of control group in Study B

none

sample size of treated group in Study B

n.stg

maximum number of analyses

B.norm

number of multivariate normal vectors to use in simulation for boundaries; default is 1e+06

alpha

desired rejection probability of the test; default is 0.05

pp

power parameter for Wang-Tsiatis boundaries; default is 0.4

inf.fraction

information fraction vector of the same length as n.stg which reflects the fraction of information at each analysis, should be positive, non-decreasing, and the last entry should be 1; default is (1:n.stg)/n.stg, user may want to specify a different vector for unequal time points

j.star

earliest stage at which futility stopping is allowed. Should be <= n.stg-1 (there is already "futility stopping" at the n.stg-th stage anyway). Default is 1.

alpha0

the part of alpha that c1 is chosen to spend in first j.star stages; default is (j.star/n.stg)*alpha

plot

TRUE or FALSE if a plot of the boundaries is desired; default is FALSE

Value

Returns a list of boundaries:

Naive

Naive boundaries

Bonf

Bonferroni boundaries

Pocock.futility

Pocock futility boundaries

Pocock.nullrejection

Pocock null rejection boundaries

OBrien_Fleming.futility

O'Brien-Fleming futility boundaries

OBrien_Fleming.nullrejection

O'Brien-Fleming null rejection boundaries

Wang_Tsiatis.futility

Wang-Tsiatis futility boundaries

Wang_Tsiatis.nullrejection

Wang-Tsiatis null rejection boundaries

Author(s)

Layla Parast and Jay Bartroff

References

Parast and Bartroff (2024). Group sequential testing of a treatment effect using a surrogate marker. Biometrics, 80(4), ujae108.

Examples

data(example.data)
data(StudyA.aids)
data(StudyB.aids)
s0.studya = StudyA.aids$s0
s1.studya = StudyA.aids$s1


bound = gs.boundaries.fut(szerop = s0.studya, sonep = s1.studya, yzerop=StudyA.aids$y0, 
nzero = nrow(StudyB.aids$s0),none = nrow(StudyB.aids$s1), n.stg=4, B.norm=1e6, 
alpha=0.05)

bound

Computes kernel density estimate

Description

Computes kernel density estimate

Usage

kern.estJ(sb.arg, band.h, sa.vec, ya.vec)

Arguments

sb.arg

surrogate marker from Study B

band.h

bandwidth

sa.vec

surrogate marker from Study A

ya.vec

primary outcome from Study A

Value

kernel density estimate

Author(s)

Jay Bartroff

Compute the operating characteristics on the group sequential test with futility stopping statistics in paths

Description

Compute the operating characteristics on the group sequential test with futility stopping statistics in paths: The expected stopping stage no., plus the probability of rejecting the null in favor of the 2-sided alternative. This is for a general GS test which uses the boundaries in bndry.vec.

Usage

op.char.gs.fut(b.vec, a.vec, paths)

Arguments

b.vec

"null-rejection" boundaries, should be >= 0, and a.vec[n.stg] = b.vec[n.stg].

a.vec

futility boundaries, should be >= 0, and a.vec[n.stg] = b.vec[n.stg];a.vec[j]=0 means no futility stopping at stage j.

paths

matrix of test statistic sample paths, each row being a sample path, no. of columns is max number

Value

Returns a list:

EM

expected stopping stage number

se.M

standard error of stopping time

prej

prob. of rejecting the null (at any stage)

Calculates the conditional mean function

Description

Helper function; calculates the condition mean of Y given S, based on Study A data

Usage

pred.smooth.2(kernel.use,kernel.apply, bw,outcome)

Arguments

kernel.use

surrogate values in the control group in Study A

kernel.apply

surrogate values in Study B

bw

bandwidth

outcome

outcome in the control group in Study A

Value

expected outcome for each surrogate value

Author(s)

Layla Parast