Function to design multi-arm multi-stage studies with ordinal or binary endpoints
ordinal.mams.RdThe function determines (approximately) the boundaries of a multi-arm multi-stage study with ordinal or binary endpoints for a given boundary shape and finds the required number of subjects.
Usage
ordinal.mams(
prob = c(0.35, 0.4, 0.25),
or = 2,
or0 = 1.2,
K = 4,
J = 2,
alpha = 0.05,
power = 0.9,
r = 1:2,
r0 = 1:2,
ushape = "obf",
lshape = "fixed",
ufix = NULL,
lfix = 0,
nstart = 1,
nstop = NULL,
sample.size = TRUE,
Q = 20,
parallel = TRUE,
print = TRUE
)Arguments
- prob
Vector of expected probabilities of falling into each category under control conditions. The elements must sum up to one (default=c(0.35, 0.4, 0.25)).
- or
Interesting treatment effect on the scale of odds ratios (default=2).
- or0
Uninteresting treatment effect on the scale of odds ratios (default=1.2).
- K
Number of experimental treatments (default=4).
- J
Number of stages (default=2).
- alpha
One-sided familywise error rate (default=0.05).
- power
Desired power (default=0.9).
- r
Vector of allocation ratios (default=1:2).
- r0
Vector ratio on control (default=1:2).
- ushape
Shape of upper boundary. Either a function specifying the shape or one of "pocock", "obf" (the default), "triangular" and "fixed".
- lshape
Shape of lower boundary. Either a function specifying the shape or one of "pocock", "obf", "triangular" and "fixed" (the default).
- ufix
Fixed upper boundary (default=NULL). Only used if shape="fixed".
- lfix
Fixed lower boundary (default=0). Only used if shape="fixed".
- nstart
Starting point for finding the sample size (default=1).
- nstop
Stopping point for finding the sample size (default=NULL).
- sample.size
Logical if sample size should be found as well (default=TRUE).
- Q
Number of quadrature points per dimension in the outer integral (default=20).
- parallel
if TRUE (default), allows parallelisation of the computation via a user-defined strategy specified by means of the function future::plan(). If not set differently, the default strategy is sequential, which corresponds to a computation without parallelisation.
if TRUE (default), indicate at which stage the computation is.
Value
An object of the class MAMS containing the following components:
- prob
Vector of expected probabilities of falling into each category under control conditions. The elements must sum up to one (default=
c(0.35, 0.4, 0.25)).- or
Interesting treatment effect on the scale of odds ratios (default=
2).- or0
Uninteresting treatment effect on the scale of odds ratios (default=
1.2).- K
Number of experimental treatments (default=
4).- J
Number of stages (default=
2).- alpha
One-sided familywise error rate (default=
0.05).- power
Desired power (default=
0.9).- r
Vector of allocation ratios (default=
1:2).- r0
Vector ratio on control (default=
1:2).- ushape
Shape of upper boundary. Either a function specifying the shape or one of
"pocock","obf"(the default),"triangular"and"fixed".- lshape
Shape of lower boundary. Either a function specifying the shape or one of
"pocock","obf","triangular"and"fixed"(the default).- ufix
Fixed upper boundary (default=
NULL). Only used ifshape="fixed".- lfix
Fixed lower boundary (default=
0). Only used ifshape="fixed".- nstart
Starting point for finding the sample size (default=
1).- nstop
Stopping point for finding the sample size (default=
NULL).- sample.size
Logical if sample size should be found as well (default=
TRUE).- N
Number of quadrature points per dimension in the outer integral (default=
20).- parallel
if
TRUE(default), allows parallelisation of the computation via a user-defined strategy specified by means of the functionfuture::plan(). If not set differently, the default strategy issequential, which corresponds to a computation without parallelisation.if
TRUE(default), indicate at which stage the computation is.
Details
This function finds the (approximate) boundaries and sample size of a multi-arm multi-stage study with ordinal or binary endpoints with K active treatments plus control in which all promising treatments are continued at interim analyses as described in Magirr et al (2012). It is a wrapper around the basic mams function to facilitate its use with ordinal and binary endpoints, following ideas of Whitehead & Jaki (2009) and Jaki & Magirr (2013). For a binary endpoint the vector prob has only two elements (success/failure, yes/no, etc.). See mams for further details on the basic methodology.
References
Jaki T., Pallmann P. and Magirr D. (2019), The R Package MAMS for Designing Multi-Arm Multi-Stage Clinical Trials, Journal of Statistical Software, 88(4), 1-25. Link: doi:10.18637/jss.v088.i04
Magirr D., Jaki T. and Whitehead J. (2012), A generalized Dunnett test for multi-arm multi-stage clinical studies with treatment selection, Biometrika, 99(2), 494-501. Link: doi:10.1093/biomet/ass002
Magirr D., Stallard N. and Jaki T. (2014), Flexible sequential designs for multi-arm clinical trials, Statistics in Medicine, 33(19), 3269-3279. Link: doi:10.1002/sim.6183
Pocock S.J. (1977), Group sequential methods in the design and analysis of clinical trials, Biometrika, 64(2), 191-199.
O'Brien P.C., Fleming T.R. (1979), A multiple testing procedure for clinical trials, Biometrics, 35(3), 549-556.
Whitehead J. (1997), The Design and Analysis of Sequential Clinical Trials, Wiley: Chichester, UK.
Examples
# \donttest{
## An example based on the example in Whitehead & Jaki (2009)
# 2-stage design with triangular efficacy and futility boundaries
prob <- c(0.075, 0.182, 0.319, 0.243, 0.015, 0.166)
ordinal.mams(prob=prob, or=3.06, or0=1.32, K=3, J=2, alpha=0.05,
power=0.9, r=1:2, r0=1:2, ushape="triangular",
lshape="triangular")
#>
#> i) find lower and upper boundaries
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#> ii) define alpha star
#> iii) perform sample size calculation
#> (maximum iteration number = 201)
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#> iv) run simulation
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#> Design parameters for a 2 stage trial with 3 treatments:
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#> Stage 1 Stage 2
#> Cumulative sample size per stage (control): 34 68
#> Cumulative sample size per stage (active): 34 68
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#> Maximum total sample size: 272
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#> Stage 1 Stage 2
#> Upper bound: 2.330 2.197
#> Lower bound: 0.777 2.197
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#> Simulated error rates based on 50000 simulations:
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#> Prop. rejecting at least 1 hypothesis: 0.919
#> Prop. rejecting first hypothesis (Z_1>Z_2,...,Z_K) 0.904
#> Prop. rejecting hypothesis 1: 0.912
#> Expected sample size: 167.115
#>
# same example with parallelisation via separate R sessions running in the
# background
future::plan(multisession)
ordinal.mams(prob=prob, or=3.06, or0=1.32, K=3, J=2, alpha=0.05,
power=0.9, r=1:2, r0=1:2, ushape="triangular",
lshape="triangular", parallel=TRUE)
#>
#> i) find lower and upper boundaries
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#> ii) define alpha star
#> iii) perform sample size calculation
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#> iv) run simulation
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#> Design parameters for a 2 stage trial with 3 treatments:
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#> Stage 1 Stage 2
#> Cumulative sample size per stage (control): 34 68
#> Cumulative sample size per stage (active): 34 68
#>
#> Maximum total sample size: 272
#>
#> Stage 1 Stage 2
#> Upper bound: 2.330 2.197
#> Lower bound: 0.777 2.197
#>
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#> Simulated error rates based on 50000 simulations:
#>
#> Prop. rejecting at least 1 hypothesis: 0.918
#> Prop. rejecting first hypothesis (Z_1>Z_2,...,Z_K) 0.902
#> Prop. rejecting hypothesis 1: 0.910
#> Expected sample size: 166.946
#>
future::plan("default")
# }