Function to design multi-arm multi-stage studies with time-to-event endpoints

The function determines (approximately) the boundaries of a multi-arm multi-stage study with time-to-event endpoints for a given boundary shape and finds the required number of events.

Usage

tite.mams(hr=1.5, hr0=1.1, 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, N=20,
           parallel=TRUE, print=TRUE)

Arguments

hr: Interesting treatment effect on the scale of hazard ratios (default=2).
hr0: Uninteresting treatment effect on the scale of hazard 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).
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 function future::plan(). If not set differently, the default strategy is sequential, which corresponds to a computation without parallelisation.
print: 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 time-to-event 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 time-to-event endpoints, following ideas of Jaki & Magirr (2013). Note that the sample size is calculated as the required number of events, from which the total sample size can be estimated (e.g., Whitehead 2001). See ?mams for further details on the basic methodology.

Value

An object of the class MAMS containing the following components:

l: Lower boundary.
u: Upper boundary.
n: Sample size on control in stage 1.
N: Maximum total sample size.
K: Number of experimental treatments.
J: Number of stages in the trial.
alpha: Familywise error rate.
alpha.star: Cumulative familywise error rate spent by each analysis.
power: Power under least favorable configuration.
rMat: Matrix of allocation ratios. First row corresponds to control while subsequent rows are for the experimental treatments.

References

Jaki T. and Magirr D. (2013), Considerations on covariates and endpoints in multi-arm multi-stage clinical trials selecting all promising treatments, Statistics in Medicine, 32(7), 1150-1163. Link: doi:10.1002/sim.5669

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

Whitehead J. (2001), Predicting the duration of sequential survival studies, Drug Information Journal, 35(4), 1387-1400.

Author

Philip Pallmann, Dominic Magirr

Examples

# \donttest{
## An example 2-stage design with triangular efficacy and futility boundaries
tite.mams(hr=2, hr0=1.5, 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
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#> Design parameters for a 2 stage trial with 3 treatments
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#>                                                  Stage 1 Stage 2
#> Cumulative number of events per stage (control):      56     112
#> Cumulative number of events per stage (active):       56     112
#> 
#> Maximum total number of events:  448 
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#>              Stage 1 Stage 2
#> Upper bound:   2.330   2.197
#> Lower bound:   0.777   2.197
# }