ordinal.mams {MAMS}

Function to design multi-arm multi-stage studies with ordinal or binary endpoints

Description

The 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, N=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).

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 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.

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.

Author(s)

Philip Pallmann

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.

See Also

print.MAMS, summary.MAMS, plot.MAMS, mams, MAMS.

Examples

## 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")
# 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)
future::plan("default")