new.bounds {MAMS} | R Documentation |
The function determines updated boundaries of a multi-arm multi-stage study based on observed number of observations per arm.
new.bounds(K=3, J=2, alpha=0.05, nMat=matrix(c(10, 20), nrow=2, ncol=4), u=NULL, l=NULL, ushape="obf", lshape="fixed", ufix=NULL, lfix=0, N=20)
K |
Number of experimental treatments (default=3). |
J |
Number of stages (default=2). |
alpha |
One-sided familywise error rate (default=0.05). |
nMat |
Jx(K+1) dimensional matrix of observed/expected sample sizes. Rows correspond to stages and columns to arms. First column is control (default: 2x4 matrix with 10 subjects per stage and arm). |
u |
Vector of previously used upper boundaries (default=NULL). |
l |
Vector of previously used upper boundaries (default=NULL). |
ushape |
Shape of upper boundary. Either a function specifying the shape or one of |
lshape |
Shape of lower boundary. Either a function specifying the shape or one of |
ufix |
Fixed upper boundary (default=NULL). Only used if |
lfix |
Fixed lower boundary (default=0). Only used if |
N |
Number of quadrature points per dimension in the outer integral (default=20). |
This function finds the boundaries for a given matrix of sample sizes in multi-arm multi-stage study with K active treatments plus control. The vectors u
and l
are the boundaries used so far while u.shape
and l.shape
specify the shape to the boundaries for the remaining analysis. By specifying u
and l
as NULL
, a design using only the shapes given by ushape
and lshape
can be found for any sample sizes per stage and arm.
The shape of the boundaries (ushape
, lshape
) are either using the predefined shapes following Pocock (1977), O'Brien & Fleming (1979) or the triangular Test (Whitehead, 1997) using options "pocock"
, "obf"
or "triangular"
respectively, are constant (option "fixed"
) or supplied in as a function. If a function is passed it should require exactly one argument specifying the number of stages and return a vector of the same length. The lower boundary shape is required to be non-decreasing while the upper boundary shape needs to be non-increasing. If a fixed lower boundary is used, lfix
must be smaller than Phi(1-alpha)/2 to ensure that it is smaller than the upper boundary.
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. |
power |
Power under least favorable configuration. |
rMat |
Matrix of allocation ratios. First row corresponds to control and second row to experimental treatments. |
Thomas Jaki and Dominic Magirr
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), pp. 1-25. doi: 10.18637/jss.v088.i04 (URL: http://doi.org/10.18637/jss.v088.i04)
Magirr D, Jaki T, Whitehead J (2012) A generalized Dunnett Test for multi-arm multi-stage clinical studies with treatment selection. Biometrika, 99(2), 494-501.
Magirr D, Stallard N, Jaki T. (2014) Flexible sequential designs for multi-arm clinical trials. Statistics in Medicine. 33(19):3269-3279.
Pocock SJ (1977) Group sequential methods in the design and analysis of clinical trials. Biometrika, 64(2), 191-199.
O'Brien PC, Fleming TR (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.
# Note that some of these examples may take a few minutes to run # 2-stage design with O'Brien & Fleming efficacy and zero futility boundary with # equal sample size per arm and stage. Results are equivalent to using # mams(K=4, J=2, alpha=0.05, power=0.9, r=1:2, r0=1:2, ushape="obf", lshape="fixed", # lfix=0, sample.size=FALSE) new.bounds(K=4, J=2, alpha=0.05, nMat=matrix(c(10, 20), nrow=2, ncol=5), u=NULL, l=NULL, ushape="obf", lshape="fixed", lfix=0) # A 2-stage design that was designed to use an O'Brien & Fleming efficacy and # zero futility boundary with equal sample size per arm and stage (n=14). # The observed sample size after stage one are 10, 10, 18, 10, 13 for each arm # while the original upper bounds used are (3.068, 2.169) for stage 1. # The updated bounds are (3.068, 2.167). new.bounds(K=4, J=2, alpha=0.05, nMat=matrix(c(10, 28, 10, 28, 18, 28, 10, 28, 13, 28), nrow=2, ncol=5), u=3.068, l=0, ushape="obf", lshape="fixed", lfix=0)