help for nstagebinoptMRC Clinical Trials Unit at UCL

Admissible multi-arm, multi-stage (MAMS) trial designs for binary outcomes

Syntax

nstagebinopt,
required_options optional_options

required
nstage(#) # = J, the number of stages in the trial

arms(#) # = K+1, the number of arms at the start of the study (including control arm)

alpha(#) overall type I error rate for each arm or for the trial as a whole (see fwer)

power(#) overall pairwise power

theta0(# [#]) absolute risk difference under H0 for the I and D outcomes

theta1(# [#]) minimum target risk difference under H1 for the I and D outcomes

ctrlp(# [#]) control arm event rate for the I and D outcomes

aratio(numlist) allocation ratios (number of patients allocated to each experimental arm per control arm patient) to consider in the search procedure

required only if intermediate (I) and definitive (D) outcomes differ
ppv(#) positive predictive value P(D=1|I=1) for all arms in the trial

optional
save(filename) name of file in which to save the admissible designs

fwer specify that the familywise error rate of the trial should be controlled at the level specified in alpha()

pi(#) minimum proportion of the maximum control arm sample size that should be recruited to the control in each stage

p(numlist) define which alpha-functions should be used in the search procedure

ltfu(# [#]) loss-to-follow-up rate for the I and D outcomes

fu(#) length of follow-up period for the I outcome

accrate(numlist) overall accrual rate in each stage

acc(#) maximum deviation in alpha and power of feasible designs from values specified in alpha() and power() respectively

plot plot the expected sample sizes used in the loss function for each admissible design

Description

nstagebinopt searches for (K+1)-arm J-stage designs with binary intermediate (I)
and definitive (D) outcomes which have the desired overall type I error rate and power
(feasible designs). The stagewise operating characteristics of feasible designs which minimise
the Bayesian loss function (1-q)E(N|H0)+qE(N|HK) for some q between 0 and 1 are then reported.
Here E(N|H0) is the expected sample size under the hypothesis that all arms in the study are
ineffective and E(N|HK) is the expected sample size assuming all arms are effective.

Options

Required

nstage(#) specifies J, the number of stages in the trial.

arms(#) specifies the total number of arms (including the control arm} at
the start of the study.

alpha(#) specifies the desired overall one-sided type I error rate of
each pairwise comparison in the trial. If the fwer option is specified the value
specified in alpha() is the desired familywise error rate of the study.

power(numlist) specifies the overall power for each pairwise comparison
of the study.

theta0(# [#]) specifies the absolute difference in
proportions under the null hypothesis for the I-outcome and D-outcome,
respectively. Typically these values are both 0. If I and D are the same
then only one value needs specifying.

theta1(# [#]) specifies the minimum target absolute difference in
proportions under the alternative hypothesis for the I-outcome and
D-outcome, respectively. Typically these values are either equal or the
target difference is smaller for the D-outcome. If I and D are the same
then only one value needs specifying.

ctrlp(# [#]) specifies the assumed control event rate for the
I-outcome and D-outcome, respectively. If I and D are the same
then only one value needs specifying.

aratio(numlist) specifies the allocation ratios (number of patients allocated
to each experimental arm per control arm patient) that are to be considered in the
search procedure for admissible designs. Allocation ratios such as 1 (equal
allocation to all arms) and/or 0.5 (1 patient allocated to each experimental arm
for every 2 patients allocated to control) are often used. Note that allocating
a higher proportion of patients to control can decrease sample size requirements
if evaluating more than one experimental arm.

Required only if I and D outcomes differ

ppv(#) specifies the positive predictive value,
that is, the probability of a patient experiencing the D-outcome given that
they have also experienced the I-outcome: P(D=1|I=1). This value is assumed
to be the same for all arms in the study.

Optional

save(filename) save the set of admissible designs in a dataset.

fwer specify that the familywise error rate (FWER) should be controlled
at the level specified in alpha() rather than the type I error rate
for each pairwise comparison. The familywise error rate is the probability
of making at least one type I error (false positive) at the end of the trial.

pi(#) specifies the minimum proportion of the maximum control arm sample size that
should be recruited during each stage of the study. For instance, if the
maximum control arm sample size is 500 and # = 0.1 then at least 50 patients will be
recruited to the control arm during each stage. A higher value of # will increase the speed of
the search procedure but may result in finding less efficient admissible designs.
Default # is 0.1.

p(numlist) defines which alpha-functions are to be used in the search procedure. Default
numlist is 0, 0.25, 0.5 if I=D and 0, 0.25, 0.5, 0.75, 1 if I and D differ.

ltfu(# [#]) specifies the loss-to-follow-up rate for the I outcome
and D outcome respectively. Typically the loss-to-follow-up rate is
larger for the D outcome than the I-outcome. If I and D are the same then only
one value needs specifying. Default # is 0 (no loss-to-follow-up for either
outcome).

fu(#) specifies the length of the follow-up period (in units of time)
for the I outcome. The follow-up period on the D outcome should be the same
or longer than that on the I outcome. If I and D are the same then only one
value needs specifying. Default # is 0 (no follow-up period, i.e. outcomes
observed immediately after randomisation).

accrate(numlist) specifies the rate per unit of time
at which patients enter the trial in each stage of the trial. Accrual rates should be on the
same time-scale as used for fu(). This option only needs specifying
if fu() is specified.

acc(#) specifies the maximum deviation in overall alpha and power allowed in feasible
designs from the desired values. Default # is 0.0005.

plot produces a plot of the expected sample sizes under H0 and HK for each admissible design.

Remarks

nstagebinopt outputs the stagewise operating characteristics of admissible multi-arm multi-stage designs which minimise the loss function (1-q)E(N|H0)+qE(N|HK) for some q between 0 and 1. These design parameters can then be entered into the nstagebin program to see each design in more detail.

Examples

Example in which a 4-arm 3-stage trial needs to be designed with overall pairwise type I error rate of 2.5% and overall pairwise power of
90%. The I and D outcomes are identical and has a follow-up period of 1 month. The accrual rate is assumed to be 10 patients/month in each
stage and the loss-to-follow-up rate is 10%. The minimum target difference under the alternative hypothesis is 15% and the control arm event rate is anticipated to be 40%. Only a 1:1 allocation ratio is to be considered.

. nstagebinopt, nstage(3) arms(4) alpha(0.025) power(0.90)
theta0(0) theta1(0.15) ctrlp(0.4) ltfu(0.1)
fu(1) accrate(10 10 10) aratio(1)

Example in which a 6-arm 4-stage trial needs to be designed with 5% familywise error rate and 80% pairwise power. The I and D outcomes
differ and have minimum targeted treatment effects of 15% and 10% respectively. Follow-up on the I-outcome is 0.25 years (13 weeks) and the loss-to-follow-up rates are assumed to be 10% and 20% for I and D respectively. The positive predictive value is assumed to be 80% for each arm. A control:experimental allocation ratio of 2:1 is used.

. nstagebinopt, nstage(4) arms(6) alpha(0.05) power(0.8)
theta0(0 0) theta1(0.15 0.1) ctrlp(0.7 0.6)
fu(0.25) ltfu(0.1 0.2) aratio(0.5)
ppv(0.8) accrate(200 200 300 600) fwer

References

Choodari-Oskooei B, Bratton DJ, Parmar MKB. 2023. Facilities for optimising and designing multi-arm multi-stage (MAMS) randomised controlled trials with binary outcomes. Stata Journal 23(3).

Choodari-Oskooei, B., M.R. Sydes, P. Royston, M.K.B Parmar. 2022.
Multi-arm Multi-stage (MAMS) Platform Randomized Clinical Trials.
Principles and Practice of Clinical Trials. Piantadosi, S., Meinert, C.L. (eds) Springer, Cham.

Bratton DJ, Phillips PPJ, Parmar MKB. 2013.
A multi-arm multi-stage clinical trial design for binary outcomes with application to tuberculosis.
BMC Medical Research Methodology 13:139.

Royston P, Barthel FMS, Parmar MKB, Choodari-Oskooei B, Isham V. 2011. Designs for clinical trials with time-to-event outcomes based on stopping guidelines for lack of benefit. Trials 12:81.

Author

Babak Choodari-Oskooei, MRC Clinical Trials Unit at UCL, London.

b.choodari-oskooei@ucl.ac.uk

Daniel Bratton, GlaxoSmithKline, Stevenage, UK.

daniel.x.bratton@gsk.com

Mahesh KB Parmar, MRC Clinical Trials Unit at UCL, London.

m.parmar@ucl.ac.uk