help for nstagebinMRC Clinical Trials Unit at UCL

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

Syntax

nstagebin,
required_options optional_options

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

accrate(numlist) overall accrual rate in each stage

alpha(numlist) one-sided alpha (type 1 error probability) for each stage

power(numlist) power (one minus type 2 error probability) for each stage

arms(numlist) number of arms recruiting at each stage (including control arm)

theta0(# [#]) target treatment effect under H0 for the I and D outcomes

theta1(# [#]) target treatment effect under H1 for the I and D outcomes

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

required only if intermediate (I) and definitive (D) outcomes differ
ppvc(#) positive predictive value for the control arm

ppve(#) positive predictive value for each experimental arm

optional
aratio(#) allocation ratio (number of patients allocated to each experimental arm per control arm patient)

fu(# [#]) length of follow-up period for the I and D outcomes

extrat(#) delay between observing last required outcome for each analysis and next stage of the trial

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

tunit(#) code for units of trial time

probs reports probabilities of the number of arms reaching each stage

ess reports the expected sample sizes

nofwer suppress the calculation of the familywise error rate

reps(#) specifies the number of replications used in the simulation to calculate the FWER

seed specifies the initial value of the random-number seed used in the simulation to calculate the FWER which is reproducible

Description

nstagebin specifies the design (sample size,
duration and overall pairwise operating characteristics) of a multi-arm,
multi-stage (MAMS) trial using a binary intermediate (I) outcome
at the interim stages and a binary definitive (D) outcome
at the final stage, both analysed using an absolute difference
in proportions. See Bratton, Phillips & Parmar (2013) for a description
of the design and Royston, Barthel, Parmar, Oskooei & Isham (2011) for
a description of a similar MAMS design for time-to-event outcomes.

Options

Required

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

accrate(numlist) specifies the rate per unit of time
(see tunit()) at which patients enter the trial during each stage.
The patients are assumed to be allocated in the ratio
(control arm:experimental arm: ...) of 1:p:...:p, where p
is the allocation ratio defined by aratio().

alpha(numlist) specifies the one-sided significance level at each
stage. For the first J - 1 stages each experimental arm is compared with the
control on the intermediate outcome, whereas at the sth stage the
comparison is on the primary outcome. Experimental arms pass a particular
stage of the trial if their observed treatment effect is significant at the
corresponding pre-specified one-sided significance level.

power(numlist) specifies the power (one minus the type 2 error
probability) for each pairwise comparison at each stage. See also alpha().

arms(numlist) specifies the number of arms assumed to be
actively recruiting patients at each stage. The number at stage 2 and
subsequently cannot exceed the number at stage 1, since arms can only
be 'dropped' not added. For example, arms(4 3 2) would say that
in a 3-stage trial of 4 arms only 3 continued to the second stage and
2 to the final stage.

theta0(# [#]) specifies the target 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 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.

Required only if I and D outcomes differ

ppvc(#) specifies the positive predictive value for the control arm,
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).

ppve(#) specifies the positive predictive value for the experimental arms
(see also ppvc()).

Optional

aratio(#) specifies the allocation ratio (number of patients allocated
to each experimental arm per control arm patient). Default # is 1 (equal
allocation to all arms).

fu(# [#]) specifies the length of the follow-up period (in units of time
- see tunit()) for the I-outcome and D-outcome, respectively.
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 for either outcome).

extrat(#) specifies the delay in units of trial time (see tunit())
between observing the final required outcome for an analysis and the beginning of
the next stage. This delay incorporates time for data cleaning, analysis and the
various committee meetings that are usually required. Default # is 0 (no delay).

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).

tunit(#) defines the code for units of trial time. The codes are 1 = one year, 2 = 6 months,
3 = one quarter (3 months), 4 = one month, 5 = one week, 6 = one day, 7 = unspecified. tunit()
has no influence on the computations and is for information only. Default # is 1 (one year).

probs reports probabilties of the number of arms reaching stages 2,...,J of the trial
under the global null (no arms effective) and the global alternative (all arms effective) hypotheses.

ess reports the expected sample size of the trial when either none or all of the experimental treatment arms are effective.

nofwer suppresses the calculation of the maximum familywise error rate of the trial (probability of making at least one type I error at the end of the trial under the global null hypothesis).

reps(#) specifies the number of replications used in the simulation to calculate the FWER. The default value is 250000 replicates.

seed(#) specifies the initial value of the random-number seed used in the simulation to calculate the FWER which is reproducible.

Remarks

nstagebin reports the sample size required for each analysis and the cumulative number of patients allocated to each remaining treatment arm at the end of each stage. Also reported is the cumulative number of patients recruited to the trial at the end of each stage (including those patients allocated to arms dropped in previous stages).

Examples

Example of a 4-arm 3-stage trial where the I-outcome and D-outcome is the same 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%. One-sided significance
levels of 30%, 15% and 2.5% and powers of 95%, 95% and 90% are used in the 1st, 2nd and 3rd stages respectively. All four arms are assumed to continue to the second stage of the trial, and only two are assumed to continue to the final stage.

. nstagebin, nstage(3) accrate(10 10 10) alpha(0.3 0.15 0.025)
power(0.95 0.95 0.90) arms(4 4 2) theta0(0)
theta1(0.15) ctrlp(0.8) fu(1) ltfu(0.1) tunit(4)

Example of a 6-arm 4-stage trial where the I-outcome and D-outcome differ and have target treatment effects of 15% and 10% respectively. Follow-up on the I-outcome is 0.25 years (13 weeks) and 1 year for the D-outcome and the loss-to-follow-up
rates are assumed to be 10% and 20% respectively. The positive predictive value is assumed to be 80% for the control and experimental arms. A control:experimental allocation ratio of 2:1 is used.

. nstagebin, nstage(4) accrate(200 200 300 600) alpha(0.5 0.25 0.1 0.05)
power(0.95 0.95 0.95 0.90) arms(6 5 4 2) theta0(0 0)
theta1(0.15 0.1) ctrlp(0.7 0.6) fu(0.25 1) ltfu(0.1 0.2)
aratio(0.5) ppvc(0.8) ppve(0.8)

Stored results

nstage stores the following in r():

Scalars:

r(WSj) = stage specific (overall) pairwise power
r(ASj) = stage specific (overall) pairwise alpha
r(totSj) = cumulative number of recruited patients across all arms (stage j)
r(totXSj) = cumulative number of recruited patients in each experimental arm (stage j)
r(totCSj) = cumulative number of recruited patients in control arm (stage j)
r(totactSj) = cumulative number of recruited patients in all active arms (stage j)
r(nSj) = cumulative number of patients across all arms required for analyses (stage j)
r(nXSj) = cumulative number of patients in each experimental arm required for analysis (stage j)
r(nCSj) = cumulative number of patients in control arm required for analysis (stage j)
r(tSj) = expected time of stage j analysis (in specified units)
r(maxfwer) = maximum FWER
r(se_fwer) = SE(FWER)
r(fwer) = Familywise type I error rate

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