multiarm

Description

multiarm provides functions to assist with the design of single- and
multi-stage multi-arm clinical trials. In either case the available
functions allow for sample size determination, trial simulation,
analytical operating characteristic calculation, and the production of
several informative plots.

Note that an R Shiny graphical user interface is also available for
designing single-stage trials; it can be accessed within R using
multiarm::gui(), or online at
https://mjgrayling.shinyapps.io/multiarm. Additional information on
this app can be found in Grayling and Wason
(2020).

Getting started

You can install the latest development version of multiarm from
Github with:

devtools::install_github("mjg211/multiarm")

An introductory example of how to make use of some of the package’s core
functionality can be found below. More detailed support, for
single-stage designs, is available in the package vignette, which can be
accessed with vignette("single_stage", package = "multiarm"). See also
Grayling and Wason (2020).
For further help, please email michael.grayling@newcastle.ac.uk.

Details

In total, 46 functions are currently available. Their naming conventions
are such that several character strings are joined together, separated
by underscores. The first string indicates the purpose of the function
(i.e., what type of calculation it performs):

• build_###_###(): Build multi-arm clinical trial design objects,
  like those returned by the des_###_###() functions. For use when a
  specific design is of interest.
• des_###_###(): Determine the sample size required by a particular
  type of multi-arm clinical trial design.
• gui(): Provides a graphical user interface to design
  determination.
• opchar_###_###(): Determine the operating characteristics (power,
  family-wise error-rates, etc.) of a supplied multi-arm clinical
  trial design, via multivariate normal integration.
• plot.multiarm_des_###_###(): Produce informative plots (power,
  false discovery rate curves, etc.) relating to a supplied multi-arm
  clinical trial design.
• sim_###_###(): Empirically estimate the operating characteristics
  (power, family-wise error-rates, etc.) of a supplied multi-arm
  clinical trial design, via simulation.

The second indicates the design:

• ###_dtl_###(): Relate to multi-stage drop-the-losers designs. See,
  e.g., Wason et al
  (2017).
• ###_gs_###(): Relate to group-sequential multi-arm multi-stage
  designs. See, e.g., Magirr et al
  (2012).
• ###_ss_###(): Relate to single-stage designs. See, e.g., Grayling
  and Wason (2020).

The third indicates what type of outcome the function is for:

• ###_###_bern(): Assume a Bernoulli distributed primary outcome.
• ###_###_norm(): Assume a normally distributed primary outcome.
• ###_###_pois(): Assume a Poisson distributed primary outcome.

Example: Single-stage design for a normally distributed outcome

Typically, a des_###_###() function would be used first to identify a
design for the trial parameters of interest. For example, consider
designing a single-stage trial for:

• Three experimental treatment arms (see K).
• Desiring a family-wise error-rate of at most 5%, controlling using
  Dunnett’s correction (see alpha and correction).
• Desiring marginal power to reject each null hypothesis of 80% for a
  clinically relevant difference of 1 (see beta, delta1, and
  power).
• Assuming the standard deviation of all responses is 1 (see sigma).
• Allocating patients equally to each arm (see ratio).

To compute the design, we would run:

des <- des_ss_norm(K          = 3,
                   alpha      = 0.05,
                   beta       = 0.2,
                   delta1     = 1,
                   sigma      = rep(1, 4),
                   ratio      = rep(1, 3),
                   correction = "dunnett",
                   power      = "marginal")

Then, the total required sample size is:

des$N
#> [1] 67.42534

In addition, the operating characteristics under the global null,
global alternative, and each of the least favourable configurations,
can be accessed with:

des$opchar
#> # A tibble: 5 x 20
#>    tau1  tau2  tau3   Pdis    Pcon     P1     P2     P3 FWERI1  FWERI2  FWERI3
#>   <dbl> <dbl> <dbl>  <dbl>   <dbl>  <dbl>  <dbl>  <dbl>  <dbl>   <dbl>   <dbl>
#> 1     0     0     0 0.0501 0.00109 0.0196 0.0196 0.0196 0.0501 0.00774 0.00109
#> 2     1     1     1 0.950  0.611   0.800  0.800  0.800  0      0       0      
#> 3     1     0     0 0.800  0.00330 0.800  0.0196 0.0196 0.0360 0.00330 0      
#> 4     0     1     0 0.800  0.00330 0.0196 0.800  0.0196 0.0360 0.00330 0      
#> 5     0     0     1 0.800  0.00329 0.0196 0.0196 0.800  0.0360 0.00330 0      
#> # … with 9 more variables: FWERII1 <dbl>, FWERII2 <dbl>, FWERII3 <dbl>,
#> #   PHER <dbl>, FDR <dbl>, pFDR <dbl>, FNDR <dbl>, Sens <dbl>, Spec <dbl>

Useful plots can also be produced with plot.multiarm_des_ss_norm() as
follows:

plot(des)

References

Grayling MJ, Wason JMS (2020) A web application for the design of
multi-arm clinical trials. BMC Cancer 20:80. DOI:
10.1186/s12885-020-6525-0.
PMID: 32005187.

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. DOI:
10.1093/biomet/ass002.

Wason J, Stallard N, Bowden J, Jennison C (2017) A multi-stage
drop-the-losers design for multi-arm clinical trials. Stat Meth Med
Res 26(1):508–524. DOI:
10.1177/0962280214550759.
PMID: 25228636.