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Traditional two-arm randomized control trials are not an optimal choicewhen multiple experimental arms are available for testing efficacy. Insuch situations, a multiple-arm trial should be preferred, which allowssimultaneous comparison of multiple experimental arms with a commoncontrol and provides substantial efficiency advantage. In multi-armtrials, several arms are monitored in a group sequential fashion, withineffective arms being dropped out of the study.gsMAMS R packageprovides a good platform for designing and planning phase-II drugtrials(e.g. TAILoR trial (continuous outcome), ASCLEPIOS trial(ordinaloutcome)) with multiple treatment arms. The package providesfunctionality for designing trials with continuous, ordinal and survivaloutcomes which offers great flexibility and makes it a comprehensivetoolkit to handle different kinds of trials. It provides functions toobtain sample size, and efficacy and futility boundaries for multiplestages and multiple experimental arms. It also provides functions thatgenerate operating characteristics for designing the trials ofcontinuous, ordinal, and survival outcomes.

The stable version ofgsMAMS, v0.7.2, is available on CRAN:

# install.packages("gsMAMS")set.seed(1234)library(gsMAMS)

For the continuous outcome, we will consider TAILoR trial, which is aphase II trial, and it compares three doses of telmisartan (20, 40,80mg) with no intervention (control) for the reduction of insulinresistance in human immunodeficiency virus-positive patients receivingcombination antiretroviral therapy. The primary outcome measure is areduction in mean homeostasis model assessment of insulin resistance(HOMA-IR) score at 24 weeks. The standardized desirable and minimaleffect sizes for efficacy are set as δ(1) = 0.545 for 80mg group andδ(0) = 0.178 for 20 and 40 mg groups, respectively, for the trialdesign. The sample size calculation is based on a one-sided type I errorof 5% and a power of 90%. Based on the trial characteristics, we willdesign the trial for a two-stage design.

#For designing a trial with continuous outcome.design_cont(delta0=0.178,delta1=0.545,alpha=0.05,beta=0.1,k=3,frac= c(0.5,1))#> $`Sample size`#>                                            Stage 1 Stage 2#> Cumulative sample size for treatment group      40      79#> Cumulative sample size for control group        40      79#>#> $`Maximum total sample size for the trial`#> [1] 316#>#> $`Boundary values`#>             Stage 1 Stage 2#> Lower bound   0.006   2.062#> Upper bound   2.910   2.062

The design output shows the cumulative sample size for treatment andcontrol groups at each stage. The SCPRT lower and upper boundaries are(0.006, 2.062) and (2.91, 2.062) respectively. Based on the designparameters, the first interim analysis can be conducted after theenrollment of 40 patients in the control arm. If the test statistic$Z_{k,l}<0.006$, the$k_{th}$ arm is rejected for futility at$1^{st}$stage and the trial continues with the remaining treatment arms and thecontrol. If the test statistic 0.006$\le$$Z_{k,l}$$\le$ 2.91 for$k$=1,2,3 then the trial continues to the next stage and 39 patients arefurther enrolled per arm. If$Z_{k,1} >2.91$ for some$k$, the trial isterminated and the arm with maximum value of$Z_{k,1}$,$k$=1,2,3 wouldbe recommend for further study.

The operating characteristics of the trial can be generated using theop_power_cont() functions for power under alternative hypothesis.

#Generating operating characteristics of the trial.op_power_cont(alpha=0.05,beta=0.1,p=3,frac= c(0.5,1),delta0=0.178,delta1=0.545,nsim=10000,seed=10)#> $Power#> [1] 0.893#>#> $`Stagewise Power`#>  look1  look2#> 0.3126 0.5804#>#> $`Stopping probability under alternative`#>  look1  look2#> 0.3258 0.6742#>#> $`Probability of futility under alternative`#>  look1  look2#> 0.0035 0.0821#>#> $`Average sample size used per arm under alternative`#> [1] 62.652

Based on the simulation results, the probability of success/power at thefirst stage is 31.26% and at the second stage is around 58.04%.Therefore, the overall power is approximately 90%. The sample sizerequired for the trial was 79 patients per arm but the trial used aroundan average of 62 subjects per arm. The stopping probability should addup to 1 which is the case here and under alternate configuration, theprobability of futility is approximately 8.5% which is less than 10%type II error. The reason is that the type II error comes from bothfailing to find any efficacious arm (futility) and finding the lessefficacious arm as the most efficacious arm. The latter part was notincluded when the probability of futility was calculated.

For detailed usage of the package, please see the paper in therepository.

If you want to contribute to the code or file an issue, we prefer themto be handled via GitHub (link to the issues page forgsMAMShere). You can alsocontact us via email (see the DESCRIPTION file).