# Single-stage design

`single-stage_design.Rmd`

In this vignette we showcase some uses of the **MAMS**
package and how to interpret the corresponding R output.

### TAILoR Study

The TAILoR study (Pushpakom et al. 2015) serves as
the motivating example, and so we consider a design that evaluates three
different experimental treatment arms against control, using a one-sided
type I error rate of 5% and 90% power. The interesting effect size is
set to \(\mathrm{p} = 0.65\), which
corresponds to an effect of \(δ =
0.545σ\) on the traditional scale. The uninteresting treatment
effect is chosen as \(\mathrm{p}_0 =
0.55\) (\(δ_0 = 0.178σ\)).
**MAMS** allows the user to choose whichever
parameterization they prefer for specifying the effect sizes.

###
`mams()`

function

Designing studies including finding the boundaries of the design and
the required sample size can be achieved with the function
`mams`

. The parameters of the function correspond to the
definition in Section 2 (Jaki, Pallmann, and Magirr 2019) so that
`K`

, e.g., specifies the number of experimental treatments
that are to be compared to control, and `J`

the number of
stages. We begin by considering a single-stage design
(`J = 1`

), which corresponds to a design based on a standard
Dunnett test (Dunnett
1955) involving `K = 3`

experimental treatments.
We use equal allocation between treatment arms, which is specified via
`r=1`

for the experimental arms and `r0=1`

for
control.

library(MAMS)

set.seed(2910)

m1 <- mams(K = 3, J = 1, p = 0.65, p0 = 0.55, r = 1, r0 = 1, alpha =
0.05, power = 0.9)

An overview of the design is displayed with `print(m1)`

or
`summary(m1)`

or simply `m1`

.

m1

The output produced specifies the number of patients required on
control and each treatment arm as well as the boundaries of the design.
A total of 316 patients, 79 on control and 79 on each of the 3
experimental treatments, are required for this study. The null
hypothesis for treatment k can be rejected if the corresponding test
statistic is larger than 2.062. The same design can also be specified on
the scale of traditional effect sizes rather than probabilities, by
setting `p`

and `p0`

to `NULL`

and
specifying values for `delta`

, `delta0`

, and
`sd`

. The output will be exactly the same as for
`m1`

.

m1d <- mams(K = 3, J = 1, p = NULL, p0 = NULL, delta = 0.545, delta0 = 0.178, sd = 1, r = 1, r0 = 1, alpha = 0.05, power = 0.9)

m1d

In the remainder of this section we will specify all effect sizes on the probability scale, but converting them is straightforward in R:

pnorm(0.545 / sqrt(2))

qnorm(0.65) * sqrt(2)

## References

*Journal of the American Statistical Association*50 (272): 1096–1121. https://doi.org/10.1080/01621459.1955.10501294.

*R*Package

**MAMS**for Designing Multi-Arm Multi-Stage Clinical Trials.”

*Journal of Statistical Software*88 (4). https://doi.org/10.18637/jss.v088.i04.

*BMJ Open*5 (10): e009566. https://doi.org/10.1136/bmjopen-2015-009566.