Single-stage design
single-stage_design.RmdIn 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)