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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.

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.


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)


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)


Dunnett, Charles W. 1955. “A Multiple Comparison Procedure for Comparing Several Treatments with a Control.” Journal of the American Statistical Association 50 (272): 1096–1121.
Jaki, Thomas, Philip Pallmann, and Dominic Magirr. 2019. “The R Package MAMS for Designing Multi-Arm Multi-Stage Clinical Trials.” Journal of Statistical Software 88 (4).
Pushpakom, Sudeep P, Claire Taylor, Ruwanthi Kolamunnage-Dona, Catherine Spowart, Jiten Vora, Marta García-Fiñana, Graham J Kemp, et al. 2015. “Telmisartan and Insulin Resistance in HIV (TAILoR): Protocol for a Dose-Ranging Phase II Randomised Open-Labelled Trial of Telmisartan as a Strategy for the Reduction of Insulin Resistance in HIV-Positive Individuals on Combination Antiretroviral Therapy.” BMJ Open 5 (10): e009566.