Reproducibility

Results of the MAMS package for studies involving more than 2 stages are seed-dependent (as the Gaussian quadrature integration of the multivariate normal distribution relies on probabilities estimated by means of the randomised Quasi-Monte-Carlo procedure of Genz and Bretz in mvtnorm::pmvnorm()).

Results are reproducible if a seed is set before the evaluation of a function of the MAMS package (typically by means of the function set.seed):

• When parallel=TRUE, the future package assigns independent streams of L’Ecuyer pseudo-random numbers to each parallelised task, allowing results to be reproducible when a seed is set, even when using a different parallelisation strategy and/or a different number of workers.
  
• When parallel=FALSE, the random number generation is handled by base R directly instead of by the future package, so that, if the number of stages is larger than 2, evaluations using the same seed will not lead to the same exact results with parallel=FALSE and parallel=TRUE.

Sequential computation

set.seed(2910)
m_seq <- mams(K = 3, J = 3, p = 0.65, p0 = 0.55, r = 1:3, r0 = 1:3, alpha = 0.05, 
              power = 0.9, parallel = FALSE)

m_seq

## Design parameters for a 3 stage trial with 3 treatments
## 
##                                             Stage 1 Stage 2 Stage 3
## Cumulative sample size per stage (control):      29      58      87
## Cumulative sample size per stage (active):       29      58      87
## 
## Maximum total sample size:  348 
## 
##              Stage 1 Stage 2 Stage 3
## Upper bound:   3.611   2.554   2.085
## Lower bound:   0.000   0.000   2.085

Parallel computation

set.seed(2910)
m_par <- mams(K = 3, J = 3, p = 0.65, p0 = 0.55, r = 1:3, r0 = 1:3, alpha = 0.05, 
              power = 0.9, parallel = TRUE)

m_par

## Design parameters for a 3 stage trial with 3 treatments
## 
##                                             Stage 1 Stage 2 Stage 3
## Cumulative sample size per stage (control):      29      58      87
## Cumulative sample size per stage (active):       29      58      87
## 
## Maximum total sample size:  348 
## 
##              Stage 1 Stage 2 Stage 3
## Upper bound:   3.612   2.554   2.085
## Lower bound:   0.000   0.000   2.085

The results of sequential and parallel computation in this case slightly differ for the upper bound at Stage 1.