The ‘BayesianPlatformDesignTimeTrend’ package simulation process requires stopping boundary cutoff screening first (details refers to demo and MAMS-CutoffScreening-GP-tutorial). After the cutoff screening process, we need to record the cutoff value of both efficacy and futility boundary for use in the trial simulation process. The data of each trail replicates will be created sequentially during the simulation. In this tutorial, the cutoff screening process for symmertic boundary will be presented. The example is a four-arm MAMS trial with one control and three treatment arms. The control arm will not be stopped during the trial. The time trend pattern are set to be ‘linear’. The way of time trend impacting the beginning response probability is set to be ‘mult’ (multiplicative). The time trend strength is set to be zero. The randomisation method used is the unfixed Thall’s approach. The early stop boundary is the symmetric OBF boundary. The model used in this example are fixed effect model (the model with only treatment effect and the model with both treatment effect and discrete stage effect). The evaluation metrics are error rate, mean treatment effect bias, rooted MSE, mean number of patients allocated to each arm and mean total number of patients in the trial.

```
ntrials = 1000 # Number of trial replicates
ns = seq(120, 600, 60) # Sequence of total number of accrued patients at each interim analysis
null.reponse.prob = 0.15
alt.response.prob = 0.35
# We investigate the type I error rate for different time trend strength
null.scenario = matrix(
c(
null.reponse.prob,
null.reponse.prob,
null.reponse.prob,
null.reponse.prob
),
nrow = 1,
ncol = 4,
byrow = T
)
# alt.scenario = matrix(c(null.reponse.prob,null.reponse.prob,null.reponse.prob,null.reponse.prob,
# null.reponse.prob,alt.response.prob,null.reponse.prob,null.reponse.prob,
# null.reponse.prob,alt.response.prob,alt.response.prob,null.reponse.prob,
# null.reponse.prob,alt.response.prob,alt.response.prob,alt.response.prob), nrow=3, ncol = 4,byrow=T)
model = "tlr" #logistic model
max.ar = 0.85 #limit the allocation ratio for the control group (1-max.ar < r_control < max.ar)
#------------Select the data generation randomisation methods-------
rand.type = "Urn" # Urn design
max.deviation = 3 # The recommended value for the tuning parameter in the Urn design
# Require multiple cores for parallel running
cl = 2
# Set the model we want to use and the time trend effect for each model used.
# Here the main model will be used twice for two different strength of time trend c(0,0,0,0) and c(1,1,1,1) to investigate how time trend affect the evaluation metrics in BAR setting.
# Then the main + stage_continuous model which is the treatment effect + stage effect model will be applied for strength equal c(1,1,1,1) to investigate how the main + stage effect model improve the evaluation metrics.
reg.inf = "main"
trend.effect = c(0,0,0,0)
result = {
}
OPC = {
}
K = dim(null.scenario)[2]
cutoffindex = 1
trendindex = 1
cutoff.information=demo_Cutoffscreening.GP (
ntrials = ntrials,
# Number of trial replicates
trial.fun = simulatetrial,
# Call the main function
grid.inf = list(
start.length = 10,
grid.min = NULL,
grid.max = NULL,
confidence.level = 0.95,
grid.length = 5000,
change.scale = FALSE,
noise = T,
errorrate = 0.1,
simulationerror = 0.01,
iter.max = 15,
plotornot = FALSE),
# Set up the cutoff grid for screening. The start grid has three elements. The extended grid has fifteen cutoff value under investigation
input.info = list(
response.probs = null.scenario[1,],
#The scenario vector in this round
ns = ns,
# Sequence of total number of accrued patients at each interim analysis
max.ar = max.ar,
#limit the allocation ratio for the control group (1-max.ar < r_control < max.ar)
rand.type = rand.type,
# Which randomisation methods in data generation.
max.deviation = max.deviation,
# The recommended value for the tuning parameter in the Urn design
model.inf = list(
model = model,
#Use which model?
ibb.inf = list(
#independent beta-binomial model which can be used only for no time trend simulation
pi.star = 0.5,
# beta prior mean
pess = 2,
# beta prior effective sample size
betabinomialmodel = ibetabinomial.post # beta-binomial model for posterior estimation
),
tlr.inf = list(
beta0_prior_mu = 0,
# Stan logistic model t prior location
beta1_prior_mu = 0,
# Stan logistic model t prior location
beta0_prior_sigma = 2.5,
# Stan logistic model t prior sigma
beta1_prior_sigma = 2.5,
# Stan logistic model t prior sigma
beta0_df = 7,
# Stan logistic model t prior degree of freedom
beta1_df = 7,
# Stan logistic model t prior degree of freedom
reg.inf = reg.inf,
# The model we want to use
variable.inf = "Fixeffect" # Use fix effect logistic model
)
),
Stop.type = "Early-OBF",
# Use Pocock like early stopping boundary
Boundary.type = "Symmetric",
# Use Symmetric boundary where cutoff value for efficacy boundary and futility boundary sum up to 1
Random.inf = list(
Fixratio = FALSE,
# Do not use fix ratio allocation
Fixratiocontrol = NA,
# Do not use fix ratio allocation
BARmethod = "Thall",
# Use Thall's Bayesian adaptive randomisation approach
Thall.tuning.inf = list(tuningparameter = "Unfixed", fixvalue = 1) # Specified the tunning parameter value for fixed tuning parameter
),
trend.inf = list(
trend.type = "linear",
# Linear time trend pattern
trend.effect = trend.effect,
# Stength of time trend effect
trend_add_or_multip = "mult" # Multiplicative time trend effect on response probability
)
),
cl = 2
)
```

Summary of the output data from cutoff screening example

```
library(ggplot2)
# Details of grid
optimdata=optimdata_sym
# Recommend cutoff at each screening round
nextcutoff = optimdata$next.cutoff
prediction = optimdata$prediction
cutoff=optimdata$cutoff
tpIE=optimdata$tpIE
cutoff=cutoff[1:sum(!is.na(tpIE))]
tpIE=tpIE[1:sum(!is.na(tpIE))]
GP.res = optimdata
prediction = data.frame(yhat = GP.res$prediction$yhat.t1E,
sd = matrix(GP.res$prediction$sd.t1E,ncol=1),
qup = GP.res$prediction$qup.t1E,
qdown = GP.res$prediction$qdown.t1E,
xgrid = GP.res$prediction$xgrid)
GPplot=ggplot(data = prediction) +
geom_ribbon(aes(x = xgrid, ymin = qdown, ymax = qup),col="#f8766d", alpha = 0.5,linetype = 2) +
geom_line(aes(xgrid, yhat),col = "#f8766d") +
geom_point(aes(cutoff[1:sum(!is.na(tpIE))], tpIE[1:sum(!is.na(tpIE))]),
data = data.frame(tpIE=tpIE,cutoff=cutoff),col = "#00bfc4") +
geom_point(aes(nextcutoff, 0.1),
data = data.frame(tpIE=tpIE,cutoff=cutoff),col = "#f8766d") +
geom_hline(yintercept = 0.1,linetype = 2) +
geom_text(aes(x=1,y=0.15,label=paste0("FWER target is 0.1")),hjust=0,vjust=1)+
geom_vline(xintercept = nextcutoff, linetype = 2) +
geom_text(aes(x=6,y=0.8,label=paste0("Next cutoff value is ",round(nextcutoff,3))))+
theme_minimal()+ylab("FWER")+xlab("Cutoff value of the OBF boundary (c*)")+
geom_point(aes(nextcutoff, 0.1),
data = data.frame(tpIE=tpIE,cutoff=cutoff),col = "#f8766d") +
theme(plot.background = element_rect(fill = "#e6dfba"))
print(GPplot)
```