Author: Ziyan Wang

# MAMS-CutoffScreening-GP-Symmetric-tutorial

#### Ziyan Wang

    library(BayesianPlatformDesignTimeTrend)

## Four arm trial cutoff screening

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)