The 'BayesianPlatformDesignTimeTrend' package.

Description

This package simulates the multi-arm multi-stage or platform trial with bayesian approach using the 'rstan' package, which provides the R interface for to the stan. The package uses Thall's and Trippa's randomisation approach for Bayesian adaptive randomisation. In addition, the time trend problem of platform trial can be studied in this package. There is a demo for multi-arm multi-stage trial for two different null scenario in this package.

References

Stan Development Team (2020). RStan: the R interface to Stan. R package version 2.21.2. https://mc-stan.org

ARmethod

Description

This function adjusts the posterior randomisation probability for each arm using many approaches. Currently Thall's approach and Trippa's approach are used. Double biased coin and other method will be added in the next version.

Usage

ARmethod(
  BARmethod,
  group,
  stats,
  post.prob.btcontrol,
  K,
  n,
  tuningparameter = NA,
  c = NA,
  a = NA,
  b = NA,
  post.prob.best,
  max.ar = NA,
  armleft,
  treatmentindex
)

Arguments

Value

randomprob: The vector of adjusted randomisation probability to each arm

Author(s)

Ziyan Wang

References

Bayesian adaptive randomized trial design for patients with recurrent glioblastoma. Trippa, Lorenzo, Eudocia Q. Lee, Patrick Y. Wen, Tracy T. Batchelor, Timothy Cloughesy, Giovanni Parmigiani, and Brian M. Alexander. Journal of Clinical Oncology 30, no. 26 (2012): 3258. A simulation study of outcome adaptive randomization in multi-arm clinical trials. Wathen, J. Kyle, and Peter F. Thall. Clinical Trials 14, no. 5 (2017): 432-440.

Examples

ARmethod(
BARmethod = "Thall",
group = 1,
stats = matrix(rep(NA, 40), ncol = 8, nrow = 5),
post.prob.btcontrol = 0.5,
K = 2,
n = c(30, 30),
tuningparameter = "fixed",
c = 1,
post.prob.best = c(0.5, 0.5),
max.ar = 0.75,
armleft = 2,
treatmentindex = 1)

ARmethod(
BARmethod = "Trippa",
group = 1,
stats = matrix(rep(NA, 40), ncol = 8, nrow = 5),
post.prob.btcontrol = c(0.5, 0.6),
K = 3,
n = c(30, 30, 40),
tuningparameter = NA,
c = NA,
a = 3,
b = 0.75,
post.prob.best = c(0.3, 0.3, 0.4),
max.ar = NA,
armleft = 3,
treatmentindex = c(1, 2))

AdaptiveRandomisation

Description

This is a function doing the randomisation process. This Function generates the Sequence for patient allocation to each arm, patient outcomes.

Usage

AdaptiveRandomisation(
  Fixratio,
  rand.algo,
  K,
  n.new,
  randomprob,
  treatmentindex,
  groupwise.response.probs,
  group,
  armleft,
  max.deviation,
  trend_add_or_multip,
  trend.function,
  trend.effect,
  ns,
  Fixratiocontrol
)

Arguments

Value

A list of patient allocation and patient outcome nstage: A vector of the number of patients allocated to each arm ystage: A vector of the patients outcome after treating with each arm znew: A vector of treatment index assigned to each patient in the current cohort ynew: A vector of outcome index record for each patient after treatment in the current cohort

Author(s)

Ziyan Wang

References

Mass weighted urn design—a new randomization algorithm for unequal allocations. Zhao, Wenle. Contemporary clinical trials 43 (2015): 209-216.

Examples

AdaptiveRandomisation(
Fixratio = FALSE,
rand.algo = "Urn",
K = 2,
n.new = 30,
randomprob = matrix(c(0.5, 0.5), ncol = 2, dimnames = list(c(),c("1","2"))),
treatmentindex = 1,
groupwise.response.probs = matrix(rep(c(0.4, 0.4), 5), byrow = TRUE, ncol = 2, nrow = 5),
group = 1,
armleft = 2,
max.deviation = 3,
trend_add_or_multip = "mult",
trend.function = function(ns, group, i, trend.effect) {delta = 0; return(delta)},
trend.effect = c(0, 0),
ns = c(30, 60, 90, 120, 150),
Fixratiocontrol = NA)

AdaptiveRandomisation(
Fixratio = TRUE,
rand.algo = "Urn",
K = 4,
n.new = 30,
randomprob = NA,
treatmentindex = c(1,3),
groupwise.response.probs = matrix(rep(c(0.4, 0.4,0.4, 0.4), 5), byrow = TRUE, ncol = 4, nrow = 5),
group = 1,
armleft = 3,
max.deviation = 3,
trend_add_or_multip = "mult",
trend.function = function(ns, group, i, trend.effect) {delta = 0; return(delta)},
trend.effect = c(0, 0),
ns = c(30, 60, 90, 120, 150),
Fixratiocontrol = 1)

Boundaryconstruction

Description

This function constructs the stopping boundary based on input information

Usage

Boundaryconstruction(Stopbound.inf = Stopbound.inf, ns = ns)

Arguments

Value

A list of the futility boundary and the efficacy boundary

Author(s)

Ziyan Wang

Examples

 Stopbound.inf=list(Stop.type="Early-Pocock",Boundary.type="Symmetric",cutoff=c(0.9928,0.0072))
 ns=c(60,120,180,240,300)
 Boundaryconstruction(Stopbound.inf, ns)

GP.optim: optimiser to give the next cutoff for evaluation

Description

A function to predict the next cutoff value for evaluation.

Usage

GP.optim(
  x,
  y.t1E,
  y.pow = NA,
  ESS = NA,
  errorrate = 0.05,
  confidence.level = 0.95,
  grid.length = 1000,
  change.scale = FALSE,
  noise = T,
  grid.min,
  grid.max,
  Boundary.type = "Symmetric"
)

Arguments

Value

A list including the next cutoff value for evaluation next.cutoff and a list of predictions for screening grid.

Author(s)

Ziyan Wang

References

Surrogates: Gaussian process modeling, design, and optimization for the applied sciences. CRC press. Gramacy, R.B., 2020. Bayesian optimization for adaptive experimental design: A review. IEEE access, 8, 13937-13948. Greenhill, S., Rana, S., Gupta, S., Vellanki, P., & Venkatesh, S. (2020).

Examples

x = c(7.123968, 6.449631, 1.984406,
3.507463, 4.972510, 2.925768,
5.816682, 4.367796,
7.349160, 1.113648)
y.t1E = c(0.0396, 0.0450,
0.5116, 0.2172,
0.1040, 0.3058,
0.0592, 0.1384,
0.0296, 0.7936)
grid.min=1
grid.max=8
GP.res=GP.optim(x=x, y.t1E=y.t1E, errorrate = 0.1, grid.min = grid.min, grid.max = grid.max)
GP.res$next.cutoff

x =  data.frame(matrix(c(
0.9563408, 0.006295626,
0.9669739, 0.014395030,
0.9959410, 0.034858339,
0.9635357, 0.048435579,
0.9794314, 0.021659226,
0.9552201, 0.018442535,
0.9655374, 0.035281833,
0.9837123, 0.010656442,
0.9974910, 0.047741842,
0.9989172, 0.012982826), byrow=TRUE, ncol = 2))
y.t1E = c(0.3044, 0.2938, 0.2573, 0.4780, 0.2923, 0.3733, 0.4263, 0.1962, 0.2941, 0.1131)
y.pow = c(0.8300, 0.8239, 0.7102, 0.7291, 0.8205, 0.7984, 0.7709, 0.8418, 0.6359, 0.5609)
ESS = data.frame(matrix(c(
594.672, 560.580,
596.148, 566.328,
597.840, 590.124,
590.052, 544.800,
597.024, 574.716,
593.952, 554.580,
593.676, 554.400,
598.500, 583.896,
595.740, 590.520,
599.580, 598.644),byrow=TRUE,ncol=2))
grid.min=c(0.95,0)
grid.max=c(1,0.05)
GP.res_asy=GP.optim(x=x, y.t1E=y.t1E, y.pow=y.pow, ESS=ESS,errorrate = 0.1,
grid.min = grid.min, grid.max = grid.max, Boundary.type="Asymmetric")
GP.res_asy$next.cutoff

Initializetrialparameter

Description

This function initialises the inner parameter used in simulate.trial function

Usage

Initializetrialparameter(response.probs, ns)

Arguments

Value

A list of initialised parameters including the number of arms for this trial 'K', the number of arm active 'armleft', the index of treatment arm 'treatmentindex', the vector of total number of patients allocated to each arm 'n' the number of total number of patients survived for each arm 'y1', the matrix for true response probability of each arm at each stage 'groupwise.response.probs' which is required for the time trend study, the vector of randomisation probability for each arm 'randomprob', the array of arm assignment for each patient 'z', the array of outcome for each patient 'y', the array of the stage index for each patient 'group_indicator', the matrix of the probability of each arm to be the best at each stage 'post.prob.best.mat'.

Author(s)

Ziyan Wang

Examples

Initializetrialparameter(response.probs = c(0.4,0.6), ns = c(15,30,45,60,75,90))

#$K
#[1] 2

#$armleft
#[1] 2

#$treatmentindex
#[1] 1

#$n
#[1] 0 0

#$y1
#[1] 0 0

#$groupwise.response.probs
#     [,1] [,2]
#[1,]  0.4  0.6
#[2,]  0.4  0.6
#[3,]  0.4  0.6
#[4,]  0.4  0.6
#[5,]  0.4  0.6
#[6,]  0.4  0.6

#$randomprob
#     1   2
#[1,] 0.5 0.5

#$z
#numeric(0)

#$y
#numeric(0)

#$group_indicator
#numeric(0)

#$post.prob.best.mat
#     0 1
#[1,] 0 0
#[2,] 0 0
#[3,] 0 0
#[4,] 0 0
#[5,] 0 0
#[6,] 0 0

Meanfunc

Description

This function reads in the output matrix of a number of trial replicates to calculate mean treatment effect estimate.

Usage

Meanfunc(res)

Arguments

Value

Mean treatment effect estimates of each treatment arm

Examples

## Not run: Meanfunc(res)

Nfunc

Description

This function reads in the output matrix of a number of trial replicates to calculate mean estimate of total number of patients allocated to each arm

Usage

Nfunc(res)

Arguments

Value

The mean estimate of total number of patients allocated to each arm

Examples

## Not run: Nfunc(res)

Operation characteristic table for Trial.simulation() null scenario

Description

Operation characteristic table for null scenario using main model.

Usage

OPC_Trial.simulation

Format

A data frame with 1 rows and 8 variables:

Type.I.Error.or.Power

Power

Bias

Treatment effect bias for treatment 1

rMSE

Rooted mean squared error for treatment effect 1

N.per.arm.1

Mean total number of patient allocated to control

N.per.arm.2

Mean total number of patient allocated to treatment 1

Survive.per.arm.1

Mean total number of patient allocated to control

Survive.per.arm.2

Mean total number of patient survived when using treatment 1

N

Mean total number of patient in a trial

Operation characteristic table for alternative scenario

Description

Operation characteristic table for alternative scenario using main + continuousstage model. The time trend pattern is step. The strength of time trend is 0.1 equally for all arm. The effect of time trend on true response probability is multiplicative.

Usage

OPC_alt

Format

A data frame with 3 rows and 16 variables:

Type.I.Error.or.Power

Power

Bias.1

Treatment effect bias for treatment 1

Bias.2

Treatment effect bias for treatment 2

Bias.3

Treatment effect bias for treatment 3

rMSE.1

Rooted mean squared error for treatment 1

rMSE.2

Rooted mean squared error for treatment 2

rMSE.3

Rooted mean squared error for treatment 3

N.per.arm.1

Mean total number of patient allocated to control

N.per.arm.2

Mean total number of patient allocated to treatment 1

N.per.arm.3

Mean total number of patient allocated to treatment 2

N.per.arm.4

Mean total number of patient allocated to treatment 3

Survive.per.arm.1

Mean total number of patient allocated to control

Survive.per.arm.2

Mean total number of patient survived when using treatment 1

Survive.per.arm.3

Mean total number of patient survived when usin treatment 2

Survive.per.arm.4

Mean total number of patient survived when usin treatment 3

N

Mean total number of patient in a trial

Operation characteristic table for null scenario

Description

Operation characteristic table for null scenario using main and main + continuousstage model. The main effect model was run for a null scenario with and without time trend. The time trend pattern is step. The strength of time trend is 0.1 equally for all arm. The effect of time trend on true response probability is multiplicative.

Usage

OPC_null

Format

A data frame with 3 rows and 16 variables:

Type.I.Error.or.Power

Family wise error rate

Bias.1

Treatment effect bias for treatment 1

Bias.2

Treatment effect bias for treatment 2

Bias.3

Treatment effect bias for treatment 3

rMSE.1

Rooted mean squared error for treatment 1

rMSE.2

Rooted mean squared error for treatment 2

rMSE.3

Rooted mean squared error for treatment 3

N.per.arm.1

Mean total number of patient allocated to control

N.per.arm.2

Mean total number of patient allocated to treatment 1

N.per.arm.3

Mean total number of patient allocated to treatment 2

N.per.arm.4

Mean total number of patient allocated to treatment 3

Survive.per.arm.1

Mean total number of patient allocated to control

Survive.per.arm.2

Mean total number of patient survived when using treatment 1

Survive.per.arm.3

Mean total number of patient survived when usin treatment 2

Survive.per.arm.4

Mean total number of patient survived when usin treatment 3

N

Mean total number of patient in a trial

OutputStats.initialising

Description

This function initializes the output matrix including all evaluation metrics based on input information

Usage

OutputStats.initialising(variable.inf, reg.inf, ns, K)

Arguments

Value

The empty output matrix including different evaluation metrics.

Author(s)

Ziyan Wang

Examples

OutputStats.initialising(
    variable.inf = "Fixeffect",
    reg.inf = "main",
    ns = c(15, 30, 45, 60, 75),
    K = 2)

Randomisation.inf

Description

This function checks the validity of the randomisation information input

Usage

Randomisation.inf(
  Random.inf = list(Fixratio = FALSE, Fixratiocontrol = NA, BARmethod = "Thall",
    Thall.tuning.inf = list(tuningparameter = "Fixed", fixvalue = 1), Trippa.tuning.inf =
    list(a = 10, b = 0.75))
)

Arguments

Value

A list of input randomisation information

Author(s)

Ziyan Wang

Examples

Randomisation.inf(Random.inf = list(
Fixratio = FALSE,
Fixratiocontrol = NA,
BARmethod = "Thall",
Thall.tuning.inf = list(tuningparameter = "Fixed",  fixvalue = 1),
Trippa.tuning.inf = list(a = NA, b = NA)
))

Save.resulttoRDatafile

Description

This function generates the name of file for output table and dataset

Usage

Save.resulttoRDatafile(
  input.info = list(response.probs = c(0.4, 0.4), ns = c(30, 60, 90, 120, 150), max.ar =
    0.75, rand.type = "Urn", max.deviation = 3, model.inf = list(model = "tlr", ibb.inf =
    list(pi.star = 0.5, pess = 2, betabinomialmodel = ibetabinomial.post), tlr.inf =
    list(beta0_prior_mu = 0, beta1_prior_mu = 0, beta0_prior_sigma = 2.5,
    beta1_prior_sigma = 2.5, beta0_df = 7, beta1_df = 7, reg.inf = "main", variable.inf =
    "Fixeffect")), Stopbound.inf = Stopboundinf(Stop.type = "Early-Pocock", Boundary.type
    = "Symmetric", cutoff = c(0.99, 
     0.01)), Random.inf = list(Fixratio = FALSE,
    Fixratiocontrol = NA, BARmethod = "Thall", Thall.tuning.inf = list(tuningparameter =
    "Fixed", fixvalue = 1)), trend.inf = list(trend.type = "step", trend.effect = c(0,
    0), trend_add_or_multip = "mult"))
)

Arguments

Value

A list of name for table and dataset

Author(s)

Ziyan Wang

Examples

Save.resulttoRDatafile(
input.info = list(
  response.probs = c(0.4, 0.4),
  ns = c(30, 60, 90, 120, 150),
  max.ar = 0.75,
  rand.type = "Urn",
  max.deviation = 3,
  model.inf = list(
    model = "tlr",
    ibb.inf = list(
      pi.star = 0.5,
      pess = 2,
      betabinomialmodel = ibetabinomial.post
    ),
    tlr.inf = list(
      beta0_prior_mu = 0,
      beta1_prior_mu = 0,
      beta0_prior_sigma = 2.5,
      beta1_prior_sigma = 2.5,
      beta0_df = 7,
      beta1_df = 7,
      reg.inf =  "main",
      variable.inf = "Fixeffect"
    )
  ),
  Stop.type = "Early-Pocock",
  Boundary.type = "Symmetric",
  Random.inf = list(
    Fixratio = FALSE,
    Fixratiocontrol = NA,
    BARmethod = "Thall",
    Thall.tuning.inf = list(tuningparameter = "Fixed",  fixvalue = 1)
  ),
  trend.inf = list(
    trend.type = "step",
    trend.effect = c(0, 0),
    trend_add_or_multip = "mult"
  )
))

Sperarmfunc

Description

This function reads in the output matrix of a number of trial replicates to calculate mean total number of survived patients of each arm

Usage

Sperarmfunc(res)

Arguments

Value

The mean total number of survived patients of each arm

Examples

## Not run: Sperarmfunc(res)

Stopboundinf

Description

This function summaries and checks stopping boundary information.

Usage

Stopboundinf(
  Stop.type = "Early-Pocock",
  Boundary.type = "Symmetric",
  cutoff = c(0.9928, 0.0072)
)

Arguments

Value

The list of information required for boundary construction function 'Stopbound.inf'

Author(s)

Ziyan Wang

Examples

Stop.type = "Early-Pocock" #(Pocock boundarty is a flat boundary across time)
Boundary.type = "Symmetric"
cutoff = c(0.9928, 0.0072)

Stopbound.inf = Stopboundinf(Stop.type, Boundary.type, cutoff)
#Stopbound.inf
#$Stop.type
# [1] "Early-Pocock"
#$Boundary.type
#[1] "Symmetric"
#$cutoff
# [1] 0.9928 0.0072

Timetrend.fun

Description

This function generate the time trend function based on trend information. This function also check the validity of the input time trend information.

Usage

Timetrend.fun(trend.inf)

Arguments

Value

A list containing the time trend function according to input trend.type variable, and a indicator of whether there is a time trend in data generation based on input trend information

Author(s)

Ziyan Wang

Examples

Timetrend.fun(trend.inf = list(
               trend.type = "step",
               trend.effect = c(0, 0),
               trend_add_or_multip = "mult"
               ))

Trial simulation

Description

This function simulates and does final analysis of a trial with one scenario. The time cost of this function depend on the cpu cores of the user's cpmputer.

Usage

Trial.simulation(
  ntrials = 5000,
  trial.fun = simulatetrial,
  input.info = list(response.probs = c(0.4, 0.4), ns = c(30, 60, 90, 120, 150), max.ar =
    0.75, test.type = "Twoside", rand.algo = "Urn", max.deviation = 3, model.inf =
    list(model = "tlr", ibb.inf = list(pi.star = 0.5, pess = 2, betabinomialmodel =
    ibetabinomial.post), tlr.inf = list(beta0_prior_mu = 0, beta1_prior_mu = 0,
    beta0_prior_sigma = 2.5, beta1_prior_sigma = 2.5, beta0_df = 7, beta1_df = 7, reg.inf
    = "main", variable.inf = "Fixeffect")), Stopbound.inf = Stopboundinf(Stop.type =
    "Early-Pocock", Boundary.type = "Symmetric", 
     cutoff = c(0.99, 0.01)),
    Random.inf = list(Fixratio = TRUE, Fixratiocontrol = 1, BARmethod = NA,
    Thall.tuning.inf = NA, Trippa.tuning.inf = NA), trend.inf = list(trend.type = "step",
    trend.effect = c(0, 0), trend_add_or_multip = "mult")),
  cl = 2
)

Arguments

Value

A list of output including the final output of each trial replicates called 'result' The analysis result table of the specific trial called 'OPC' and the file name for saving these output on the computer

Author(s)

Ziyan Wang

Examples

set.seed(1)
Trial.simulation(ntrials = 2, cl = 2)

alphaspending

Description

This function estimates the mean error rate spent at each interim analysis for a trial Example usage:

1. sapply(res = result, fun = alphaspending) will generate list of the proportion of trial replicates are stopped at each stage for all scenarios in result where result is a list containing output data for different scenario

2. sapply(sapply(result,FUN = alphaspending),sum) will generate the type I error rate or power for all scenario on the result list

3. alpha(result) generate the proportion of trial replicates are stopped at each stage where result is the output data for one specific scenario

4. sum(alpha(result)) will generate the type I error rate or power for a specific scenario

Usage

alphaspending(res)

Arguments

Value

The error rate at each interim analysis

Author(s)

Ziyan Wang

Examples

## Not run: alphaspending(res)

conjuncativepower_or_FWER

Description

This function reads in the output matrix of a number of trial replicates to calculate the Family wise error rate or Conjunctive power

Usage

conjuncativepower_or_FWER(res, scenario, test.type)

Arguments

Value

Family wise error rate or Conjunctive power

Examples

## Not run: conjuncativepower_or_FWER(res)

Cutoff screening example: the details of grid

Description

Details of grid including famliy wise error rate of a cutoff value, the cutoff value and the square of cutoff value for modelling and prediction

Usage

dataloginformd

Format

A data frame with 24 rows and 3 variables:

tpIE

FWER

cutoff

Cutoff value

cutoff2

Square of cutoff value

demo_Cutoffscreening

Description

This function does a cutoff screening for trial simulation.

Usage

demo_Cutoffscreening(
  ntrials = 1000,
  trial.fun = simulatetrial,
  grid.inf = list(start = c(0.9, 0.95, 1), extendlength = 15),
  input.info = list(response.probs = c(0.4, 0.4), ns = c(30, 60, 90, 120, 150), max.ar =
    0.75, rand.algo = "Urn", max.deviation = 3, test.type = "Twoside", model.inf =
    list(model = "tlr", ibb.inf = list(pi.star = 0.5, pess = 2, betabinomialmodel =
    ibetabinomial.post), tlr.inf = list(beta0_prior_mu = 0, beta1_prior_mu = 0,
    beta0_prior_sigma = 2.5, beta1_prior_sigma = 2.5, beta0_df = 7, beta1_df = 7, reg.inf
    = "main", variable.inf = "Fixeffect")), Stop.type = "Early-Pocock", Boundary.type =
    "Symmetric", Random.inf = list(Fixratio = FALSE, 
     Fixratiocontrol = NA,
    BARmethod = "Thall", Thall.tuning.inf = list(tuningparameter = "Fixed", fixvalue =
    1)), trend.inf = list(trend.type = "step", trend.effect = c(0, 0),
    trend_add_or_multip = "mult")),
  cl = 2
)

Arguments

Value

A vector of recommended cutoff. The final value is the latest recommended value. A plot for all tested cutoff and error rate

Author(s)

Ziyan Wang

Examples

demo_Cutoffscreening(ntrials = 2, cl = 2,
    grid.inf = list(start = c(0.9, 0.95, 1), extendlength = 2))

A demo for cutoff screening using Bayesian optimisation

Description

This function does a cutoff screening for trial simulation using Bayesian optimisation.

Usage

demo_Cutoffscreening.GP(
  ntrials = 1000,
  trial.fun = simulatetrial,
  grid.inf = list(start.length = 10, grid.min = NULL, grid.max = NULL, confidence.level =
    0.95, grid.length = 5000, change.scale = FALSE, noise = TRUE, errorrate = 0.1,
    simulationerror = 0.01, iter.max = 15, plotornot = FALSE),
  power.type = NA,
  response.probs.alt = NA,
  input.info = list(response.probs.null = c(0.4, 0.4, 0.4, 0.4), ns = c(120, 240, 360,
    480, 600), max.ar = 0.85, rand.algo = "Urn", max.deviation = 3, test.type =
    "Twoside", model.inf = list(model = "tlr", ibb.inf = list(pi.star = 0.5, pess = 2,
    betabinomialmodel = ibetabinomial.post), tlr.inf = list(beta0_prior_mu = 0,
    beta1_prior_mu = 0, beta0_prior_sigma = 2.5, beta1_prior_sigma = 2.5, beta0_df = 7,
    beta1_df = 7, reg.inf = "main", variable.inf = "Fixeffect")), Stop.type =
    "Early-OBF", Boundary.type = "Symmetric", 
     Random.inf = list(Fixratio = FALSE,
    Fixratiocontrol = NA, BARmethod = "Thall", Thall.tuning.inf = list(tuningparameter =
    "Unfixed", fixvalue = 1)), trend.inf = list(trend.type = "step", trend.effect = c(0,
    0, 0, 0), trend_add_or_multip = "mult")),
  cl = 2
)

Arguments

Value

A vector of recommended cutoff. The final value is the latest recommended value. A plot for all tested cutoff and error rate

Author(s)

Ziyan Wang

Examples

#Two arm asymmetric boundary screening. Default is OBF boundary.
demo_Cutoffscreening.GP(ntrials = 2, cl = 2,
 power.type = NA,
 response.probs.alt = NA,
 grid.inf = list(
 start.length = 10,
 confidence.level = 0.95,
 grid.length = 5000,
 change.scale = FALSE,
 noise = TRUE,
 errorrate = 0.1,
 simulationerror = 0.01,
 iter.max = 15,
 plotornot = FALSE))

 #Four arm asymmetric OBF boundary screening where conjunctive power is optimised.
 demo_Cutoffscreening.GP(ntrials = 2, cl = 2,
 power.type = "Conjunctive",
 response.probs.alt = c(0.4,0.6,0.6,0.4),
 grid.inf = list(
 start.length = 10,
 confidence.level = 0.95,
 grid.length = 101,
 change.scale = FALSE,
 noise = TRUE,
 errorrate = 0.1,
 simulationerror = 0.01,
 iter.max = 15,
 plotornot = FALSE))
 input.info = list(
 response.probs.null = c(0.4,0.4,0.4,0.4),
 ns = c(120, 240, 360, 480, 600),
 max.ar = 0.85,
 rand.algo = "Urn",
 max.deviation = 3,
 test.type = "Twoside",
 model.inf = list(
 model = "tlr",
 ibb.inf = list(
 pi.star = 0.5,
 pess = 2,
 betabinomialmodel = ibetabinomial.post
 ),
 tlr.inf = list(
 beta0_prior_mu = 0,
 beta1_prior_mu = 0,
 beta0_prior_sigma = 2.5,
 beta1_prior_sigma = 2.5,
 beta0_df = 7,
 beta1_df = 7,
 reg.inf =  "main",
 variable.inf = "Fixeffect"
 )
 ),
 Stop.type = "Early-OBF",
 Boundary.type = "Asymmetric",
 Random.inf = list(
 Fixratio = FALSE,
 Fixratiocontrol = NA,
 BARmethod = "Thall",
 Thall.tuning.inf = list(tuningparameter = "Unfixed",  fixvalue = 1)
 ),
 trend.inf = list(
 trend.type = "step",
 trend.effect = c(0, 0, 0, 0),
 trend_add_or_multip = "mult"
 )
 )
 

demo_multscenario

Description

This is a demo function simulating multi-arm multi-stage design with two different null scenarios where the response probability of control is 0.15 and 0.4, respectively. The clinically meaningful increment on probability scale is 0.2. The stopping boundary is the OBF. The cutoff vector in the demo is tuned to keep Type I error rate to be 0.05. The output data can be saved as .RData file

Usage

demo_multscenario(ntrials = 1000, cl = 2, save_data = FALSE)

Arguments

Value

A list of data for plotting. One is results of trial replicates for all scenarios. The other one is a data frame containing all summarised evaluation metrics for all scenarios

Author(s)

Ziyan Wang

Examples

demo_multscenario(ntrials = 2, cl = 2, save_data = FALSE)

disconjunctivepowerfunc

Description

This function reads in the output matrix of a number of trial replicates to calculate the Family wise error rate or disconjunctive power

Usage

disconjunctivepowerfunc(res)

Arguments

Value

Disconjunctive power

Examples

## Not run: disconjunctivepowerfunc(res)

ibetabinomial.post

Description

This function calculates the posterior probability of each active treatment arm better than control using betabinomial model

Usage

ibetabinomial.post(n, y, pi.star = 0.5, pess = 2)

Arguments

Value

A vector posterior probability of each active treatment arm better than control

Author(s)

Ziyan Wang

Examples

n <- c(20,20,20,20)
y <- c(12,12,12,6)
ibetabinomial.post(n, y, pi.star = 0.5, pess = 2)
#[1] 0.5000000 0.5000000 0.0308018

intbias

Description

This function estimates the mean bias of treatment - stage interaction effect

Usage

intbias(res)

Arguments

Value

A matrix of mean treatment - stage interaction effect bias

Examples

## Not run: intbias(res)

modelinf.fun

Description

This function summarize the input parameters describing the model for analysis and transfer them into a list

Usage

modelinf.fun(
  model = "tlr",
  ibb.inf = list(pi.star = 0.5, pess = 2, betabinomialmodel = ibetabinomial.post),
  tlr.inf = list(beta0_prior_mu = 0, beta1_prior_mu = 0, beta0_prior_sigma = 2.5,
    beta1_prior_sigma = 2.5, beta0_df = 7, beta1_df = 7, reg.inf = "main", variable.inf =
    "Fixeffect")
)

Arguments

Value

A list of model information including model, ibb.inf and tlr.inf

Author(s)

Ziyan Wang

Examples

modelinf.fun(model = "tlr",
  ibb.inf = list(pi.star = 0.5,
                 pess = 2,
                 betabinomialmodel = ibetabinomial.post),
  tlr.inf = list(beta0_prior_mu = 0,
                 beta1_prior_mu = 0,
                 beta0_prior_sigma = 2.5,
                 beta1_prior_sigma = 2.5,
                 beta0_df = 7,
                 beta1_df = 7,
                 reg.inf =  "main",
                 variable.inf = "Fixeffect"
                 ))

A list of data from Gaussian process and trial simulation for asymmetric cutoff screening.

Description

A list of data from Gaussian process and trial simulation for asymmetric cutoff screening.

Usage

optimdata_asy

Format

A list with four element:

next.cutoff

The cutoff value for the next evaluation

prediction

A list of values from Gaussian process model

ESS

A two column twenty five rows matrix with the effective sample size for each cutoff pair under both null (first column) and alternative (second column) scenario

testeddata

A data frame containing each tested cutoff pair (column two and three for efficacy and futility, respectively), their FWER under null (column one) and conjunctive power under alternative (column four)

A list of data from Gaussian process for symmetric cutoff screening.

Description

A list of data from Gaussian process for symmetric cutoff screening.

Usage

optimdata_sym

Format

A list with two element:

next.cutoff

The cutoff value for the next evaluation

prediction

A list of values from Gaussian process model

tpIE

A vector of type I error rate data

cutoff

A vector of cutoff data

perHtypeIerror_powerfunc

Description

This function reads in the output matrix of a number of trial replicates to calculate the error rate

Usage

perHtypeIerror_marginalpowerfunc(res)

Arguments

Value

"per-hypothesis" Type I error rate or power (marginal power) for each treatment - control comparison

Author(s)

Ziyan Wang

Examples

## Not run: perHtypeIerror_powerfunc(res)

Cutoff screening example: the predicted value from quadratic model

Description

The predicted value from quadratic model for famliy wise error rate vs cutoff value plotting

Usage

predictedtpIEinformd

Format

A data frame with 1001 rows and 1 variables:

predictedtpIEinformd

The predicted FWER value of a large grid

Cutoff screening example: the recommended grid value at each time point

Description

he recommended grid value at each time point. There are 20 cutoff value explored

Usage

recommandloginformd

Format

A data frame with 20 rows and 1 variables:

recommandloginformd

The cutoff value at each time point

resultrtostats

Description

This is an inner function of the function resultstantoRfunc

Usage

resultrtostats(
  trteff = NA,
  treatmentindex = NA,
  armleft,
  K,
  group,
  reg.inf,
  fit,
  ns
)

Arguments

Value

A list of stan result inference stats1: A vector of posterior probability for all treatment arms including dropped and active treatment arm stats4: The mean treatment effect estimate of each treatment compared to control stats5: The variance of treatment effect estimate of each treatment compared to control post.prob.btcontrol: a vector including Posterior probability of each active treatment arm better than control

Author(s)

Ziyan Wang

Examples

## Not run: resultrtostats(trteff = NA, treatmentindex = NA, armleft, K, group, reg.inf, fit, ns)

resultrtostats.rand

Description

The inner function of function resultstantoRfunc.rand

Usage

resultrtostats.rand(
  trteff = NA,
  treatmentindex = NA,
  armleft,
  K,
  group,
  fit,
  ns
)

Arguments

Value

A list of stan result inference stats1: A vector of posterior probability for all treatment arms including dropped and active treatment arm stats4: The mean treatment effect estimate of each treatment compared to control stats5: The variance of treatment effect estimate of each treatment compared to control post.prob.btcontrol: a vector including Posterior probability of each active treatment arm better than control

Author(s)

Ziyan Wang

Examples

## Not run: resultrtostats.rand(trteff = NA, treatmentindex = NA, armleft, K, group, fit, ns)

resultstantoRfunc

Description

This function summarise the fix effect stan output data to and transform them to be readable.

Usage

resultstantoRfunc(
  group,
  reg.inf,
  variable.inf,
  fit,
  armleft,
  treatmentindex,
  K,
  ns
)

Arguments

Value

A list of stan result inference stats1: A vector of posterior probability for all treatment arms including dropped and active treatment arm stats4: The mean treatment effect estimate of each treatment compared to control stats5: The variance of treatment effect estimate of each treatment compared to control post.prob.btcontrol: a vector including Posterior probability of each active treatment arm better than control stats6: A vector of mean stage (time trend) effect estimate stats7: A vector of mean treatment - stage (time trend) interaction effect estimate sampefftotal: The posterior samples of response probability of each active arm on logit scale. This can be transformed to probit scale by using inv.logit() function.

Author(s)

Ziyan Wang

Examples

## Not run: resultstantoRfunc(group, reg.inf, fit, armleft, treatmentindex, K, ns)

resultstantoRfunc.rand

Description

This function summarise the mix effect stan output data to and transform them to be readable.

Usage

resultstantoRfunc.rand(group, fit, armleft, treatmentindex, K, ns)

Arguments

Value

A list of stan result inference stats1: A vector of posterior probability for all treatment arms including dropped and active treatment arm stats4: The mean treatment effect estimate of each treatment compared to control stats5: The variance of treatment effect estimate of each treatment compared to control post.prob.btcontrol: a vector including Posterior probability of each active treatment arm better than control stats6: A vector of mean stage (time trend) effect estimate stats7: A vector of mean treatment - stage (time trend) interaction effect estimate sampefftotal: The posterior samples of response probability of each active arm on logit scale. This can be transformed to probit scale by using inv.logit() function.

Author(s)

Ziyan Wang

Examples

## Not run: resultstantoRfunc.rand(group, fit, armleft, treatmentindex, K, ns)

simulatetrial

Description

This function simulates a MAMS trial applying adaptive methods where the time trend effect can be studied.

Usage

simulatetrial(
  ii,
  response.probs = c(0.4, 0.4),
  ns = c(30, 60, 90, 120, 150),
  test.type = "Twoside",
  max.ar = 0.75,
  rand.algo = "Urn",
  max.deviation = 3,
  model.inf = list(model = "tlr", ibb.inf = list(pi.star = 0.5, pess = 2,
    betabinomialmodel = ibetabinomial.post), tlr.inf = list(beta0_prior_mu = 0,
    beta1_prior_mu = 0, beta0_prior_sigma = 2.5, beta1_prior_sigma = 2.5, beta0_df = 7,
    beta1_df = 7, reg.inf = "main", variable.inf = "Fixeffect")),
  Stopbound.inf = Stopbound.inf,
  Random.inf = Random.inf,
  trend.inf = trend.inf
)

Arguments

Value

A matrix including all evaluation metrics

Author(s)

Ziyan Wang

Examples

set.seed(1)
simulatetrial(response.probs = c(0.4, 0.4),
               ns = c(30, 60, 90, 120, 150),
               max.ar = 0.75,
               test.type = "Twoside",
               rand.algo = "Urn",
               max.deviation = 3,
               model.inf = list(
               model = "tlr",
               ibb.inf = list(
               pi.star = 0.5,
               pess = 2,
               betabinomialmodel = ibetabinomial.post
               ),
               tlr.inf = list(
               beta0_prior_mu = 0,
               beta1_prior_mu = 0,
               beta0_prior_sigma = 2.5,
               beta1_prior_sigma = 2.5,
               beta0_df = 7,
               beta1_df = 7,
               reg.inf =  "main",
               variable.inf = "Fixeffect"
               )
               ),
               Stopbound.inf = Stopboundinf(
               Stop.type = "Early-Pocock",
               Boundary.type = "Symmetric",
               cutoff = c(0.99,0.01)
               ),
               Random.inf = list(
               Fixratio = FALSE,
               Fixratiocontrol = NA,
               BARmethod = "Thall",
               Thall.tuning.inf = list(tuningparameter = "Fixed",  fixvalue = 1),
               Trippa.tuning.inf = list(a = 10, b = 0.75)
               ),
               trend.inf = list(
               trend.type = "step",
               trend.effect = c(0, 0),
               trend_add_or_multip = "mult"
               ))

stan.logisticmodeltrans

Description

This function transform the data in trial simulation to the data required for stan modelling

Usage

stan.logisticmodeltrans(
  z,
  y,
  randomprob,
  group_indicator,
  armleft,
  group,
  variable.inf,
  reg.inf
)

Arguments

Value

A list of information require for the stan model including: zdropped: The vector of treatment index for each patient whose treatment arm is active at current stage. ydropped: The vector of outcome index for each patient whose treatment arm is active at current stage. Ndropped: The total number of patients that are treated with active treatment arms at current stage. group_indicator_dropped: The vector of stage index for each patient whose treatment arm is active at current stage. zlevel: The active treatment arm index at current stage xdummy: A design matrix transformed from zdropped and group_indicator_dropped for modelling

Author(s)

Ziyan Wang

Examples

stan.logisticmodeltrans(
z = c(1,2,1,2,2,1,2,1),
y = c(0,0,0,0,1,1,1,1),
randomprob = matrix(c( 0.5, 0.5), ncol = 2, dimnames = list(c("Stage1"), c("1", "2"))),
group_indicator = c(1,1,1,1,1,1,1,1),
armleft = 2,
group = 1,
variable.inf = "Fixeffect",
reg.inf = "main")

testing_and_armdropping

Description

This function makes a decision on whether any active arm should be dropped based on posterior probability and return the vector of decision on each arm, the vector of active arms index and the number of arms left for further study.

Usage

testing_and_armdropping(
  K,
  armleft,
  post.prob.btcontrol,
  group,
  cutoffeff,
  cutoffful,
  treatmentindex,
  test.type
)

Arguments

Value

A list of information including armleft: the number of active arms after this interim analysis; treatmentindex: the index vector of active arm after this interim analysis; stats3: the vector of conclusion on whether null hypothesis is rejected

Examples

testing_and_armdropping(
K = 4,
armleft = 4,
post.prob.btcontrol = c(0.5,0.99,0.02),
group = 3,
cutoffeff = c(1, 0.99, 0.975, 0.96, 0.95),
cutoffful = c(0, 0.01, 0.025, 0.04, 0.05),
treatmentindex = c(1,2,3),
test.type = "Oneside")

testing_and_armdropping(
K = 4,
armleft = 4,
post.prob.btcontrol = c(0.5,0.99,0.02),
group = 3,
cutoffeff = c(1, 0.99, 0.975, 0.96, 0.95),
cutoffful = c(0, 0.01, 0.025, 0.04, 0.05),
treatmentindex = c(1,2,3),
test.type = "Twoside")

trtbias

Description

This function estimates the mean bias of treatment effect

Usage

trtbias(res, trueeffect)

Arguments

Value

A matrix of mean treatment effect bias

Examples

## Not run: trtbias(res, trueeffect)

trteffect

Description

This function estimates the mean treatment effect bias and its rooted mean squared error

Usage

trteffect(res, trueeff)

Arguments

Value

A vector of mean treatment effect bias and its rooted mean squared error

Examples

## Not run: trteffect(res, trueeff)

varfunc

Description

This function reads in the output matrix of a number of trial replicates to calculate the variance of treatment effect estimate.

Usage

varfunc(res)

Arguments

Value

The variance of Treatment effect estimates of each treatment arm

Examples

## Not run: varfunc(res)